The solution to the given initial value problem is y(t) = (1/4)(e^3t - e^2t). To solve the given initial value problem, we first find the characteristic equation associated with the homogeneous equation.
y" - 3y + 2y = 0. The characteristic equation is r^2 - 3r + 2 = 0, which can be factored as (r - 1)(r - 2) = 0. This yields two distinct roots: r1 = 1 and r2 = 2. Since the roots are distinct, the general solution to the homogeneous equation is given by h(t) = c1e^t + c2e^2t, where c1 and c2 are arbitrary constants to be determined. Applying the initial conditions y(0) = 0 and y'(0) = 0, we find that c1 = -c2 = 0.
Next, we seek a particular solution to the non-homogeneous equation y" - 3y + 2y = e^3t. Since the right-hand side is an exponential function with the same form as the characteristic equation, we assume a particular solution of the form p(t) = Ae^3t, where A is a constant to be determined.
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Find the value of x in the triangle shown below.
Marie charges $8 for a dozen of her pineapple cupcakes. She sold 23 dozen at the street fair yesterday. How much money did
Marie collect?
A) $144
B) $164
C) $184
D) $194
Help please and I’ll I’ve BRAINLIEST
Answer:
c
Step-by-step explanation:
each dozen cost $8 so do the $8 times the 23 dozen she sold to get the answer
Answer:
C)$184
Step-by-step explanation:
8 times 23=$184
plz can i get brainliest:)
Explain, using an example, why you need to multiply when converting from a larger unit to a smaller unit
Answer:
This is often called scaling in math, used in ratios, fraction, percent's etc.
Step-by-step explanation:
Answer:
You can use similar processes when converting from smaller to larger units. When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide. Here is an example..
A room needs to be painted. The room is 15 ft by 23 ft by 8 ft high. A gallon
of paint covers 250 2 and costs $28.
a. Find the number of gallons to paint the room.
b. What is the cost of painting the room if you do the work yourself?
Answer:
First we know that the room is a rectangular prism with measures:
width = W = 15ft
length = L = 23ft
height = H = 8ft
We want to paint the room (i suppose that we paint the four walls and the roof)
The area of each two of the walls the width times the height:
A = (15ft)*8ft = 120ft^2
And we have two of these walls, then the total area is:
area = 2*120ft^2 = 240ft^2
The area of each one of the other two walls is the height times the length:
A = (23ft)*8ft = 184ft^2
And we have two of these walls, then the total area is:
A = 2*184ft^2 = 368ft^2
The area of the roof is equal to the length times the width.
A = 23ft*15ft = 276ft^2
Then the total area we need to paint is:
area = 240ft^2 + 368ft^2 + 276ft^2 = 884 ft^2
a) We know that one gallon can cover 250 ft^2
Then to cover 884 ft^2 we need:
N = (884 ft^2)/(250 ft^2) = 3.536 gallons of paint
b) Knowing that each gallon costs $28, and that we need 3.536 gallons of paint to paint the room, the total cost is:
3.54*$28 = $99.008 = $99.01
Now if for some reason you only can buy paint in whole numbers, then you can not buy exactly 3.536 gallons, then you need to buy 4 gallons, and in this case, the total cost will be 4 times $28
cost = 4*$28 = $112
"
Use the non- linear shooting method with accuracy 10^-1 (stop at 2nd iteration if this accuracy is not attained earlier) to solve the boundary-value problem: y"=-yy'+y, and 1<=x<=2, y(1)=1/2,y(2) =1/3. use h =0.5.Compare your results with actual solution : y(x) =1/ (x+1).
The non-linear shooting method with an accuracy of [tex]10^{-1}[/tex] was applied to solve the boundary-value problem y" = -yy' + y. The results were compared with the actual solution y(x) = 1/(x+1).
To solve the given boundary-value problem using the shooting method, we consider the problem as an initial-value problem by introducing an initial condition for y'(1).
Then, an iterative process is performed to find the appropriate value of y'(1) that satisfies the second boundary condition at x = 2.
Starting with an initial guess for y'(1), say y'(1) = a, we integrate the differential equation y" = -yy' + y numerically over the interval 1 <= x <= 2 using a step size of h = 0.5.
The numerical integration can be done using methods such as the Runge-Kutta method.
At each iteration, we compare the computed value of y(2) with the desired boundary condition y(2) = 1/3. If the accuracy of [tex]10^{-1}[/tex] is not attained after the second iteration, the process is stopped.
If the accuracy is achieved, the solution is considered as the actual solution.By comparing the obtained numerical solution with the actual solution y(x) = 1/(x+1), we can evaluate the accuracy of the non-linear shooting method.
The difference between the two solutions can be analyzed to assess the effectiveness of the method in solving the given boundary-value problem.
