a. The integrating factor α(x) = [tex]e^{x^{2} +C[/tex]
b. The general solution is: y = -(4/3)x² - (C/2) + D
c. The solution to the initial value problem is: y(x) = -(4/3)x² - (C/2) + D
How do we calculate?(a)The integrating factor is given by
α(x) = e∫P(x)dx,
P(x) = 2x,
so α(x) = e∫2xdx.
P(x) = ∫2xdx = x² + C, where C is the constant of integration
.(b) Find the general solution, y(x):
Multiply the given equation by the integrating factor α(x):
xy' - 2y = -4x² - Cx
d/dx(xy) = -4x² - Cx.
Integrating both sides with respect to x gives:
∫d/dx(xy)dx = ∫(-4x² - Cx)dx
xy = -(4/3)x³ - (C/2)x + K
Divide both sides by x:
y = -(4/3)x² - (C/2) + (K/x)
(c)The solution to the initial value problem is given: y(x) = -(4/3)x² - (C/2) + D, where C and D are arbitrary constants.
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what is the approximate area of the hexagon? 224 cm2 336 cm2 448 cm2 672 cm2
The value of area of hexagon is,
A = 672 cm²
Given that;
In a hexagon;
Apothem of the hexagon = 14 cm
And, perimeter of the hexagon: 96 cm
Since, We know that,
Area of the hexagon = [(3√3) / 2] a²
where, a is the measure of the side
Since, hexagon has 6 sides.
Perimeter = 6a
96 cm = 6a
96 cm / 6 = a
16 = a
We can also use the area of a triangle to approximate the area of the hexagon. There are 6 triangles in the hexagon .
Area of a triangle = (height x base) / 2
A = (14 cm x 16 cm) / 2
A = 224 / 2
A = 112 cm²
So, Area of hexagon is,
A = 112 cm² x 6 triangles
A = 672 cm²
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Complete question is,
A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm.
What is the approximate area of the hexagon?
224 cm2
336 cm2
448 cm2
672 cm2
If the data point is at (3, 10.5) and the prediction equation is y = -6.1x + 12.5, what is the value of the residual for this data point?
Given:
The data point is (3,10.5).
The prediction equation is [tex]y=-6.1x+12.5[/tex].
To find:
The value of the residual for this data point.
Step-by-step explanation:
The data point is (3,10.5). So, the actual value is 10.5 at [tex]x=3[/tex].
Prediction equation is
[tex]y=-6.1x+12.5[/tex]
Putting [tex]x=3[/tex], we get
[tex]y=-6.1(3)+12.5[/tex]
[tex]y=-18.3+12.5[/tex]
[tex]y=-5.8[/tex]
The formula for residual is:
Residual = Actual value - Expected value
[tex]Residual=10.5-(-5.8)[/tex]
[tex]Residual=10.5+5.8[/tex]
[tex]Residual=16.3[/tex]
Therefore, the residual for the given data point is 16.3.
Given the data set, calculate the mean
{9, 3, 1, 8, 3, 6}
Please help!!!
Answer:
mean: 5
Step-by-step explanation:
(9 + 3 + 1 + 8 + 3 + 6) / 6 = 5
determine whether the following equations are second-order linear differential equations.(a)y'' = −3x(y')2
To determine whether the equation y'' = −3x([tex]y')^2[/tex]is a second-order linear differential equation, we need to examine its form.
A second-order linear differential equation has the general form:
[tex]y'' + p(x)y' + q(x)y = r(x)[/tex]
where y is the dependent variable, x is the independent variable, and p(x), q(x), and r(x) are functions of x.
In the given equation, [tex]y'' = -3x(y')^2,[/tex]we can observe that the dependent variable y only appears in the squared term [tex](y')^2.[/tex]This indicates that the equation is not linear in y or its derivatives. It contains a non-linear term [tex](y')^2[/tex]multiplied by the function -3x.
Therefore, the equation [tex]y'' = -3x(y')^2 i[/tex] is not a second-order linear differential equation.
