The given statement "When an additional explanatory or independent variable is introduced into a multiple regression model, the coefficient of multiple determination or R-square will never decrease."
The statement is FALSE.
Because when an additional explanatory or independent variable is introduced into a multiple regression model, the coefficient of multiple determination or R-Squared will never decrease.
Multiple Regression Model:A multiple regression model differs from a single variable linear regression model in a way that it uses more than one variable as independent variable. The R-Squared measures the percentage change in the dependent variable that can be explained by the change in independent variable.
It is false because as we know that, R-Squared measures the percentage change in the dependent variable that can be explained by the change in independent variable , any variable introduced which is not related with the dependent variable may easily reduce the R - squared. R-Squared is the square of correlation and if a negatively correlated variable is introduced, R-Squared can very well decreases.
Learn more about Multiple Regression Model at:
https://brainly.com/question/25814703
#SPJ4
The given question is incomplete, complete question is:
True or False: When an additional explanatory or independent variable is introduced into a multiple regression model, the coefficient of multiple determination or R-square will never decrease.
which equation represents the relationship show in the graph?
let's firstly get the EQUATion, of the graph before we get the inequality.
so we have a quadratic with two zeros, at -6 and 8, hmmm and we also know that it passes through (-2 , 10)
[tex]\begin{cases} x = -6 &\implies x +6=0\\ x = 8 &\implies x -8=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +6 )( x -8 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-2\\ y=10 \end{cases}[/tex]
[tex]a ( -2 +6 )( -2 -8 ) = 10\implies a(4)(-10)=10\implies -40a=10 \\\\\\ a=\cfrac{10}{-40}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{1}{4}(x+6)(x-8)=y\implies -\cfrac{1}{4}(x^2-2x-48)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{x}{2}+12=y \end{array}}~\hfill[/tex]
now, hmmm let's notice something, the line of the graph is a solid line, that means the borderline is included in the inequality, so we'll have either ⩾ or ⩽.
so hmmm we could do a true/false region check by choosing a point and shade accordingly, or we can just settle with that, since the bottom is shaded, we're looking at "less than or equal" type, or namely ⩽, so that's our inequality
[tex]{\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{x}{2}+12\geqslant y \end{array}}[/tex]
Please help!!!
006
A survey was conducted at a local mall in which 100 customers were asked what flavor of soft drink they preferred. The results of the survey are in the chart. Based on this survey if 300 customers were asked their preference how many would you expect to select cola as their favorite flavor? Answer in units of customers.
Answer: 87
Step-by-step explanation: 3 x 29=87 because you are multiplying the amount of people in the survey by 3
4x5= divided (-10) +1
Answer:
= 8
Step-by-step explanation:
4/5 * 10 = 8/
1
= 8
find the length of the curve. note: you will need to evaluate your integral numerically. round your answer to one decimal place. x = cos(2t), y = sin(3t) for 0 ≤ t ≤ 2
The length of the curve is approximately 4.7 units when rounded to one decimal place.
Explanation:
To find the length of the curve, follow these steps:
Step 1: To find the length of the curve, we need to use the formula:
length = ∫(a to b) √(dx/dt)^2 + (dy/dt)^2 dt
Step 2: In this case, we have x = cos(2t) and y = sin(3t) for 0 ≤ t ≤ 2, First, find the derivatives dx/dt and dy/dt so we can find dx/dt and dy/dt as:
dx/dt = -2sin(2t)
dy/dt = 3cos(3t)
Step 3: Substituting these into the formula, we get:
length = ∫ (0 to 2) √((-2sin(2t))^2 + (3cos(3t))^2) dt
length = ∫ (0 to 2) √(4sin^2(2t) + 9cos^2(3t)) dt
This integral must be evaluated numerically.
Step 4: Using a calculator or software to evaluate the integral numerically, we get:
length ≈ 4.7
Therefore, the length of the curve is approximately 4.7 units when rounded to one decimal place.
Know more about the length of the curve click here:
https://brainly.com/question/31376454
#SPJ11
find the arc length of the polar curve =2 from =0 to =2. keep all radicals in your answer, and enter if appropriate.
The arc length of the polar curve r = 2 from θ = 0 to θ = 2 is 4.
Explanation:
To find the arc length of the polar curve r = 2 from θ = 0 to θ = 2, Follow these steps:
Step 1: To find the arc length of the polar curve r = 2 from θ = 0 to θ = 2, we can use the arc length formula for polar coordinates:
Arc length (L) = ∫√(r^2 + (dr/dθ)^2) dθ, from θ = 0 to θ = 2
Given r = 2, dr/dθ = 0 (since r is a constant)
Step 2: Now substitute r and dr/dθ into the formula:
L = ∫√(2^2 + 0^2) dθ, from θ = 0 to θ = 2
L = ∫√(4) dθ, from θ = 0 to θ = 2
L = ∫2 dθ, from θ = 0 to θ = 2
Step 3: Integrate with respect to θ:
L = 2θ | from θ = 0 to θ = 2
Step 4: Evaluate the definite integral:
L = 2(2) - 2(0) = 4
So the arc length of the polar curve r = 2 from θ = 0 to θ = 2 is 4.
