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3 years ago

8

An author signed copies of her newest book for 57 minutes until the bookstore closed at 5:00 What time did the author begin sign

ing books?
4:03
4:57
5:03
5:57

1 answer:

maks197457 [2]3 years ago

8 0

Answer:

4:03

Step-by-step explanation:

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Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant

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Find the intercepts for both planes.

Plane 1, <em>x</em> + <em>y</em> + 2<em>z</em> = 2:

$y=z=0\implies x=2\implies (2,0,0)$

$x=z=0\implies y=2\implies(0,2,0)$

$x=y=0\implies 2z=2\implies z=1\implies(0,0,1)$

Plane 2, 4<em>x</em> + 4<em>y</em> + <em>z</em> = 8:

$y=z=0\implies4x=8\implies x=2\implies(2,0,0)$

$x=z=0\implies4y=8\impliesy=2\implies(0,2,0)$

$x=y=0\implies z=8\implies(0,0,8)$

Both planes share the same <em>x</em>- and <em>y</em>-intercepts, but the second plane's <em>z</em>-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (<em>x</em>, <em>y</em>)-plane where <em>z</em> = 0, we see the bounded region projects down to the triangle in the first quadrant with legs <em>x</em> = 0, <em>y</em> = 0, and <em>x</em> + <em>y</em> = 2, or <em>y</em> = 2 - <em>x</em>.

So the volume of the region is

$\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx$

$=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}$

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2 years ago

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Step-by-step explanation:

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Jamal has run 7 miles from point a to point b of a race. the entire race from point a to point c is 26 miles. how many

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The number of more miles he needs to run to complete the race is 19 miles.

<h3 /><h3>How to find distance in miles?</h3>

He has run 7 miles from point a to point b of a race.

The entire race from point a to point c is 26 miles.

Therefore, the number of more miles he needs to run to complete the race is as follows:

let

x = the more miles he needs to run

Hence,

x = 26 - 7

x = 19 miles

Therefore, he needs to run 19 more miles to complete the race.

learn more on distance(miles) here: brainly.com/question/9950097

#SPJ1

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