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IrinaK [193]
3 years ago
8

*PLEASE ANSWER, MAKE SURE YOU ANSWER CORRECTLY* What dimensions would you need to measure the volume of the following prism?

Mathematics
1 answer:
Digiron [165]3 years ago
3 0

Answer:

base of the triangle, height of the triangle, height of the prism.

Step-by-step explanation:

The formula for calculating the volume of the right triangle prism above is given as base area * height of prism.

The base is a right triangle. Area of the right triangular base = ½*base*height of the triangle.

Therefore, the dimensions needed to find the volume of the prism are: "base of the triangle, height of the triangle, and height of the prism.

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20+3(7+4)+5+2(7+9)?????
lisov135 [29]

Answer:

90

Step-by-step explanation:

Be sure to use PEMDAS. Begin with parentheses, the move to multiplication, then adding.

20 + 3(7 + 4) + 5 + 2(7+9)

20 + 3(11) + 5 + 2(16)

20 + 33 + 5 + 32

You can add those final four numbers in any order you want, to get a sum of 90.

4 0
3 years ago
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Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫
Pavel [41]

The area of the ellipse E is given by

\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy

To use Green's theorem, which says

\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy

(\partial E denotes the boundary of E), we want to find M(x,y) and L(x,y) such that

\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1

and then we would simply compute the line integral. As the hint suggests, we can pick

\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1

The line integral is then

\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy

We parameterize the boundary by

\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}

with 0\le t\le2\pi. Then the integral is

\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt

=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi

###

Notice that x^{2/3}+y^{2/3}=4^{2/3} kind of resembles the equation for a circle with radius 4, x^2+y^2=4^2. We can change coordinates to what you might call "pseudo-polar":

\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}

which gives

x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}

as needed. Then with 0\le t\le2\pi, we compute the area via Green's theorem using the same setup as before:

\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt

=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt

=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt

=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt

=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt

=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi

3 0
3 years ago
Stephen and Alice are both reading the same book for a book club. Stephen reads 278 pages in 7 weeks. Alice reads 31 pages each
zhenek [66]
Answer:
8 5/7
Step-by-step explanation:
278/7 = 39 5/7
39 5/7 - 31 = 8 5/7
3 0
3 years ago
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What is the probability?
ikadub [295]
Answer: 0.04

That is four as a percent
3 0
2 years ago
How do you solve 12x =144
julia-pushkina [17]
1st. Try to make x by itself. Divide 12 on each side.
After it will look like this

x=12
8 0
3 years ago
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