To know more about the polar curve click here:
https://brainly.com/question/31405088
#SPJ11
Let R be a relation on the set of all integers such that aRb if and only if 3a - 5b is even. 1) Is R reflexive? If yes, justify your answer; if no, give a counterexample. 2) Is R symmetric? If yes, justify your answer; if no, give a counterexample. Hint: 3b - 5a = 3a - 5b + 86-8a 3) Is R anti-symmetric? If yes, justify your answer, if no, give a counterexample. 4) Is R transitive? If yes, justify your answer, if no, give a counterexample. 5) Is R an equivalence relation? Is R a partial order? Justify your answer
R is not reflexive. To show this, we need to find an integer a such that a is not related to itself under R. Let a = 1, then 3a - 5a = -2, which is not even. Therefore, 1R1 is not true, and R is not reflexive.
R is not symmetric. To show this, we need to find integers a and b such that aRb but bRa is not true. Let a = 1 and b = 2, then 3a - 5b = -13, which is odd. Therefore, 1R2 is false. However, 3b - 5a = 1, which is also odd, so 2Ra is false. Therefore, R is not symmetric.
R is anti-symmetric. To show this, we need to show that if aRb and bRa, then a = b. Suppose 3a - 5b and 3b - 5a are both even. Then we can write 3a - 5b = 2k and 3b - 5a = 2m for some integers k and m. Adding these equations gives 2a - 2b = 2(k + m), or a - b = k + m, which is even. Therefore, aRb and bRa implies that a = b, and R is anti-symmetric.
R is transitive. To show this, suppose aRb and bRc, then 3a - 5b and 3b - 5c are both even. We can write 3a - 5b = 2k and 3b - 5c = 2m for some integers k and m. Substituting the first equation into the second gives 3a - 5c = 3b - 5b - 5c = -2b - 5c + 10b = 8b - 5c = 2(4b - 5c/2) = 2n for some integer n. Therefore, aRc, and R is transitive.
R is not an equivalence relation because it is not reflexive and not symmetric. However, R is a partial order because it is anti-symmetric and transitive.
Learn more about equivalence relation
https://brainly.com/question/14307463
#SPJ4
A cell tower is located 48 miles east and 19 miles north of the center of a small town. The cell tower services everything within a radius of 24.5 miles from it. Write an equation for all possible positions. (x,y), on the boundary of the cell tower's service coverage
(x - (a+48))² + (y - (b+19))² = 24.5² This is the equation for all possible positions (x,y) on the boundary of the cell tower's service coverage.
To write an equation for all possible positions (x,y) on the boundary of the cell tower's service coverage, we first need to determine the coordinates of the center of the coverage.
We know that the cell tower is located 48 miles east and 19 miles north of the center of the small town, so we can add these distances to the coordinates of the town's center. If we let (a,b) be the coordinates of the town's center, then the coordinates of the cell tower would be (a+48,b+19).
Next, we know that the cell tower services everything within a radius of 24.5 miles from it. This means that any point (x,y) on the boundary of the coverage circle would be exactly 24.5 miles away from the cell tower. We can use the distance formula to write an equation for this:
√[(x - (a+48))² + (y - (b+19))²] = 24.5
Know more about coordinates here:
https://brainly.com/question/16634867
#SPJ11
Find the average value fave of the function f on the given interval. f(x) = x2 (x3 + 30) [-3, 3] = fave Find the average value have of the function h on the given interval. In(u) h(u) = [1, 5] u = h ave Find all numbers b such that the average value of f(x) = 6 + 10x - 9x2 on the interval [0, b] is equal to 7. (Enter your answers as a comma-separated list.) b = Suppose the world population in the second half of the 20th century can be modeled by the equation P(t) = 2,560e0.017185t. Use this equation to estimate the average world population to the nearest million during the time period of 1950 to 1980. million people
Answer:
Step-by-step explanation:
To find the average value of the function f(x) = x^2(x^3 + 30) on the interval [-3, 3], we use the formula:
fave = (1/(b-a)) * ∫[a,b] f(x) dx
where a = -3 and b = 3.
So, we have:
fave = (1/(3-(-3))) * ∫[-3,3] x^2(x^3 + 30) dx
fave = (1/6) * [∫[-3,3] x^5 dx + 30∫[-3,3] x^2 dx]
fave = (1/6) * [0 + 30(2*3^3)]
fave = 2430
Therefore, the average value of the function f on the given interval is 2430.
To find the average value of the function h(u) = In(u) on the interval [1, 5], we use the formula:
have = (1/(b-a)) * ∫[a,b] h(u) du
where a = 1 and b = 5.
