To find the length of the path defined by r(t) = 2t, 3t, 3t from t = 5 to t = 6, we can use the formula for arc length of a parametric curve. The arc length formula for a parametric curve r(t) = x(t), y(t), z(t) over an interval [a, b] is given by:
L = ∫[a,b] √((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2) dt
In this case, we have r(t) = 2t, 3t, 3t and we want to find the length of the curve from t = 5 to t = 6.
Using the formula, we calculate the derivatives:
dx/dt = 2
dy/dt = 3
dz/dt = 3
Now, we substitute these values into the formula and integrate over the interval [5, 6]:
L = ∫[5,6] √((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2) dt
= ∫[5,6] √(2^2 + 3^2 + 3^2) dt
= ∫[5,6] √(4 + 9 + 9) dt
= ∫[5,6] √22 dt
To calculate the integral, we can simplify the expression under the square root:
L = ∫[5,6] √22 dt
= √22 ∫[5,6] dt
= √22 [t] from 5 to 6
= √22 (6 - 5)
= √22
Therefore, the length of the path r(t) = 2t, 3t, 3t from t = 5 to t = 6 is √22.
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Center: (-10, -4), Point on Circle: (4, -2)
Use the information given to write an equation of the vircle.
Answer:
Step-by-step explanation:
Left hand side.
The left hand side is the general equation that includes the center of the circle.
The center is at -10,-4
(x + 10)^2 + (y + 4)^2 = r^2
Finding the radius.
the radius is found from the given point on the circle
Givens
x1 = -10
x2 = 4
y1 = - 4
y2 = - 2
Equation
r^2 = (y2 - y1)^2 + (x2 - x1)
r^2 = (-2 - - 4)^2 + (4 - - 10)^2
r^2 = 2^2 + 14^2
r^2 = 200
Note:
The graph below shows two things: the first is that the center is at -10,-4The second is that the radius is a little more than 14. The equation of a circle always expresses the radius as r^2What is a function
Answer:
In mathematics, a function is a binary relation between two sets that associates to each element of the first set exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers
Step-by-step explanation:
Events A and B are mutually exclusive. P(A) = 0.9 and P(B) = 0.1. Find P(AUB) to one decimal place. P(AUB) =
Since events A and B are mutually exclusive, they cannot occur together. Therefore, the probability of the union of events A and B is equal to the sum of their individual probabilities. P(AUB) = P(A) + P(B) - P(A ∩ B) Where, P(A) = 0.9P(B) = 0.1Since the events are mutually exclusive, P(A ∩ B) = 0Thus,P(AUB) = P(A) + P(B) - P(A ∩ B)= 0.9 + 0.1 - 0= 1 Hence, the value of P(AUB) is 1.
The most common method for distinguishing between integers and non-integers is the decimal numeral system. It is the expansion to non-number quantities of the Hindu-Arabic numeral framework. Decimal notation is the method used to represent numbers in the decimal system.
Decimal spots are places of the digits to one side of a decimal point. The process of reducing a decimal number to a specified degree of accuracy is known as rounding. To do this we find the decimal spot we wish to adjust to and check out at the digit to one side of that number.
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please help, tysm if you do
Answer: It’s 3
Step-by-step explanation:
Hoped I help :)
I need help thank you
Answer: 4x-3
Step-by-step explanation: use the slope formula to calculate the slope, then add the y-int to the equation and ur done hope this helps
At a high school soccer league, each team has m players. There are 20 teams in
the league. Write the expression of the total number of players at the league.
Answer:
20m
Step-by-step explanation:
Given:
Number of players per team = m
Number of teams in the league = 20
The number of players in the league is the product of the number of payers in each team and the number of teams in the league.
This the expression to obtain the total number of players goes thus :
Total number of players in the league = 20 * m
Total Numbr of players in the league = 20m
A rectangle has a length of 2x + 1 and a width
of 5x - 4. Which expression best describes the
area of the rectangle?
F 7x - 3
H 10x2 – 3x - 4
J 10x2 + 13x - 4
G 14x - 6
Answer:
H
Step-by-step explanation:
The rectangle has a length of (2x + 1) and a width of (5x - 4).
And we want to select the expression that represents the rectangle's area.
