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3 years ago

6

A pump can fill a swimming pool in 8 hours. The pool also has a drain that can empty the pool in 10 hours. If someone turns on t

he pump to fill the pool, but forgets to shut the drain, how long would it take for the pool to fill?

1 answer:

cluponka [151]3 years ago

7 0

Answer:

40 hours will it take for the pool to fill.

Step-by-step explanation:

A pump can fill a swimming pool in 8 hours.

Work done by pump to fill in 1 hour is $\frac{1}{8}$

The pool also has a drain that can empty the pool in 10 hours.

Work done by pump to drain in 1 hour is $\frac{1}{10}$

If someone turns on the pump to fill the pool, but forgets to shut the drain.

Work done by both pipe in 1 hour is

$W=\frac{1}{8}-\frac{1}{10}$

$W=\frac{10-8}{80}$

$W=\frac{2}{80}$

$W=\frac{1}{40}$

Both pipe filled $\frac{1}{40}$ part of pool in hours = 1

Both pipe filled complete pool in hours = $\frac{1}{\frac{1}{40}}=40$

Therefore, 40 hours will it take for the pool to fill.

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Step-by-step explanation:

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The line 10x + py = q is a tangent at the point (5, 4) in another circle with centre

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Answer:

(p, q) = (8, 82)

Step-by-step explanation:

When a circle is centered at the origin, the radius to point (a, b) will have slope m = b/a. The tangent is perpendicular to the radius, so the tangent at point (a, b) will have slope -a/b. In point-slope form, the equation of the tangent line will be ...

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b(y -b) = -a(x -a)

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For (a, b) = (5, 4), the standard form equation of the tangent can be written ...

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Your given equation has an x-coefficient that is twice the value shown in this equation, so we need to multiply this equation by 2:

2(5x +4y) = 2(41)

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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

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

$z = 7 \sin (v)$

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