So, we have:
have = (1/(5-1)) * ∫[1,5] ln(u) du
have = (1/4) * [u ln(u) - u] from 1 to 5
have = (1/4) * [(5 ln(5) - 5) - (ln(1) - 1)]
have = (1/4) * (5 ln(5) - 4)
have = 0.962
Therefore, the average value of the function h on the given interval is approximately 0.962.
To find all numbers b such that the average value of f(x) = 6 + 10x - 9x^2 on the interval [0, b] is equal to 7, we use the formula:
fave = (1/(b-a)) * ∫[a,b] f(x) dx
where a = 0 and b = b.
So, we have:
7 = (1/b) * ∫[0,b] (6 + 10x - 9x^2) dx
7b = [6x + 5x^2 - 3x^3/3] from 0 to b
7b = 2b^2 - 3b^3/3 + 6
21b = 6b^2 - b^3 + 18
b^3 - 6b^2 + 21b - 18 = 0
Using synthetic division, we find that b = 2 is a root of this polynomial equation. Dividing by (b-2), we get:
(b-2)(b^2 - 4b + 9) = 0
The quadratic factor has no real roots, so the only solution is b = 2.
Therefore, the only number b such that the average value of f(x) on the interval [0, b] is equal to 7 is 2.
To estimate the average world population to the nearest million during the time period of 1950 to 1980, we need to find:
ave = (1/(1980-1950)) * ∫[1950,1980] P(t) dt
ave = (1/30) * ∫[1950,1980] 2560e^(0.017185t) dt
Using the formula for integrating exponential functions, we get:
ave = (1/30) * [2560
there is no 3 × 3 matrix a so that a2 = −i3.
Based on the analysis, there is no 3x3 matrix A such that A^2 = -I_3. To understand this analysis let's consider whether there exists a 3x3 matrix A such that A^2 = -I_3, where I_3 is the 3x3 identity matrix.
Step:1. Start by assuming that there is a 3x3 matrix A such that A^2 = -I_3.
Step:2. Recall that the determinant of a matrix squared (det(A^2)) is equal to the determinant of the matrix (det(A)) squared: det(A^2) = det(A)^2.
Step:3. Compute the determinant of both sides of the equation A^2 = -I_3: det(A^2) = det(-I_3).
Step:4. For the 3x3 identity matrix I_3, its determinant is 1. Therefore, the determinant of -I_3 is (-1)^3 = -1.
Step:5. From step 2, we know that det(A^2) = det(A)^2. Since det(A^2) = det(-I_3) = -1, we have det(A)^2 = -1.
Step:6. However, no real number squared can equal -1, which means det(A)^2 cannot equal -1.
Based on the analysis, there is no 3x3 matrix A such that A^2 = -I_3.
Learn more about matrix here, https://brainly.com/question/11989522
#SPJ11
Find g' (-1/5), where g is inverse of f(x) = {x^7} / {x^4 + 4}. (Express numbers in exact form. Use symbolic notation and fractions where needed.)
The inverse of g' (-1/5) is -15625 / 4^{5/4}.
To find g' (-1/5), we first need to find g(x) which is the inverse of f(x). To do this, we start by setting y = f(x) and solving for x.
y = f(x) = {x^7} / {x^4 + 4}
Multiplying both sides by x^4 + 4, we get:
y(x^4 + 4) = x^7
Expanding the left side, we get:
y(x^4) + 4y = x^7
Substituting u = x^4, we get:
yu + 4y = u^(7/4)
Rearranging and solving for y, we get:
y = (u^(7/4)) / (u + 4)
Substituting back u = x^4, we get:
y = (x^7) / (x^4 + 4)
Thus, g(x) = (x^7) / (x^4 + 4).
Now, to find g'(-1/5), we need to take the derivative of g(x) and evaluate it at x = -1/5.
Using the quotient rule, we get:
g'(x) = [7x^6(x^4+4) - x^7(4x^3)] / (x^4+4)^2
Substituting x = -1/5, we get:
g'(-1/5) = [7(-1/5)^6((-1/5)^4+4) - (-1/5)^7(4(-1/5)^3)] / ((-1/5)^4+4)^2
Simplifying and expressing in exact form, we get:
g'(-1/5) = [-(4/3125)^(3/4)] / (4/3125)^2 = -1 / (4/3125)^{5/4} = -15625 / 4^{5/4}
Know more about inverse here:
https://brainly.com/question/3831584
#SPJ11
in a clinical test with 9300 subjects 1860 showed improvement from the treatment find the margin of error for the 99onfidence interval used to estimate the population proportion algebra
The margin of error for the 99% confidence interval used to estimate the population proportion is approximately 0.00992 or 0.992%.
To find the margin of error for a 99% confidence interval for a population proportion, we need to follow these steps:
Step 1: Determine the sample proportion (p-hat)
In this case, 1860 out of 9300 subjects showed improvement. So, the sample proportion is:
p-hat = 1860/9300 ≈ 0.2
Step 2: Find the critical value (z-score) for the 99% confidence interval
For a 99% confidence interval, the critical value (z-score) is approximately 2.576. This can be found using a z-table or statistical calculator.
