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Alex787 [66]
2 years ago
9

Find the volume, V, of the solid obtained by rotating the bounded region in the first quadrant enclosed by the graphs of

Mathematics
1 answer:
Delicious77 [7]2 years ago
4 0

Answer:

\frac7{15}\pi

Step-by-step explanation:

First of all, let's draw the two curves. First one (red) is a classic parabola, second (blue) is a similar curve with a tigher form. Imagine is made with paint so it's not high quality. The intersection between the two curves are easily found by solving a system of equations and are (0;0) and (1;1). At this point, the volume comes from the rotation of the shaded area, and can be obtained as difference from the rotation of the blue curve minus the red curve.

Remembering that the volume of the solid of revolution bound between y=0; y=f(x); x=a; x=b is given by \pi \int_a^b [f(x)]^2dx, in our case the volume is given by the expression

\pi [\int_0^1 (\sqrt[4]{x})^2-(x^2)^2 dx] = \pi[\int_0^1 \sqrt{x}-x^4 dx]  = \pi[\frac23x^\frac32 -\frac15 x^5 ] _0^1 = \pi (\frac23 -\frac15) = \frac7{15}\pi

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It cost $75 to rent a limo, plus $20 per hr. Write an equation to represent the total cost,c, of renting the limo for T hours.
qwelly [4]

We must create the equation from the information. Well, we know that there is a 75 dollar fee right off the top, and there is the word "plus" in the information meaning there will be adding.

1. Add the given cost plus the addition sign.

75 + ___ = ?

Now, we must find out what fills in "__." It says that it costs $20 per hour to rent the limo. However, it doesnt tell you how many hours it is being rented for, however it does say that the amount of hours is represented by T. So, fill in that information.

2. Fill in the second number.

75 + 20T = ?

Since there isn't a number to finish the second number to the equation, we know that there isn't going to be a completed answer. So, fill in the final cost with "c" as explained in the equation.

3. Write the answer.

75 + 20T = c

So, the equation to this problem is:

75 + 20T = c

Which is how to find out how much the limo costs to rent it.

5 0
3 years ago
HELPPPPPPP PLEASE !!!!!
Igoryamba

Answer:

(-1,5)

Step-by-step explanation:

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8 0
3 years ago
Evaluate the integral. (Use C for the constant of integration.) <br> cos(x) (8 + 7 sin^2(x)) dx
UNO [17]

Answer: 8 \sin x +7(\dfrac{\sin^3x}{3})+C

Step-by-step explanation:

Consider \int \cos(x) (8+7 \sin^2(x)) \, dx

Substitute  t= sinx

then dt = cos x dx

\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C

[\int x^ndx=\dfrac{x^{n+1}}{n+1}+C]

=8 \sin x +7(\dfrac{\sin^3x}{3})+C

Hence, \int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C

5 0
3 years ago
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yarga [219]

Answer:

8+8+8+8

Step-by-step explanation:

it can't be any negatives because the questions asking how many ladder rungs he climed not how far he went down. It can't be the first one cause Yan did not climb 16 rungs.

3 0
3 years ago
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