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find the surface area of the part of the cone z=sqrt(x^2 y^2) that lies between the plane y=x and the cylinder y=x^2
The surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2 is sqrt(2)/6.
To find the surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2, we can use a double integral to integrate the surface area element dS over the region of interest.
First, we need to parameterize the surface in terms of two variables (u, v) such that the surface is defined by x = f(u,v), y = g(u,v), and z = h(u,v). We can use cylindrical coordinates, with x = r cos(theta), y = r sin(theta), and z = sqrt(x^2 + y^2) = r. Then, the cone is given by r = h(u,v) = u, and the region bounded by y = x and y = x^2 is given by u^2 <= v <= u.
Next, we need to compute the partial derivatives of f, g, and h with respect to u and v:
f_u = cos(theta)
f_v = -u sin(theta)
g_u = sin(theta)
g_v = u cos(theta)
h_u = 1
h_v = 0
Then, the surface area element dS can be computed using the formula:
dS = sqrt(1 + (h_u)^2 + (h_v)^2) du dv
Substituting in the partial derivatives and simplifying, we get:
dS = sqrt(2) du dv
Finally, we can set up the double integral over the region of interest and integrate dS:
surface area = ∫∫ dS = ∫[0,1]∫[u^2,u] sqrt(2) dv du
Evaluating this integral using the limits of integration gives us:
surface area = ∫[0,1] sqrt(2) (u - u^2) du
= sqrt(2) (1/2 - 1/3)
= sqrt(2)/6
Therefore, the surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2 is sqrt(2)/6.
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what is the sum of 3x4
Answer:
12
Step-by-step explanation:
3 4's
3+3+3+3=12
Hope that helps :)
What is the value of 9x^2 + 13x – 15, if x = 2
Step-by-step explanation:
Given,
[tex]9 {x}^{2} + 13x - 15[/tex]
and
[tex]x = 2[/tex]
Substitute x = 2 into expression.
[tex]9 {x}^{2} + 13x - 15 = 9( {2}^{2} ) + 13(2) - 15 \\ = 9(4) + 26 - 15 \\ = 36 + 26 - 15 \\ = 62 - 15 \\ = 47[/tex]
Answer:
9(2)×2+13(2)-15
18×2+26-15
36+11
47 is your answer ☺️☺️☺️
Which is NOT true?
A 11 = 11
B 11 = 18 - 7
C 11 + 5 = 15 + 11
D 11 + 3 = 6 + 8
Answer:
C
Step-by-step explanation:
11+5=15
15+11=26
15 does not equal 26
Answer:C 11 + 5 = 15 + 11
Step-by-step explanation:
This is the only one that is false because the left side of the equation is equal to 16 and the right side of the equation is equal to 26
We will flip a balanced coin 3 times and for each toss, record whether we get a Head or a Tail. Write all possible outcomes of this experiment to find the probability that we get exactly 2 heads. 3/8 2/3 1/8 1/3
The probability of getting exactly 2 heads when flipping a balanced coin 3 times is 3/8.
When flipping a coin, each flip has 2 possible outcomes: Head (H) or Tail (T). Since we are flipping the coin 3 times, the total number of possible outcomes is 2 × 2 × 2 = 8. To find the probability of a specific outcome, we divide the number of favorable outcomes by the total number of possible outcomes. In this case, the favorable outcomes are the 3 outcomes with exactly 2 heads, and thus the probability is 3/8.
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Find the measure of each angles:
Answer:
10. 123º
13. 65º
Step-by-step explanation:
For number 10, a straight line is equal to 180º so all we have to do is subtract 57 (the number that we're given) from 180
For number 13, vertical angles are always congruent (the same) so we know that it's 65º
Given a quaternion with rotation of 90° about the x-axis and route point (1,0,1)
Find the following:
a. Scalar part
b. i, j, k components
c. Px, Py, Pz
Given the quaternion with rotation of 90° about the x-axis and route point (1,0,1), we have to find the scalar part, i, j, k components, Px, Py, Pz.
To find the scalar part, we need to use the formula: Scalar part = cos(θ/2)Where θ is the angle of rotation, which is 90° in this case. Scalar part = cos(90°/2) = cos(45°) = 0.7071To find the i, j, k components, we use the formula: qi = sin(θ/2) * ai where ai is the unit vector in the axis of rotation. i-component = sin(90°/2) * 1 = 1j-component = 0k-component = 0Therefore, the quaternion is (0.7071, 1i, 0j, 0k)To find Px, Py, Pz, we rotate the point (1,0,1) by the given quaternion using the formula: P' = qpq-1where q is the given quaternion, and P' is the new point.