Step 3: Calculate the standard error
The standard error can be found using the formula:
SE = sqrt((p-hat * (1 - p-hat))/n)
Where n is the number of subjects. In this case:
SE = sqrt((0.2 * (1 - 0.2))/9300) ≈ 0.00385
Step 4: Calculate the margin of error
Finally, the margin of error can be found by multiplying the critical value and the standard error:
Margin of Error = z-score * SE
Margin of Error = 2.576 * 0.00385 ≈ 0.00992
So, the margin of error for the 99% confidence interval used to estimate the population proportion is approximately 0.00992 or 0.992%.
In summary, the margin of error for this clinical test is 0.992%, which represents the uncertainty around the estimated population proportion of subjects who show improvement after treatment. This means that we can be 99% confident that the true population proportion lies within 0.2 ± 0.00992.
To know more about margin of error refer here:
https://brainly.com/question/29101642
#SPJ11
recall that the variance of a bernoulli random variable is p(1-p). what value of probability p maximizes this variance?
To find the value of probability p that maximizes the variance of a Bernoulli random variable, we need to take the derivative of the variance formula with respect to p and set it equal to 0: d/dp [p(1-p)] = 1-2p = 0.
The value of probability p that maximizes the variance of a Bernoulli random variable is 1/2.The variance of a Bernoulli random variable is given by the formula Var(X) = p(1-p), where p is the probability of success. To find the value of p that maximizes the variance, you can take the derivative of the variance formula with respect to p and set it to zero.d(Var(X))/dp = d(p(1-p))/dp = 1 - 2pSetting the derivative equal to zero:1 - 2p = 0Solving for p:p = 1/2So, the value of probability p that maximizes the variance of a Bernoulli random variable is 0.5 or 1/2.
Learn more about probability here: brainly.com/question/11234923
#SPJ11
At the same time a 70 feet building casts a 50 foot shadow, a nearby pillar casts a 10 foot shadow. Which proportion could you use to solve for the height of the pillar?
The height of the pillar is 14 feet.
How to find height ?We can use the ratio of the building's height to the length of its shadow to solve for the pillar's height and apply it to the pillar as well. This is because similar-shaped objects will produce shadows that are proportional to their size.
Let h represent the pillar's height, and let's establish a proportion:
height of building / length of building's shadow = height of pillar / length of pillar's shadow
Substituting the given values:
70 / 50 = h / 10
We can simplify this proportion by cross-multiplying:
70 x 10 = 50h
700 = 50h
And solving for h:
h = 700 / 50 = 14
Therefore, the height of the pillar is 14 feet.
In conclusion, we can solve for the pillar's height by establishing a ratio between the building's height and the length of its shadow and applying that ratio to the pillar.
know more about proportion visit :
https://brainly.com/question/30675547
#SPJ1
An object is placed 16.2 cm from a first converging lens of focal length 11.6 cm. A second converging lens with focal length 5.00 cm is placed 10.0 cm to the right of the first converging lens.(a) Find the position q1 of the image formed by the first converging lens. (Enter your answer to at least two decimal places.)cm(b) How far from the second lens is the image of the first lens? (Enter your answer to at least two decimal places.)cm beyond the second lens(c) What is the value of p2, the object position for the second lens? (Enter your answer to at least two decimal places.)cm(d) Find the position q2 of the image formed by the second lens. (Enter your answer to at least two decimal places.)cm(e) Calculate the magnification of the first lens.(f) Calculate the magnification of the second lens.(g) What is the total magnification for the system?(h) Is the final image real or virtual (compared to the original object for the lens system)?realvirtualIs it upright or inverted (compared to the original object for the lens system)? upright
The final image is real since it is located to the right of the second lens. It is also upright since the magnification is positive.
(a) Using the thin lens formula, 1/f = 1/p + 1/q, where f is the focal length, p is the object distance, and q is the image distance, we have:
1/f = 1/p - 1/q1
Substituting the given values, we get:
1/11.6 = 1/16.2 - 1/q1
Solving for q1, we get:
q1 = 6.97 cm
Therefore, the image formed by the first lens is located 6.97 cm to the right of the lens.
(b) The image formed by the first lens acts as an object for the second lens. Using the thin lens formula again, we have:
1/f = 1/p2 + 1/q1
Substituting the given values, we get:
1/5 = 1/p2 + 1/6.97
Solving for p2, we get:
p2 = 3.32 cm
The distance from the second lens to the image of the first lens is then:
q2 = p2 + q1 = 3.32 + 6.97 = 10.29 cm
Therefore, the image of the first lens is located 10.29 cm to the right of the second lens.