Recall that a rectangle's area is simply its length multiplied by its width. Thus:
[tex]A=(2x+1)(5x-4)[/tex]
Expand by distributing:
[tex]A=(2x+1)(5x)+(2x+1)(-4)[/tex]
Distribute:
[tex]A=(10x^2+5x)+(-8x-4)[/tex]
Simplify:
[tex]A=10x^2-3x-4[/tex]
Hence, our answer is H.
How many four-digit numbers ABCD have the property that ABCDis equal 26 times BCD?
Note that x1x2...xn represents the n-digit number with digits x1x2...xn.
9514 1404 393
Answer:
9
Step-by-step explanation:
There are 9 such numbers:
1040, 2080, 3120, 4160, 5200, 6240, 7280, 8320, 9360
_____
For each ABCD, where BCD = x, we want ...
26x = 1000A +x
25x = 1000A
x = 40A
The digit A ranges from 1 to 9 for a 4-digit number. That means there are 9 such numbers. For A=1, for example, x = 40·1 = 40, so the number ABCD is 1040. 26·BCD = 26·040 = 1040 as required.
Answer:
9 is correct but if you are here from caribou math it is 7
Step-by-step explanation:
don't dislike what they said because it is the right formula. 25x = 1000A
you get 1040 2080 3120 4160 5200 6240 7280 8320 9360. But since caribou asks for bcd, b > 0 because its a 3 digit number. from that we can eliminate 1040 and 2080 getting 7
[x-2]/4=[3x-7]/10 its x-2 dived by 4 not 2/4 same with other side
Answer:
x = 4
Step-by-step explanation:
Given
[tex]\frac{x-2}{4}[/tex] = [tex]\frac{3x-7}{10}[/tex] ( cross- multiply )
4(3x - 7) = 10(x - 2) ← distribute parenthesis on both sides )
12x - 28 = 10x - 20 ( subtract 10x from both sides )
2x - 28 = - 20 ( add 28 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
Let w = { 9:,ber) with the standard operations in M22. Which of the following statements is true? W is not a subspace of Mzxz because it does not contain the zero matrix the above is true The 2x2 identity matrix is in W W is a subspace of M2x2. the above is true None of the mentioned
The correct statement is : W is a subspace of M2x2.
TO show that W is a subspace of M2x2, we need to verify that it satisfies the three properties of a subspace:
1. W contains the zero matrix:
The zero matrix in M2x2 is the 2x2 matrix with all entries equal to zero, which is not in W . However , we can see that the matrix {0,0;0,0} can be obtained as the difference between two matrices in W: {9,0;0,0} -{0,ber;0,0} = {0,0;0,0}. So , W does contain the zero matrix.
2. W is closed under addition:
Let A and B be two matrices in W. Then, A ={9,0;0,0} + {0,ber;0,0} and B = {9,0;0,0} + {0,ber;0,0}, which is also in W. Therefore, W is closed under addition.
3. W is closed under scalar multiplication:
Let A be a matrix in W and c be a scalar. Then ,A = {9,0;0,0} + {0,ber;0,0}, and c A = c {9,0;0,0} + c{0,ber;0,0}.
Since {9,0;0,0} and {0,ber;0,0} are both scalar multiples of A, c {9,0;0,0} and c{0,ber;0,0} are also in W . Therefore , W is closed under scalar multiplication.
Since W satisfies all three properties of a subspace, we can conclude that W is a subspace of M2x2.
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If 3 inches represents 25 feet on a scale
drawing, how long will a line segment be
that represents 15 feet?
Answer:
1.8 inches
Step-by-step explanation:
1. find the # of inches that represents 1 foot.
3/25 = 0.12in
2. to find the length of the line segment that represents 15 feet, multiply 0.12 inches by 15.
0.12*15 = 1.8in
HELP!!! 100 POINTS!!! Find the total surface area of a cylinder with a height of 7 cm and radius of 3 cm. Leave your answer in terms of π.
140π cm2
91π cm2
60π cm2
51π cm2
Just put the answer below for brainly.
The surface area of the cylinder is 60π cm².
What is the surface area of a cylinder?
The surface area of a cylinder indicates the total area of two plane surfaces (bases) and one curved surface.
If a cylinder has a radius of r cm and height of h cm, then the total surface area of the cylinder = 2πr(r + h)
Given, r = 3 cm and h = 7 cm.