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The length of a rectangle is five more than three time its width. The perimeter of a rectangle is 234. What is the width of the rectangle
Answer:
28 units
Step-by-step explanation:
Given data
Let the width be x
The length is =3x+5
Perimeeter= 234
The expression for the perimeter is
P=2L+2W
Substitute
234= 2*x+2(3x+5)
234= 2x+6x+10
Collect like terms
234= 8x+10
234-10= 8x
224=8x
x= 224/8
x=28
Hence the width is 28 units
Please help ASAP I’ll give u brilliant
Answer: I’m sorry I meant B
Step-by-step explanation: 9.6/3=3.2
3.2•8=25.6
Find b given that A (-6, 2), B (b, 0), and C (3,-4) are collinear.
Answer:
b = -3.
Step-by-step explanation:
If the 3 points are collinear then:
Slope of AB = Slope of BC and so
(0-2)/(b + 6) = (-4-0)/( 3 - b)
-4(b + 6) = -2(3 - b)
-4b - 24 = -6 + 2b
-24 + 6 = 2b + 4b
6b = -18
b = -3.
Ahmad throws dice find the probability that it is:not a 2
yah it's not probably it's not 2 mmmm
how many 5-digit passwords can I make out of the English alphabet. lowercase only
Answer:
7,893,600 different combinations
Step-by-step explanation:
Answer:
We have a total.of 26 alphabets in the english language and numbers 0 to 9 will be 10.
Since there are no other limitations, we have to arrange 8 places with the 36 options we have.
It will simply be 36c8.
The answer will be 3,02,60,340.
Use the spinner below for each of the following
questions. Place an "x" along the number line to
represent how likely the event is to occur.
How likely is it for the spinner to land on a 5?
Solve for x and then answer
Answer:
Value of x = 70'
Step-by-step explanation:
Given:
Given quadrilateral is a cyclic quadrilateral, in a cyclic quadrilateral sum of opposite angle is 180' .
Find:
Value of x
Computation:
x' + 110' = 180'
x' = 180' - 110'
Value of x = 70'
f(x)=x^2. what is g(x)?
please help asap!!
The equation of the red graph, g(x) is g(x) =1/3x²
How to calculate the equation of the red graphFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
In the graph, we can see that
The blue graph passes through the vertex (0, 0)The red graph passes through the vertex (0, 0) but it is 3 times widerThis means that
g(x) = 1/3f(x)
Recall that
f(x) = x²
This means that
g(x) =1/3x²
This means that the equation of the red graph is g(x) =1/3x²
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what two steps are necessary to put this equation into standard form?
x^2-3 x 27=8 x-3x 2 −3x 27=8x−3
A. Add 3 to both sides and substract 8x from both sides
B. The equation is already in standard from
C. Substract 3 from sides and substract 8x from both sides
D. Add 3 to both sides and add 8x from both sides
The two necessary steps to put this equation into standard form is A) Add 3 to both sides and subtract 8x from both sides.
To put the equation x² - 3x + 27 = 8x - 3 into standard form, the two necessary steps are:
A. Add 3x to both sides: By adding 3 to both sides of the equation, we eliminate the constant term -3 on the right side and move it to the left side.
x² - 3x + 3x + 27 = 8x - 3 + 3x
x² + 27 = 11x
B. Subtract 11x from both sides: By subtracting 8x from both sides of the equation, we eliminate the term 8x on the right side and move it to the left side.
x² + 27 - 11x = 11x - 11x
x² - 11x + 27 = 0
Therefore, the equation in standard form is x² - 11x + 27 = 0. Therefore, the correct answer is option A.
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Please help me I know it's A but I don't know why.
Answer:
Maybe try explaining that if you narrow it down and simplify the numbers by dividing them by 8 or somewhere around there.
2+2x+x2 but x=5 need help
Answer:
22
Step-by-step explanation:
Answer:
6x
Step-by-step explanation:
because i said so 2+2+2=6 and x=5 but two x=10
The temperature at the point (x, y, z) in a substance with conductivity
K = 7.5 is u(x, y, z) = 3y² + 3z².
Find the rate of heat flow inward across the cylindrical surface
y² + z² = 6, 0 ≤ x ≤ 3
The integration is ∫∫(q · dS) = ∫[0 to √6] ∫[0 to √6] (-45y - 45z) dy dz.
The rate of heat flow inward across the cylindrical surface y² + z² = 6, 0 ≤ x ≤ 3 can be determined by calculating the flux of the heat vector field through the surface.
To find the rate of heat flow, we need to calculate the surface integral of the heat flux vector across the given cylindrical surface. The heat flux vector is given by q = -K∇u, where K is the conductivity and ∇u is the gradient of the temperature function u(x, y, z).