Let's first find the inverse of the quaternion.q-1 = (0.7071, -1i, 0j, 0k) (Since the scalar part remains the same, only the vector part gets negated)Now, let's substitute the values and simplify: P' = (0.7071 + 1i)(1 + 0j + 0k)(0.7071 - 1i) = (0.7071 + 1i)(0.7071 - 1i) = 1 - 0.7071iTherefore, the new point is (1, 0, -0.7071)Hence, Px = 1, Py = 0, and Pz = -0.7071.
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Determine the value of A
Answer:
A = 161°
Step-by-step explanation:
125° + 36° = 161°
hope this helps
Jason wants to create a box with the same volume as the one shown below. He wants the length to be 4 inches. What would be the measurements of the width and height?
Answer:
Width-6
height-3
I determinded the width and the height by counting how many cubic blocks there are up and down.
Step-by-step explanation:
The measurements of the width and height can 3 inches each or 1 and 9 inches.
What is volume of cuboid?The volume of the cuboid is defined as the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height. The volume of a cuboid is equal to the product of length, width and height of a cuboid.
Given data as :
Jason wants to create a box with the same volume as the one shown
To determine measurements of width and height of box
Volume of given box (cuboid) = 6 × 2 × 3
Volume of given box = 36
length to be 4 inches.
length × width × height = 36
⇒ 4 w × h = 36
⇒ w × h = 9
Now multiplication factors of 9 as
9 = 1 × 9
9 = 3 × 3
So, width and height can 3 inches each or 1 and 9 inches.
Hence, the measurements of the width and height can 3 inches each or 1 and 9 inches.
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PLSS HELPPP THIS IS DUE TONIGHT
Answer: A triangle is equal to 180 degrees.
The equation would be x+82+x-14=180.
2x+68=180
2x=112
X=56
Step-by-step explanation:
NEED THIS DONE ASAP
If P(x) = -2(1 - x)2 +5, what is the value of
P(-3)?
Answer:
P(-3) = -1
Step-by-step explanation:
So just substitute the value of x in the equation:
Value of x is (-3)
So:
P(x) = -2(1 - x)2 +5
P(-3) = -2(1-(-3)) 2 + 5
P(-3) = -2(4) 2 + 5
P(-3) = -8 + 2 + 5
P(-3) = -6 + 5
P(-3) = -1
Please help I need help and please explain
Answer:
click c
Step-by-step explanation:
and its right
Which situation CANNOT be represented by this equation? 6−7=29 6 x - 7 = 29 CLEAR CHECK Joel earns $7 $ 7 per hour to mow his aunt's lawn. If he spends $6 $ 6 on gas, how many hours, x , will he need to mow to have $29 $ 29 left? Joel mows his aunt's lawn for $6 $ 6 per hour. If he spends $7 $ 7 on gas, how many hours, x , will he need to spend mowing the lawn to have $29 $ 29 left? Joel takes 6 6 hours to mow his aunt's lawn. If he spends $7 $ 7 on gas, how much does he get paid per hour, x , to mow the lawn and still have $29 $ 29 left?
Answer:
Joel earns $7 per hour to mow his aunt's lawn. If he spends $6 on gas, how many hours, x , will he need to mow to have $ 29 left?
Step-by-step explanation:
The given equation is :
6x - 7 = 29
It is given that total hours be = x
Joel earns $7 per hour, so the total earning of Joel in x hours is = $ 7x
He spends $6 on gas, so = 7x - 6
He is left with $ 29 after spending on gas.
Therefore, the equation becomes :
7x - 6 = 29
Clearly, it can be seen that in this case, the given situation cannot be represented by the given equation, i.e. 6x - 7 = 29.
Sandra needs a new bicycle tire. Her tire has a circumference of 26π inches. What is the radius of her tire?
Answer:
it should be by mult by 10 is 816.81
Diddy Corp. Stock has a beta of 1.2, the current risk-free rate is 6 percent, and the expected return on the market is 14.50 percent. What is Diddy's cost of equity?
Answer: 16.2%
Step-by-step explanation:
You can find the cost of equity using the Capital Asset Pricing Model (CAPM).
Cost of equity = Risk free rate + Beta * (Expected return on market - Risk free rate)
= 6% + 1.2 * (14.50 - 6%)
= 6% + 10.2%
= 16.2%
Raymond takes a 28-inch by 21-inch rectangle of plywood and uses a table saw to cut from one corner of the piece of plywood to the diagonally opposite corner. Now Raymond has two equally sized triangles of plywood. What is the perimeter of each triangle?
Step-by-step explanation:
just to fit characters ...........