Therefore, the total surface area of the cylinder
= 2πr(r + h)
= 2π × 3(3 + 7) cm²
= 2π × 3 × 10 cm²
= 60π cm²
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Answer:
C. 60π cm2
Step-by-step explanation:
PLSSS HELP!!!! in need of help immediately! (check whole picture) and pls don’t leave a link.
Answer: C!!!!!!!
Step-by-step explanation:
Decomposers ( however you spell it ) are things that eat and uhh remove the waste and let other decompopers eat they waste
PLEASE HELP ASAP!! WILL GIVE BRANLIEST!!!
Answer:
Brand A
Step-by-step explanation:
The volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )
Brand A
V = [tex]\frac{1}{3}[/tex]π × 6² × 15 = [tex]\frac{1}{3}[/tex]π × 36 × 15 = π × 12 × 15 = 180π in³
Brand B
V = [tex]\frac{1}{3}[/tex]π × 5² × 18 = π × 25 × 6 = 150π in³
Brand A have the largest volume
A pool has a length that is 3 times the width. Write the algebra radical value of the corner to corner distance
Answer:
The distance between corner to corner is equal to √10 times the width.
D = √10*W
Step-by-step explanation:
For a rectangle of length L and width W, the distance between two opposite corners can be calculated if we use the Pythagorean's theorem, where we can think on the length as one cathetus, the width as another cathetus and the diagonal as the hypotenuse.
Then the length of the diagonal is:
D^2 = L^2 + W^2
D = √( L^2 + W^2)
In this case we know that the length is 3 times the width, then:
L = 3*W
Replacing this in the equation for the diagonal we have:
D = √( (3*W)^2 + W^2) = √( 9*W^2 + W^2)
D = √( 10*W^2) = √10*√W^2 = √10*W
D = √10*W
The distance between corner to corner is equal to √10 times the width.
20. Solve for x,
(x-2y) = 12
P
mathemat
I
vision oro
How do you do this?
Answer:
x= 24 and y = 6
Step-by-step explanation:
I think that the right answer
Plz help ASAP !!!!!!!! Plzz
Answer:
option a is the answer to the question
Now consider the so-called random walk with absorbing barriers on 1 = {0, 1, 2, 3, 4}. This is also a Markov chain on N = {0,1,2,3,4} with the following transition probability matrix P =
[1 0 0 0 0]
[1/2 0 1/2 0 0]
[0 1/2 0 1/2 0]
[0 0 1/2 0 1/2]
[0 0 0 0 1]
(a) Draw a graphical diagram that shows how this chain moves. (b) Is this chain irreducible? Why or why not? (c) Find E(X5 | X3 = 1, X0 = 2).
The random walk with absorbing barriers on the set {0, 1, 2, 3, 4} can be represented as a Markov chain with a transition probability matrix. This chain is irreducible since it is possible to reach any state from any other state. By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.
(a) The graphical diagram representing the random walk with absorbing barriers on {0, 1, 2, 3, 4} can be visualized as a directed graph. Each state is represented by a node, and the arrows indicate the transition probabilities between states according to the given transition probability matrix P.
(b) The chain is irreducible because it is possible to reach any state from any other state. Starting from any state, there is always a positive probability of transitioning to any other state, including the absorbing states (0 and 4). This means that the chain does not have any disjoint subsets of states that are unreachable from one another.
(c) To find E(X5 | X3 = 1, X0 = 2), we condition on the starting state X0 = 2 and the state at time step 3, X3 = 1. Given this condition, we can calculate the expected value of X5, which represents the expected state at time step 5.
To compute this expectation, we can use the Markov property, which states that the future behavior of the chain depends only on its current state. Since X3 = 1 is known, we only need to consider the possible transitions from state 1 to other states according to the transition probability matrix P. By following these transitions, we can calculate the probability of reaching each state at time step 5 and then compute the expected value of X5 accordingly.
By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.
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HELP MEEE
Review
Question 11 of 40
11 Which ordered pairs are solutions to the inequality graphed in the coordinate plane?
Select all that apply.