First, we find the gradient of u:
∇u = (∂u/∂x)i + (∂u/∂y)j + (∂u/∂z)k
= 0i + (6y)j + (6z)k
Then, we calculate the heat flux vector:
q = -K(∇u)
= -7.5(0i + (6y)j + (6z)k)
= -45yj - 45zk
Next, we calculate the surface area element vector, dS, of the cylindrical surface. Since the surface is defined by y² + z² = 6, we can parameterize it as r(y,z) = yi + zk. Taking the cross product of the partial derivatives, we obtain dS = (∂r/∂y) x (∂r/∂z) dy dz = (-j -k) dy dz.
Finally, we can calculate the surface integral by integrating the dot product of q and dS over the given cylindrical surface:
∫∫(q · dS) = ∫∫(-45yj - 45zk) · (-j -k) dy dz
To find the limits of integration, we note that the surface extends from y² + z² = 6 to the origin, which corresponds to 0 ≤ y² + z² ≤ 6. Since the surface is symmetric, we can integrate over a quarter of the surface, from y = 0 to y = √6 and z = 0 to z = √6.
Performing the integration, we get:
∫∫(q · dS) = ∫[0 to √6] ∫[0 to √6] (-45y - 45z) dy dz
Evaluating this double integral will give us the rate of heat flow inward across the cylindrical surface.
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Help with these will give brainliest
Answer:
$ 45,600
Step-by-step explanation:
Jessie needs to earn more than $160 every month.
B. Enter the minimum number of hours, to the nearest whole, Jessie would have to work to earn $160 in a month.
Answer:
divide 460/60
Step-by-step explanation:
60 rep one hour and you will find your answer
(450) + (28.75x) = 967.50
solve for x
Answer:
x=18
Step-by-step explanation:
Answer:
x= 18
Step-by-step explanation:
To solve this equation you have to work backwards
Start by dealing with the numbers that we know:
450 + (28.75 × x) = 967.5
-450 -450
28.75x = 967.5
(when a number and a letter in mathematics are next to each other they are multiplying)
Now divide to find the value of x:
967.5 ÷ 28.75 = 18
18 is the value of x
20 points helppppppppppppppppppppppppppppp
PLZZ anyone solve this ASAP
Answer:
[tex] cos^{-1}(cos\frac{ 7π}{6})=cos^{-1}(cos\frac{7*180}{6})[/tex]
[tex] cos^{-1}(cos{210})[/tex]
[tex] cos^{-}(cos(180+30))[/tex]
[since in third quadrant cos 30=-[tex] \frac{\sqrt{3}}{2}][/tex]
[tex] cos^{-}(- \frac{\sqrt{3}}{2})[/tex]
:150°or [tex] \frac{5π}{6}[/tex]
150°or [tex] \frac{5π}{6}[/tex]is a required answer.
TRIG HELP NEED TO FIND C IS IT NOT ALT ANGLES?????
[tex]c+20=55\\c=55-20\\c=35[/tex]
Bobby purchased a brand new car for $23,000 every year the car depreciates 20%. The function f(x)=23,000 × 0.8^x models this situation. How much will the car be worth after 6 years?
Answer:
that earns 3% interest compounded annually. He ... Is the equation A = 21000(1 – 0.12)'a model of ... (1+0.03)= 1.03 ... The value of a car purchased for $20,000 decreases ... Kathy plans to purchase a car that depreciates. ... B) P= 10,000(0.8) ... YEARS. Wolves d is less than 1! d is more than 11. 1 Growth f(x) = 80(0.1165).
Step-by-step explanation:
PLz help
how would you represent this situation( Write the equation or inequality.)
On a carnival ride you must be at least 42 inches tall to ride
Answer:
x≥k y for you y≥42 inches tall
Step-by-step explanation:
can i have brainliest if right
Calculate the volume
2. One of the goals of this lab is to become familiar with different shapes of simple molecules. a. What is the name of the theory used to predict molecular geometries? b. Suppose a molecule consists of a central atom bonded to 2 outer atoms. There are two lone pairs on the central atom. What is the name of the molecular shape of this molecule? c. Suppose a molecule consists of a central atom bonded to 4 outer atoms. There are no lone pairs on the central atom. What is the name of the molecular shape of this molecule?
a. The name of the theory used to predict molecular geometries is the VSEPR (Valence Shell Electron Pair Repulsion) theory.
b. The name of the molecular shape for a molecule consisting of a central atom bonded to 2 outer atoms with two lone pairs on the central atom is "bent" or "angular." This molecular shape is also sometimes referred to as "V-shaped" due to its characteristic angular structure.
c. The name of the molecular shape for a molecule consisting of a central atom bonded to 4 outer atoms with no lone pairs on the central atom is "tetrahedral." This molecular shape is characterized by a central atom at the center with four symmetrically arranged outer atoms, forming a three-dimensional tetrahedron-like structure.