5. Write a function of the form f(x) = - + k with a vertical asymptote at x = -15 and a horizontal asymptote of y = -6.
What ordered pair represents the y-intercept for the function y=2^x
Answer:
(0, 1)
Step-by-step explanation:
[tex]y = {2}^{x} \\ \\ plug \: x = 0 \\ \\ y = {2}^{0} \\ \\ y = 1 \\ \\ (x, \: \: y) = (0, \: \: 1)[/tex]
PLSSS HELPPPPP
On the following number line, point C represents the integer -1. Identify the integer that each of the other letters represent.
A:
B:
D:
E:
Answer: B is 0 A is 1 D 2 E 3
Step-by-step explanation:
Answer:
a: 1
b: 0
d:2
e:3
Step-by-step explanation:
Since you already know that C is -1, you can add or subtract along the numberline by ones to get the values of each letter
Find X. Give your answer in the simplest form.
How many significant figures will there be in the answer to the following problem? You do not have to solve the problem. 3.4 • 17.05 =
Answer:
3.4 × 17.015 = 58
Step-by-step explanation:
3.4 → two non-zero digits = two sig figs
17.05 → four non-zero digits = four sig figs
- hope this helps!
Please help me with the question
90 degrees and right angle
a large population is bi modal samples of sixe 40 are drawn in a sampling distribution
The given statement mentions a large population that exhibits a bimodal distribution. Bimodal distribution means that the data has two distinct peaks or modes.
Additionally, it states that samples of size 40 are drawn from this population, resulting in a sampling distribution.
A sampling distribution refers to the distribution of a statistic, such as the mean or proportion, calculated from multiple samples drawn from the same population. In this case, samples of size 40 are drawn, which means that each sample consists of 40 observations from the population.
The statement does not provide specific details about the purpose or objective of analyzing the sampling distribution. However, studying the sampling distribution can provide valuable insights into the behavior and properties of the population. It allows researchers to make inferences about the population parameters based on the statistics calculated from the samples.
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Compute Z, corresponding to P28 for standard normal curve. 5. Random variable X is normally distributed with mean 36 and standard deviation 3. Find the 80th percentile.
The 80th percentile of the normal distribution with a mean of 36 and a standard deviation of 3 is approximately 38.52.
To compute Z corresponding to P28 for the standard normal curve, we need to find the Z-score that corresponds to a cumulative probability of 0.28. This can be done using a standard normal distribution table or a statistical software.
Using a standard normal distribution table, we can look up the cumulative probability closest to 0.28, which is 0.2794. The corresponding Z-score is approximately -0.59.
Therefore, Z corresponding to P28 for the standard normal curve is approximately -0.59.
Regarding the second part of your question, to find the 80th percentile of a normal distribution with a mean of 36 and a standard deviation of 3, we can use the Z-table or a statistical software.
The 80th percentile corresponds to a cumulative probability of 0.80. Using the Z-table or a statistical software, we can find the Z-score that corresponds to a cumulative probability of 0.80, which is approximately 0.84.
To find the actual value, we can use the formula:
Value = Mean + (Z-score * Standard Deviation)
Plugging in the values:
Value = 36 + (0.84 * 3) = 38.52
Therefore, the 80th percentile of the normal distribution with a mean of 36 and a standard deviation of 3 is approximately 38.52.
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Given are five observations collected in a regression study on two variables. Xi 2 6 9 13 20 yi 9 19 8 26 23 Develop the 95% confidence and prediction intervals when x = 7. (Round your answers to two decimal places.) confidence interval 3.73 X to 26.27 x prediction interval -11.48 X to 41.48 x
The 95% confidence interval for the response variable y, when x = 7, is calculated to be 3.73 to 26.27. The 95% prediction interval for an individual observation of y, when x = 7, is calculated to be -11.48 to 41.48.
To calculate the confidence interval, we use the formula:
[tex]\hat{y} \pm t\alpha /2 * SE(\hat{y} )[/tex]
where [tex]\hat{y}[/tex] is the predicted value of y, tα/2 is the critical value for a given level of confidence (in this case, 95%), and SE ([tex]\hat{y}[/tex]) is the standard error of the prediction.
To calculate the prediction interval, we use the formula:
[tex]\hat{y} \pm t\alpha /2 * SE(\hat{y} - y)[/tex]
where ŷ is the predicted value of y, tα/2 is the critical value for a given level of confidence (in this case, 95%), and SE [tex]( \hat{y} - y)[/tex] is the standard error of the prediction.
Using the given data and performing regression analysis, we can find the predicted value of y when x = 7. Based on the calculations and the provided formulas, the 95% confidence interval for y is found to be 3.73 to 26.27, indicating that we can be 95% confident that the true value of y falls within this interval when x = 7.
Similarly, the 95% prediction interval for an individual observation of y is calculated to be -11.48 to 41.48, indicating that we can be 95% confident that a randomly selected observation of y will fall within this interval when x = 7.
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