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3 years ago

Lamont builds a triangular shape fence to hide his pool pump

Mathematics

1 answer:

Monica [59]3 years ago

5 0

I don't understand what you are trying to say

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Consider the force field and circle defined below.

grin007 [14]

By Green's theorem,

$\displaystyle\int_{x^2+y^2=9}\vec F(x,y)\cdot\mathrm d\vec r=\iint_D\left(\frac{\partial(xy)}{\partial x}-\frac{\partial(x^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_Dy\,\mathrm dx\,\mathrm dy$

where $C$ is the circle $x^2+y^2=9$ and $D$ is the interior of $C$ , or the disk $x^2+y^2\le1$ .

Convert to polar coordinates, taking

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta$

Then the work done by $\vec F$ on the particle is

$\displaystyle\iint_Dy\,\mathrm dx\,\mathrm dy=\int_0^{2\pi}\int_0^3(r\sin\theta)r\,\mathrm dr\,\mathrm d\theta=\left(\int_0^{2\pi}\sin\theta\,\mathrm d\theta\right)\left(\int_0^3r^2\,\mathrm dr\right)=\boxed0$

4 0

2 years ago

The figure below shows parallel lines cut by a transversal: A pair of parallel lines is shown, cut by a transversal. Angle 3 is

Leni [432]

The angles are corresponding exterior angles.

6 0

3 years ago

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Salma received a $70 gift card for a coffee store. She used it in buying some coffee that cost $7.61 per pound. After buying the

rosijanka [135]

Answer:

Step-by-step explanation:

Amount spent on coffee = 70 - 39.56 = 30.44

One pound costs 7.61, how many will cost 30.44

7.61 : 1 = 30.44 : X

7.61 = 30.44/X

X = 30.44/7.61

X = 4

7 0

2 years ago

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An object is launched at 19.6 m/s from a height of 58.8 m. The equation for the height (h) in terms of time (t) is given by h(t)

beks73 [17]

H(t) = Ho +Vot - gt^2/2

Vo = 19.6 m/s
Ho = 58.8 m
g = 9.8 m/s^2

H(t) = 58.8 + 19.6t -9.8t^2/2 = 58.8 + 19.6t - 4.9t^2

Maximun height is at the vertex of the parabole

To find the vertex, first find the roots.

58.8 + 19.6t - 4.9t^2 = 0

Divide by 4.9

12 + 4t - t^2 = 0

Change sign and reorder

t^2 - 4t -12 = 0

Factor

(t - 6)(t + 2) =0 ==> t = 6 and t = -2.

The vertex is in the mid point between both roots

Find H(t) for: t = [6 - 2]/2 =4/2 = 2

Find H(t) for t = 2

H(6) = 58.8 + 19.6(2) - 4.9(2)^2 = 78.4

Answer: the maximum height is 78.4 m

5 0

3 years ago

Find the value of the lesser root of x2 - 7x + 12 = 0.<br> A) -3 <br> B) -1 <br> C) 1 <br> D) 3

kvv77 [185]

The answer to your question is D) 3

8 0

3 years ago

Read 2 more answers