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Zigmanuir [339]
3 years ago
7

Four more than three times n equals -5

Mathematics
1 answer:
Verizon [17]3 years ago
5 0
3n+4=-5

do the opposite of adding 4. this means you have to subtract 4 from 4. whatever you do to the problem, you must do to the answer. now subtract 4 from -5.

-5-4=-9

since 4-4=0, we can take 4 out of the equation. now you have:

3n=-9

now divide -9 by 3

-9/3=-3

n=-3

hope this helps :)
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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.)
Aleonysh [2.5K]
\mathbf r(t)=x(t)\,\mathbf i+y(t)\,\mathbf j+z(t)\,\mathbf k=t\,\mathbf i+(4t-t^2)\,\mathbf k
\implies \begin{cases}x(t)=t\\y(t)=0\\z(t)=4t-t^2\end{cases}

So the paraboloid is given by

z(t)=x(t)^2y(t)^2\iff 4t-t^2=0

which holds for t^2-4t=t(t-4)=0, i.e. when t=0 and t=4.

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.

\mathbf r(0)=0\,\mathbf i+0\,\mathbf j+0\,\mathbf k\implies (0,0,0)
0=0^2\times0^2

\mathbf r(4)=4\,\mathbf i+0\,\mathbf j+(4\times4-4^2)\,\mathbf k\implies (4,0,0)
0=4^2\times0^2

Both of these hold, so the answer is correct.
8 0
3 years ago
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