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3 years ago

11

Jorge bought 16 apples for $8.00.

1 answer:

dem82 [27]3 years ago

7 0

Answer:

x=16

y=8.00

8/16=0.5 (50 cents per apple)

y=0.5x+0

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Louis built a swimming pool. The depth of the swimming pool is 5 feet. What is the volume of water that it will take to fill the

julia-pushkina [17]

Answer:

For a rectangular prism-like swimming pool: $V = w\cdot l \cdot h$ . $V = 360\,ft^{3}$ when $h = 5\,ft$ , $l = 12\,ft$ and $w = 6\,ft$ .

Step-by-step explanation:

Let assume that swimming pool has a rectangular base and depth is the same at any point at the bottom. In addition, let $w$ and $l$ be the width and length of the swimming pool. Then, the volume needed to fill the swimming pool is:

$V = w\cdot l \cdot h$ , where $h$ is the depth of the pool.

Let be $h = 5\,ft$ , $l = 12\,ft$ and $w = 6\,ft$ . The volume of the swimming pool is:

$V = (6\,ft)\cdot (12\,ft)\cdot (5\,ft)$

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3 years ago

Find a parametric representation for the part of the cylinder y2 + z2 = 49 that lies between the planes x = 0 and x = 1. x = u y

sweet-ann [11.9K]

Answer:

The equation for z for the parametric representation is $z = 7 \sin (v)$ and the interval for u is $0\le u\le 1$ .

Step-by-step explanation:

You have the full question but due lack of spacing it looks incomplete, thus the full question with spacing is:

Find a parametric representation for the part of the cylinder $y^2+z^2 = 49$ , that lies between the places x = 0 and x = 1.

$x=u\\ y= 7 \cos(v)\\z=? \\ 0\le v\le 2\pi \\ ?\le u\le ?$

Thus the goal of the exercise is to complete the parameterization and find the equation for z and complete the interval for u

Interval for u

Since x goes from 0 to 1, and if x = u, we can write the interval as

$0\le u\le 1$

Equation for z.

Replacing the given equation for the parameterization $y = 7 \cos(v)$ on the given equation for the cylinder give us

$(7 \cos(v))^2 +z^2 = 49 \\ 49 \cos^2 (v)+z^2 = 49$

Solving for z, by moving $49 \cos^2 (v)$ to the other side

$z^2 = 49-49 \cos^2 (v)$

Factoring

$z^2 = 49(1- \cos^2 (v))$

So then we can apply Pythagorean Theorem:

$\sin^2(v)+\cos^2(v) =1$

And solving for sine from the theorem.

$\sin^2(v) = 1-\cos^2(v)$

Thus replacing on the exercise we get

$z^2 = 49\sin^2 (v)$

So we can take the square root of both sides and we get

$z = 7 \sin (v)$

4 0

3 years ago