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k0ka [10]
3 years ago
14

What is a word phrase for 1/2x+5

Mathematics
1 answer:
bulgar [2K]3 years ago
5 0

Answer:

One Half X plus 5

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Need help with AP CAL
anzhelika [568]

Answer: Choice C

\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)

============================================================

Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve y = e^{-x}

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is e^{-x} where 0 < x < 1

Let's compute the area of each general cross section.

\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

\displaystyle \int_{0}^{1}e^{-2x}dx\\\\

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

  • If x = 0, then u = -2x = -2(0) = 0
  • If x = 1, then u = -2x = -2(1) = -2

This means,

\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\

I used the rule that \displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx which says swapping the limits of integration will have us swap the sign out front.

--------

Furthermore,

\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

In short,

\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

This points us to choice C as the final answer.

5 0
2 years ago
write the number of digits in the square root of the 6407522209 i can't solve this question please can you hepl me​
Contact [7]

Answer:

The square root of this is 80047

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Find the value of x .
guajiro [1.7K]
Try photomath it might help
3 0
3 years ago
Read 2 more answers
Which equation would graph as a straight line? x2 – y = 0 y = x 2y = x2 y=1/2×2-1 x2 = 0
Gwar [14]

Answer:

y=1/2×2-1

Step-by-step explanation:

x2 – y = 0 yields a parabola.

y = x is straight but has a slope to make it increase/decrease.

2y = x2 yields a parabola.

x2 = 0 yields a parabola.

3 0
2 years ago
Zach is 6 inches shorter than two times his cousin’s height, c. How tall is Zach? To see what Gabriel did wrong, consider that c
irakobra [83]

Answer:

74 inches

Step-by-step explanation:

If his cousin is 40 inches tall, and Zach is 6 inches less than twice his height, solve for 40*2-6, which is 74.

3 0
2 years ago
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