(c) The object distance for the second lens is simply the image distance of the first lens:
p2 = q1 = 6.97 cm
(d) Using the thin lens formula again, we have:
1/f = 1/p2 + 1/q2
Substituting the given values, we get:
1/5 = 1/6.97 + 1/q2
Solving for q2, we get:
q2 = 13.95 cm
Therefore, the final image is located 13.95 cm to the right of the second lens.
(e) The magnification of the first lens is given by:
m1 = -q1/p = -6.97/16.2 ≈ -0.43
(f) The magnification of the second lens is given by:
m2 = -q2/p2 = -13.95/3.32 ≈ -4.20
(g) The total magnification of the system is given by the product of the magnifications of the two lenses:
m = m1 × m2 ≈ 1.81
(h) The final image is real since it is located to the right of the second lens. It is also upright since the magnification is positive.
To learn more about magnification visit:
https://brainly.com/question/21370207
#SPJ11
The two triangles shown are similar. Find the value of y
Answer:
[tex] \frac{y}{28} = \frac{7}{25} [/tex]
[tex]25y = 196[/tex]
[tex]y = 7.84[/tex]
Consider the curve x2/3+y2/3=4.
Let L be the tangent line to this curve at the point (1,3√3), and let A and B be the x- and y-intercepts of L.
What is the length of the line segment AB?
(a) 8
(b) √38
(c) 8√3
(d) √3
(e) 31/38
If the curve x2/3+y2/3=4 and Let L be the tangent line to this curve at the point (1,3√3), and let A and B be the x- and y-intercepts of L, then the length of line segment AB is √38 (option b).
Explanation:
To find the length of line segment AB, follow these steps:
Step 1: We need to first find the equation of tangent line L at the given point (1, 3√3) on the curve x^(2/3) + y^(2/3) = 4.
Step 1. Find the derivative dy/dx using implicit differentiation:
(2/3)x^(-1/3) + (2/3)y^(-1/3)(dy/dx) = 0
Step 2. Solve for dy/dx (the slope of tangent line L) at point (1, 3√3):
(2/3)(1)^(-1/3) + (2/3)(3√3)^(-1/3)(dy/dx) = 0
dy/dx = -1/2
Step 3. Use the point-slope form to find the equation of tangent line L:
y - 3√3 = -1/2(x - 1)
Step 4. Find the x- and y-intercepts (A and B) of line L:
x-intercept (A): y = 0
0 - 3√3 = -1/2(x - 1)
x = 2 + 6√3
y-intercept (B): x = 0
y - 3√3 = -1/2(0 - 1)
y = 3√3 + 1/2
Step 5. Calculate the length of the line segment AB using the distance formula:
AB = √[(2 + 6√3 - 0)^2 + (3√3 + 1/2 - 0)^2] = √38
The length of line segment AB is √38 (option b).
Know more about the tangent line click here:
https://brainly.com/question/31326507
#SPJ11
What is the overall order of the following reaction, given the rate law?
X + 2 Y → 4 Z Rate = k[X][Y]
3rd order
1st order
2nd order
5th order
6th order
The overall order of the reaction is 2nd order.
Option B is the correct answer.
We have,
The overall order of a chemical reaction is the sum of the orders of the reactants in the rate law.
In this case,
The rate law is given as:
Rate = k[X][Y]
The order with respect to X is 1, and the order with respect to Y is 1.
Therefore, the overall order of the reaction is:
1 + 1 = 2
Thus,
The overall order of the reaction is 2nd order.
Learn more about rate law here:
https://brainly.com/question/30379408
#SPJ11
consider a wave form s(t)=5 sin 10 π t 2 sin 12 π t. the signal s(t) is sampled at 10 hz. do you expect to see aliasing? select true if the answer is yes or false otherwise.
The statement "consider a wave form s(t)=5 sin 10 π t 2 sin 12 π t. the signal s(t) is sampled at 10 hz. do you expect to see aliasing" is true because aliasing is expected.
When sampling a signal s(t) = 5 sin(10πt) * 2 sin(12πt) at 10 Hz, you can expect to see aliasing. The Nyquist sampling theorem states that a signal should be sampled at least twice the highest frequency present in the signal to avoid aliasing.
The two sinusoids in s(t) have frequencies of 5 Hz (10πt) and 6 Hz (12πt). The highest frequency is 6 Hz, so according to the Nyquist theorem, the signal should be sampled at least at 12 Hz (2 times the highest frequency) to avoid aliasing. Since the signal is sampled at 10 Hz, which is lower than the required 12 Hz, aliasing will occur.
To know more about Nyquist sampling theorem click on below link:
https://brainly.com/question/16895594#
#SPJ11
Find an equation for the line tangent to y=-1-7x^2 at (-2,-29)
the equation for the line tangent yo y=-17x^2 at (-2,-29) is y=
The equation for the line tangent to y = [tex]-1 - 7x^2[/tex] at (-2, -29) is y = 28(x + 2) - 29.
