3 years ago

Slope-intercept equation for (0, 1)(4 ,3)

Mathematics

1 answer:

Leno4ka [110]3 years ago

5 0

y=3/4x-1

the -1 is the intercept.

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At what points does the curve r(t) = ti (4t − t2)k intersect the paraboloid z = x2 y2? (if an answer does not exist, enter dne.)

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$\mathbf r(t)=x(t)\,\mathbf i+y(t)\,\mathbf j+z(t)\,\mathbf k=t\,\mathbf i+(4t-t^2)\,\mathbf k$
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To make sure this is correct, plug in $t=0$ and $t=4$ to find out the value of $\mathbf r(t)$ , and see if these points are on the paraboloid.

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$\mathbf r(4)=4\,\mathbf i+0\,\mathbf j+(4\times4-4^2)\,\mathbf k\implies (4,0,0)$
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Both of these hold, so the answer is correct.

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