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nikklg [1K]
3 years ago
8

A square with an area of 49 in2 is rotated to form a cylinder. What is the volume of the cylinder

Mathematics
1 answer:
svlad2 [7]3 years ago
8 0
<span>343 pi in^3 ; exact volume 1078 in^3 ; Approximate volume Since it's not specified, I will assume the axis of rotation will be one edge of the square. With that in mind, here's the solution. Since the shape specified is a square with an area of 49 in^2, the length of any edge will be sqrt(49) = 7 inches. Since we're rotating along one edge, we will create a cylinder with a radius of 7 inches and a height of 7 inches. The volume will be the area of a circle with a 7 inch radius multiplied by the height of the cylinder. So V = pi*h*r^2 V = pi*7*7^2 V = pi*7*49 V = pi*343 V = 343pi V = 1077.56628; approximately. So the exact volume is 343pi in^3 and an approximate volume is 1078 in^3</span>
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Step-by-step explanation:

x=90

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y=58

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58+90+z=180

148+z=180

z=180-148

z=32

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What is 10 1/12 as a decimal
cricket20 [7]

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Step-by-step explanation:

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Solve for x. Write your answer in the space below,<br><br><br> x + 5 <br> —— = 10<br> 2
Travka [436]

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Step-by-step explanation:

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Please help I don't under stand how to do this ​
stealth61 [152]
You want to figure out what the variables equal to, all of these are parallelograms meaning opposite sides and angles are equal to each other.

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Same thing can be done with the sides 124=4(4y-1), start by getting rid of the parentheses with multiplication to get 124=16y-4, this means that 16y is 4 more than 124, so how many times does 16 go into 128? 8 times, so x=11 and y=8

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6 0
2 years ago
Let y(t) be the solution to y˙=3te−y satisfying y(0)=3 . (a) Use Euler's Method with time step h=0.2 to approximate y(0.2),y(0.4
OLEGan [10]

Answer:

  • y(0.2)=3, y(0.4)=3.005974448, y(0.6)=3.017852169, y(0.8)=3.035458382, and y(1.0)=3.058523645
  • The general solution is y=\ln \left(\frac{3t^2}{2}+e^3\right)
  • The error in the approximations to y(0.2), y(0.6), and y(1):

|y(0.2)-y_{1}|=0.002982771

|y(0.6)-y_{3}|=0.008677796

|y(1)-y_{5}|=0.013499859

Step-by-step explanation:

<em>Point a:</em>

The Euler's method states that:

y_{n+1}=y_n+h \cdot f \left(t_n, y_n \right) where t_{n+1}=t_n + h

We have that h=0.2, t_{0}=0, y_{0} =3, f(t,y)=3te^{-y}

  • We need to find y(0.2) for y'=3te^{-y}, when y(0)=3, h=0.2 using the Euler's method.

So you need to:

t_{1}=t_{0}+h=0+0.2=0.2

y\left(t_{1}\right)=y\left(0.2)=y_{1}=y_{0}+h \cdot f \left(t_{0}, y_{0} \right)=3+h \cdot f \left(0, 3 \right)=

=3 + 0.2 \cdot \left(0 \right)= 3

y(0.2)=3

  • We need to find y(0.4) for y'=3te^{-y}, when y(0)=3, h=0.2 using the Euler's method.

So you need to:

t_{2}=t_{1}+h=0.2+0.2=0.4

y\left(t_{2}\right)=y\left(0.4)=y_{2}=y_{1}+h \cdot f \left(t_{1}, y_{1} \right)=3+h \cdot f \left(0.2, 3 \right)=

=3 + 0.2 \cdot \left(0.02987224102)= 3.005974448

y(0.4)=3.005974448

The Euler's Method is detailed in the following table.

<em>Point b:</em>

To find the general solution of y'=3te^{-y} you need to:

Rewrite in the form of a first order separable ODE:

e^yy'\:=3t\\e^y\cdot \frac{dy}{dt} =3t\\e^y \:dy\:=3t\:dt

Integrate each side:

\int \:e^ydy=e^y+C

\int \:3t\:dt=\frac{3t^2}{2}+C

e^y+C=\frac{3t^2}{2}+C\\e^y=\frac{3t^2}{2}+C_{1}

We know the initial condition y(0) = 3, we are going to use it to find the value of C_{1}

e^3=\frac{3\left(0\right)^2}{2}+C_1\\C_1=e^3

So we have:

e^y=\frac{3t^2}{2}+e^3

Solving for <em>y</em> we get:

\ln \left(e^y\right)=\ln \left(\frac{3t^2}{2}+e^3\right)\\y\ln \left(e\right)=\ln \left(\frac{3t^2}{2}+e^3\right)\\y=\ln \left(\frac{3t^2}{2}+e^3\right)

<em>Point c:</em>

To compute the error in the approximations y(0.2), y(0.6), and y(1) you need to:

Find the values y(0.2), y(0.6), and y(1) using y=\ln \left(\frac{3t^2}{2}+e^3\right)

y(0.2)=\ln \left(\frac{3(0.2)^2}{2}+e^3\right)=3.002982771

y(0.6)=\ln \left(\frac{3(0.6)^2}{2}+e^3\right)=3.026529965

y(1)=\ln \left(\frac{3(1)^2}{2}+e^3\right)=3.072023504

Next, where y_{1}, y_{3}, \:and \:y_{5} are from the table.

|y(0.2)-y_{1}|=|3.002982771-3|=0.002982771

|y(0.6)-y_{3}|=|3.026529965-3.017852169|=0.008677796

|y(1)-y_{5}|=|3.072023504-3.058523645|=0.013499859

3 0
3 years ago
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