To find the equation for the line tangent to y = [tex]-1 - 7x^2[/tex] at (-2, -29), we'll need to first find the derivative of the given function to determine the slope of the tangent line.
The given function is y = [tex]-1 - 7x^2.[/tex]
Differentiate y with respect to x:
dy/dx = -14x
Now, evaluate the derivative at the point (-2, -29) to find the slope of the tangent line:
dy/dx| (x=-2) = -14(-2) = 28
The slope of the tangent line is 28. To find the equation of the tangent line, use the point-slope form: y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point (-2, -29).
y - (-29) = 28(x - (-2))
y + 29 = 28(x + 2)
Now, solve for y:
y = 28(x + 2) - 29
For more such questions on Tangent line equation.
https://brainly.com/question/6617153#
#SPJ11
Consider the following function.f(x, y) = y2Describe the surface given by the function.Because the variable x is missing, the surface is a cylinder with rulings parallel to the x-axis . The generating curve isz = y2. The domain is the entire xy-plane and the range is z ≥ ??????
The surface given by the function f(x, y) = y² is a cylinder with rulings parallel to the x-axis. The generating curve is described by z = y². The domain of the function is the entire xy-plane, and the range is z ≥ 0.
The function f(x, y) = y² describes a surface in three-dimensional space. Since the variable x is missing, the surface will not depend on x, and the rulings (lines) of the surface will be parallel to the x-axis. This makes the surface a cylinder with rulings parallel to the x-axis.
The generating curve of the surface is given by z = y², which means that the z-coordinate of any point on the surface is equal to the square of the y-coordinate. This generates a parabolic shape along the y-axis, extending infinitely in the positive and negative y-directions.
The domain of the function is the entire xy-plane, which means that the function is defined for all values of x and y. There are no restrictions on the values of x and y in the domain.
The range of the function is z ≥ 0, which means that the z-coordinate of any point on the surface will always be greater than or equal to zero. This is because the function f(x, y) = y² always produces non-negative values for z, since any real number squared is always non-negative.
Therefore, the surface described by the function f(x, y) = y² is a cylinder with rulings parallel to the x-axis, the generating curve is given by z = y², the domain is the entire xy-plane, and the range is z ≥ 0.
To learn more about curve here:
brainly.com/question/29990557#
#SPJ11
find all real and complex roots of the equation z 10 = 910
Using De Moivre's theorem, we have: z = r^(1/10) * (cos(θ/10) + i*sin(θ/10)). As we are looking for 10 roots, we need to find each root by varying k from 0 to 9: z_k = (√910)^(1/10) * (cos(2πk/10) + i*sin(2πk/10))Substitute k from 0 to 9 to obtain all the real and complex roots of the equation z^10 = 910.
To find all real and complex roots of the equation z^10 = 910, we can use the polar form of complex numbers. First, we can write 910 in polar form: 910 = 910(cos(0) + i sin(0)) Next, we can express z in polar form as well: z = r(cos(θ) + i sin(θ)) Substituting these expressions into the equation z^10 = 910 and using De Moivre's Theorem, we get: r^10(cos(10θ) + i sin(10θ)) = 910(cos(0) + i sin(0)) Equating the real and imaginary parts, we get: r^10 cos(10θ) = 910 cos(0) = 910 r^10 sin(10θ) = 910 sin(0) = 0
The second equation gives us two possible values of θ: θ = 0 and θ = π (since sin(π) = 0). For θ = 0, the first equation gives us: r^10 cos(0) = 910 r^10 = 910 r = (910)^(1/10) So one possible solution is z = (910)^(1/10). For θ = π, the first equation gives us: r^10 cos(10π) = 910 r^10 (-1) = 910 r^10 = -910 Since r must be real, this equation has no real solutions.
However, we can find 5 complex solutions by using the 5th roots of -910: (-910)^(1/5) = 2(cos(π/5) + i sin(π/5)) (-910)^(1/5) = 2(cos(3π/5) + i sin(3π/5)) (-910)^(1/5) = 2(cos(5π/5) + i sin(5π/5)) = -2 (-910)^(1/5) = 2(cos(7π/5) + i sin(7π/5)) (-910)^(1/5) = 2(cos(9π/5) + i sin(9π/5)) Using these values of r and θ, we can write the 6 solutions to z^10 = 910 as: z = (910)^(1/10) z = 2(cos(π/5) + i sin(π/5)) z = 2(cos(3π/5) + i sin(3π/5)) z = -2 z = 2(cos(7π/5) + i sin(7π/5)) z = 2(cos(9π/5) + i sin(9π/5))
Learn more about De Moivre's theorem here: brainly.com/question/31156683
#SPJ11
what is the easiest way to solve quadratic problems using the quadratic formula in a step by step sequence?
The text is asking for a step-by-step sequence to solve quadratic problems using the quadratic formula.
A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one squared term. The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The quadratic formula is used to find the solution(s) of a quadratic equation. The formula is x = (-b ± sqrt(b² - 4ac)) / 2a.
