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2 years ago

12

The theater arts committee estimated that it would sell 200 tickets for its upcoming play. The committee actually sold 224 ticke

ts.
What was the percent error in the committee’s estimate
|--------| %

1 answer:

MA_775_DIABLO [31]2 years ago

3 0

12% error. To find out subtract the difference between the estimate and the actual amount sold and divide the difference by the estamite.

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How many 5/8s are in 3?

stira [4]

I believe it to be 4 because 3=24/8

So 5/8 + 5/8 = 10/8 + 5/8 = 15/8 + 5/8 = 20/8 + 5/8 = 25/8, which is the closest number to 3

4 0

3 years ago

Solve the following problems:<br> Find x, y

vladimir1956 [14]

Answer:

x=1.25, y=1.75

Step-by-step explanation:

The two triangles formed (one triangle with side lengths of 5, 7, 8 and another with sides 5+x, 10, and 7+y) are similar, because they share the same angle measures.

Now, 2 sides given that we can compare ratios with are the side with length 8, and the side with length 10. 10/8= 1.25, which is the ratio of the sides on these 2 triangles.

Now we want to find what the side '5+x' is equal to. To do that we can use our ratio, and multiply 5 by 1.25 to find '5+x'. This is 6.25. To find x, all we need to do is subtract 5 from 6.25, which is 1.25.

Let's find y now. Do the same thing that we did with the side '5+x'; find what '7+y' is by multiplying 7 by 1.25, which is 8.75. 8.75-7= 1.75.

Hope this helps! :)

8 0

2 years ago

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

3 years ago

Michel is building an in-ground swimming pool. it has a length of 16 feet, a width of 10 feet, and a depth of 8 feet. How many c

jonny [76]

The swimming pool is a <span>rectangular prism</span> (which means it's a 3D rectangle). To find the volume of a rectangular prism you multiply Length x Width x Height.

In this case that would mean 16*10*8 (height and depth are the same in this problem).

16*10*8=<span>1280 ft</span>³<span>
</span>

4 0

3 years ago

Is the origin a solution to the system graphed?

Neporo4naja [7]

Answer:

Step-by-step explanation:

y < - 3x

y ≥ 2x + 2

5 0

2 years ago