A(-3, -8)
B
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Answer:
this is hard to tell and sorry if I'm wrong but I would say it is only a
Step-by-step explanation:
Aanything in the shaded area is correct if it's not it's wrong
Janna is buying a netbook with a flash drive. The total cost c will include the price p of the netbook plus $12.50 for the flashdrive. Which is the dependent variable?
Han and Andre were comparing the miles they ran during one week of cross country practice Hantan 12 which was three times as much as Andre
How many they run together during the one week
Answer:
I don't know.
Step-by-step explanation:
A brand of uncooked spaghetti comes in a box that is a rectangular prism with a length of 9 inches, a width of 2 inches, and a height of 1 1/2 inches. What is the surface area of the box?
Answer:
SA = 157 in²Steps:
SA = 2LW + 2WH + 2LH
SA = 2(9×2) + 2(2×11/2) + 2(9×11/2)
SA = 2×18 + 2×22/2 + 2×99/2
SA = 36 + 22 + 99
SA = 157 in²
Help wit this? 10m-8m+2+10
Answer:
2m+12
Step-by-step explanation:
add like terms
2m+12
Ruth read a total of 14 books over 7 months. After belonging to the book
club for 10 months, how many books will Ruth have read in all? Assume
the relationship is directly proportional.
Answer:
20 books
Step-by-step explanation:
Well 14 books in 7 months.
Find the unit rate
14/7=2
So 2 books each month
We have Ruth here that was in the book club for 10 months.
And since 2 books each month,
2*10=20
20 books
Two boys want to balance a seesaw perfectly. One boy weighs 240 pounds and is sitting four feet from the fulcrum. The other boy weighs 160 pounds. Where should the lighter boy sit to balance the seesaw?
Answer:
Step-by-step explanation:
Two boys want to balance a seesaw perfectly. One boy weighs 240 pounds and is sitting four feet from the fulcrum. The other boy weighs 160 pounds. Where should the lighter boy sit to balance the seesaw?
We solve using the formula
Distance on the fulcrum × Weight of the boy
= 4 × 240 = x × 160
4 × 240 = 160x
x = 4 × 240/169
You measure a wound to be 2.5 inches long. How many millimetres long is the wound? Round to the nearest tenth.
You measure the depth of a wound to be 0.25 inches. How many millimetres is this? Round to the nearest whole number.
(a) If you measure a wound to be 2.5 inches long, the corresponding length in millimeters is 63.5 mm.
(b) If you measure the depth of a wound to be 0.25 inches, the corresponding length in millimeters is 6.35 mm.
What is the measure of the lengths?If you measure a wound to be 2.5 inches long, the corresponding length in millimeters is calculated as follows;
1 in = 25.4 mm
2.5 in = ?
? = 2.5 x 25.4 mm
? = 63.5 mm
If you measure the depth of a wound to be 0.25 inches, the corresponding length in millimeters is calculated as follows;
1 in = 25.4 mm
0.25 in = ?
? = 0.25 x 25.4 mm
? = 6.35 mm
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What is the value of x in this equation?
2x + 2 = -52
pls someone help
Answer: x= −27 or x = 27
Step-by-step explanation:
Answer:
-27
Step-by-step explanation:
Subtract 2 from both sides
2x= -54
Divide both sides by 2
x = -27
ASAP. If a central angle has a measure of 100 degrees, determine the approximate length of the arc created by the two radii measuring 4 inches. Convert your answer to radians. Round your answer to two decimal places.
Answer:
234.9 million km
Step-by-step explanation:
The central angle is a quarter of a circle: 360° / 4 = 90°. Use the central angle calculator to find arc length. You can try the final calculation yourself by rearranging the formula as: L = θ * r. Then convert the central angle into radians: 90° = 1.57 rad, and solve the equation: L = 1.57 * 149.6 million km. L = 234.9 million km.
Evaluate 3f(2) what is it
Answer:
the eanswer should be 12
Step-by-step explanation:
i took the test
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Answer:
Step-by-step explanation:
To find each probability you will state the probability of the first event happening and multiply it by the chance of the second event happening.
P(2 Nickels): 6/10 x 5/9 = 30/90 (1/3 chance)
P(2 Dimes): 4/10 x 3/9 = 12/90 (4/30 chance)
P(1 nickel and 1 dime): 6/10 x 4/9 = 24/90 (8/30 chance)
I hope this helps :D