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Suppose Y varies directly with X and Y equals 10 when X equals -3 what direct variation equation relates XNY what is the value of Y when X equals -1
Answer:
Expression: Y = -10/3 X
Y = 10/3
Step-by-step explanation:
If Y varies directly as X, then;
Y∝X
Y = kX
k is the constant of variation
If Y = 10 and X = -3
10 = -3k
k = -10/3
Substitute k = -10/3 into the expression Y = kX
Y = -10/3 X
This gives the required expression
To get the value of Y when X = -1
Recall that Y = kX
Y = -10/3 (-1)
Y = 10/3
Hence the value of Y is 10/3
Please help me!! No files allowed. I need the answer and an explanation!
Answer:
I belive the answer is 1/324
Which of the following describes the fraction 2/5?
5 is the part, 2 is the whole, and the fraction is equivalent to 25%.
2 is the part, 5 is the whole, and the fraction is equivalent to 25%.
5 is the part, 2 is the whole, and the fraction is equivalent to 40%.
2 is the part, 5 is the whole, and the fraction is equivalent to 40%.
The correct description of the fraction 2/5 is,
⇒ 2 is the part, 5 is the whole, and the fraction is equivalent to 40%.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
The fraction is,
⇒ 2/5
Now, We can change into percent as;
⇒ 2/5 × 100%
⇒ 2 × 20%
⇒ 40%
Thus, The correct description of the fraction 2/5 is,
⇒ 2 is the part, 5 is the whole, and the fraction is equivalent to 40%.
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Factor 64u–40.
Write your answer as a product with a whole number greater than 1.
Answer: 8(8u-5)
Step-by-step explanation:
Find a number that goes into both 64 and 40 the GCF of both is 8 so 8 goes on the outside of the new factor 8u-5 because if we distribute back we should arrive at the original equation
8(8u-5)
Find the deflection u (x, y, t) satisfying the wave equation utt = 4 (uxx + Uyy) for a rect- = angular plate with fixed ends and dimensions: horizontal a = 2pi and vertical b initial velocity is g(x, y) = 0 The initial displacement is f(x, y) = - 3sin(5x) * sin(6y) + 11sin(6x) * sin(9y)
TheThe general solution to the wave equation utt = 4 (uxx + Uyy) is given by the D’Alembert’s formula. Therefore, the solution to the given problem is obtained by finding the specific form of the initial conditions u (x, y, 0) = f (x, y) and ut (x, y, 0) = g (x, y) and then use these values to find u (x, y, t) using the D’Alembert’s formula.
Let us find the form of the wave u(x,y,t) that satisfies the wave equation utt = 4 (uxx + Uyy) given the initial displacement f(x,y) = -3sin(5x)sin(6y) + 11sin(6x)sin(9y) and g(x,y) = 0.
Solution:
The D’Alembert’s formula for the wave equation is given by:
`u(x,y,t) = (1/2) [f(x+ct,y) + f(x-ct,y)] + (1/(2c)) ∫_((x-ct))^(x+ct)∫_((y-c(t-s)))^(y+c(t-s)) g(s,r) dr ds`
where c is the speed of the wave. Comparing with the wave equation `utt = c^2(uxx + uyy)` we have `c = 2`
Therefore, the solution to the wave equation is given by:
`u(x,y,t) = (1/2) [-3sin(5(x+2t))sin(6y) -3sin(5(x-2t))sin(6y) +11sin(6(x+2t))sin(9y) +11sin(6(x-2t))sin(9y)]`
Hence, the solution is:
`u(x,y,t) = (1/2) [-3sin(5(x+2t))sin(6y) -3sin(5(x-2t))sin(6y) +11sin(6(x+2t))sin(9y) +11sin(6(x-2t))sin(9y)]`
So, this is the required solution.