Answer:
Step-by-step explanation:
put your equation into
ax²+bx+c
determine a, b, and c
plug into formula
simplify numbers under the square root first (b²-4ac)
then simplify the root. ex. √12 can be simplified to 2√3
then reduce if the bottom can be reduced with both of the terms on top
Write the transformation matrix and the resultant matrix that will translate the triangle, (-2, 4), given the triangles vertices are at A(-1, 3), B(0, -4) and C(3, 3).
The resultant matrix represents the vertices of the translated triangle, with A' at (-3, 7), B' at (-2, 0), and C' at (1, 7).
Define the term transformation matrix?A transformation matrix is a mathematical matrix that represents a geometric transformation of space.
To translate the triangle by (-2, 4), we need to add -2 to the x-coordinates and add 4 to the y-coordinates of each vertex. The transformation matrix for this translation is:
[tex]\left[\begin{array}{ccc}1&0&-2\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0&1&4\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0&0&1\end{array}\right][/tex]
To apply this transformation to the vertices of the triangle, we can represent each vertex as a column vector with a third coordinate of 1:
[tex]A=\left[\begin{array}{ccc}-1&3&1\end{array}\right][/tex]
[tex]B=\left[\begin{array}{ccc}0&-4&1\end{array}\right][/tex]
[tex]C=\left[\begin{array}{ccc}3&3&1\end{array}\right][/tex]
To apply the translation, we multiply each vertex by the transformation matrix:
[tex]A'=\left[\begin{array}{ccc}1&0&-2\end{array}\right] \left[\begin{array}{ccc}-1&3&1\end{array}\right] \left[\begin{array}{ccc}-3&7&1\end{array}\right][/tex]
[0 1 4] × [ 0 -4 1] = [-2 0 1]
[0 0 1] [ 1 3 1] [-1 7 1]
[tex]B'=\left[\begin{array}{ccc}1&0&-2\end{array}\right] \left[\begin{array}{ccc}0&-4&1\end{array}\right] \left[\begin{array}{ccc}-2&-4&1\end{array}\right][/tex]
[0 1 4] × [ 0 -4 1] = [-2 0 1]
[0 0 1] [ 0 3 1] [-2 7 1]
[tex]C'=\left[\begin{array}{ccc}1&0&-2\end{array}\right] \left[\begin{array}{ccc}3&3&1\end{array}\right] \left[\begin{array}{ccc}1&7&1\end{array}\right][/tex]
[0 1 4] × [ 3 3 1] = [ 1 7 1]
[0 0 1] [ 3 3 1] [ 1 7 1]
The resultant matrix represents the vertices of the translated triangle, with A' at (-3, 7), B' at (-2, 0), and C' at (1, 7).
To know more about matrix, visit:
https://brainly.com/question/30389548
#SPJ1
help quick/100 points Select all of the following statements that are true. If 6 > 10, then 8 · 3 = 24. 6 + 3 = 9 and 4 · 4 = 16 If 6 · 3 = 18, then 4 + 8 = 20 5 · 3 = 15 or 7 + 5 = 20
Answer:
The statements that are true are:
6 + 3 = 9 and 4 · 4 = 16 (both are true statements)
5 · 3 = 15 or 7 + 5 = 20 (at least one of these statements is true, since the word "or" means that only one of the two statements needs to be true for the entire statement to be true)
The other two statements are false:
If 6 > 10, then 8 · 3 = 24 (this statement is false, because the premise "6 > 10" is false, and a false premise can never imply a true conclusion)
If 6 · 3 = 18, then 4 + 8 = 20 (this statement is false, because the conclusion "4 + 8 = 20" does not follow logically from the premise "6 · 3 = 18")
What is the equation that can be used to find a percent of a number?
1. part= percent/whole
2.part= while/percent
3.part=percent+whole
4. part=percent•whole
Answer:
Step-by-step explanation:
4. percent x whole
6 soccer players share 5 oranges as fraction
Answer:5/6
Step-by-step explanation: Theres 6 people that you are splitting 5 oranges among. so you do the equation 5÷6 or 5/6 which is the answer your looking for
Answer:
5/6
Step-by-step explanation:
=0.8333.......................
find the critical numbers of the function. (enter your answers as a comma-separated list.) g(t) = t 5 − t , t < 4
the critical numbers of g(t) are approximately -0.690 and 0.690
To find the critical numbers of the function g(t) = t⁵ - t, we need to first find the derivative of the function.
g'(t) = 5t⁴ - 1
Then we set the derivative equal to zero and solve for t:
5t⁴ - 1 = 0
5t⁴ = 1
t⁴ = 1/5
t = [tex]±(1/5)^{(1/4)}[/tex]
However, we need to check if these values are in the domain of the function, which is t < 4.
[tex](1/5)^{(1/4)}[/tex]≈ 0.690, which is less than 4, so it is a valid critical number.
