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alexdok [17]
3 years ago
13

What is the area of a 20 square inch tile

Mathematics
1 answer:
Evgesh-ka [11]3 years ago
4 0
I think it's 25 in. squared
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Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant
Alex787 [66]

Find the intercepts for both planes.

Plane 1, <em>x</em> + <em>y</em> + 2<em>z</em> = 2:

y=z=0\implies x=2\implies (2,0,0)

x=z=0\implies y=2\implies(0,2,0)

x=y=0\implies 2z=2\implies z=1\implies(0,0,1)

Plane 2, 4<em>x</em> + 4<em>y</em> + <em>z</em> = 8:

y=z=0\implies4x=8\implies x=2\implies(2,0,0)

x=z=0\implies4y=8\impliesy=2\implies(0,2,0)

x=y=0\implies z=8\implies(0,0,8)

Both planes share the same <em>x</em>- and <em>y</em>-intercepts, but the second plane's <em>z</em>-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (<em>x</em>, <em>y</em>)-plane where <em>z</em> = 0, we see the bounded region projects down to the triangle in the first quadrant with legs <em>x</em> = 0, <em>y</em> = 0, and <em>x</em> + <em>y</em> = 2, or <em>y</em> = 2 - <em>x</em>.

So the volume of the region is

\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx

=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx

=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}

3 0
2 years ago
Assume that y varies directly as x.
Anon25 [30]
75/15=5
3*5=15
y would equal 15

Hope this helps :)
4 0
3 years ago
Read 2 more answers
In the United States 5 million Farmers provide food for 260 million people
ycow [4]
If I am understanding the question correctly, farmers make up .02% (rounded to the nearest hundredth, full answer is .0192307) of the population. I calculated this by dividing 5,000,000 by 260,000,000. I then moved my decimal over 2 places to the right to convert it to a percent.
6 0
3 years ago
PLEASE HELP AS SOON AS POSIBLE
Tema [17]
I believe the answer should be f-there are 3/4 times as many cups of flour as there are cups of sugar
8 0
2 years ago
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(-2,3) and slope m =9
AlladinOne [14]
So what is this about???

8 0
3 years ago
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