4 years ago

Suppose you have a cat and live on a busy city street. choose your most likely point of view

SAT

1 answer:

Nimfa-mama [501]4 years ago

6 0

Answer:

It is like a perspective, but from where you are at. Like if I'm at home, and I can see from the window.

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jeyben [28]

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I think D might me the answer.

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3 years ago

Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through , , and

irina1246 [14]

Let's assume a plane

$ax+by+cz=1$

with each of a, b, and c greater than 0. Then the plane has intercepts with coordinates

$y=z=0 \implies ax = 1 \implies x = \dfrac1a$

$x=z=0 \implies by = 1 \implies y = \dfrac1b$

$x=y=0 \implies cz = 1 \implies z = \dfrac1c$

The volume of the tetrahedron is then

$\displaystyle \int_0^{\frac1a} \int_0^{\frac{1-ax}b} \int_0^{\frac{1-ax-by}c} dz \, dy \, dx = \boxed{\frac1{6abc}}$

i.e. 1/6 times the product of the intercepts' non-zero coordinates

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2 years ago