-[tex](1/5)^{(1/4)}[/tex] ≈ -0.690, which is also less than 4, so it is also a valid critical number.
Therefore, the critical numbers of g(t) are approximately -0.690 and 0.690, and we can write them as a comma-separated list:
-0.690, 0.690
To know more about Critical Numbers refer here:
https://brainly.com/question/29743892
#SPJ11
HELP PLEASE HURRY <3 Use the graphs to identify the following: axis of symmetry, x-intercept(s), y-intercept, & vertex.
Determine the interval in which the function is increasing.
Question 2 options:
(-∞, 2)
(2, ∞)
(1, 3)
(-∞, ∞)
The axis of symmetry is 2, x-intercept are (3,0) and (1,0) , y-intercept is (0,3) vertex is 2
Here we have to point the values on the given graph.
Then we get the graph like the following.
Now, we have to identify the value of axis of symmetry, x-intercept(s), y-intercept, & vertex through the following definition.
The axis of symmetry is a vertical line that divides the graph of a function into two mirror images. It passes through the vertex, which is the highest or lowest point on the graph. To find the axis of symmetry, we need to look for the vertical line that divides the graph into two equal parts is x = 2.
The x-intercept(s) are the points where the graph of a function crosses the x-axis. To find the x-intercepts, we need to look for the points where the graph intersects the x-axis, which is the horizontal line with a y-coordinate of (3,0) and (1,0)
The y-intercept is the point where the graph of a function crosses the y-axis. To find the y-intercept, we need to look for the point where the graph intersects the y-axis, which is the vertical line with an x-coordinate of 0 that is (0,3)
The vertex is the highest or lowest point on the graph of a function, depending on whether the function opens upward or downward. To find the vertex, we need to locate the point where the function reaches its maximum or minimum value is 2.
The completed graph is illustrated below.
To know more about graph here
https://brainly.com/question/17267403
#SPJ1
Use the limit comparison test to determine whether the following series converge or diverge. A. X [infinity] n=3 n 7 + n2 B. X [infinity] n=1 3n 3 − 2n 6n5 + 2n + 1 C. X [infinity] n=1 2 n 4 n − n2 D. X [infinity] n=1 sin 1 n n (Hint: Try comparing this to X [infinity] n=1 1 n2 .
Using the limit comparison test, we determined that the series (A) diverges, (B) converges, (C) diverges, and (D) converges.
We can use the limit comparison test with the series 1/n to determine whether the series converges or diverges:
lim n→∞ (n7 + n2) / n = lim n→∞ (n7/n + n2/n) = ∞
Since this limit diverges to infinity, we cannot use the limit comparison test with the series 1/n. We can try another convergence test.
We can use the limit comparison test with the series 1/n3 to determine whether the series converges or diverges:
lim n→∞ (3n3 − 2n) / (6n5 + 2n + 1) = lim n→∞ (n2 − 2/n2) / (2n5 + 1/n + 1/n5) = 1/2
Since this limit is a positive finite number, the series converges if and only if the series ∑ 1/n^3 converges. Since the p-series with p = 3 converges, the series ∑ (3n^3 - 2n) / (6n^5 + 2n + 1) also converges.
We can use the limit comparison test with the series 1/n to determine whether the series converges or diverges:
lim n→∞ 2n / (4n − n2) = lim n→∞ 2/n(4 − n) = 0
Since this limit is a finite number, the series converges if and only if the series ∑ 1/n converges. Since the harmonic series diverges, the series ∑ 2n / (4n - n^2) also diverges.
We can use the limit comparison test with the series 1/n^2 to determine whether the series converges or diverges:
lim n→∞ sin(1/n) / (1/n^2) = lim n→∞ sin(1/n) * n^2 = 1
Since this limit is a positive finite number, the series converges if and only if the series ∑ 1/n^2 converges. Since the p-series with p = 2 converges, the series ∑ sin(1/n) / n also converges.
To know more about limit comparison test, here
https://brainly.com/question/31362838
#SPJ4
Vectors Maths question!!
(can't get option b)
The two vectors parallel to the plane are AB(8, -5, 4) and AC(0, 7, 6).
The vector perpendicular to the plane is (-58, -48, 56).
What are two vectors parallel and perpendicular to the plane?Vector AB is parallel to the plane since it connects two points on the plane, A and B.
The coordinate point is calculated as;
AB = B - A
= (11, -5, 2) - (3, 0, -2)
= (8, -5, 4)
Vector AC is also parallel to the plane since it connects two points on the plane, A and C.
The coordinate point is calculated as;
AC = C - A
= (3, 7, 4) - (3, 0, -2)
= (0, 7, 6)
To find a vector perpendicular to the plane, we will take the cross product of two vectors in the plane, such as AB and AC.
AB x AC = (8, -5, 4) x (0, 7, 6)
= (-58, -48, 56)
Learn more about parallel and perpendicular vector here: https://brainly.com/question/31042385
#SPJ1