3 years ago

Write 2 expressions for the perimeter

Mathematics

1 answer:

Rainbow [258]3 years ago

8 0

Answer:

With brackets

(t + 9) + (t + 9) + (t + 9) + (t + 9)

4(t + 9)

Without brackets

4t + 36

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Let r3 have the euclidean inner product. let u = (-1, 1, 1) and v = (-7, 6, 15). if ||ku + v||= 7, what is k? give the exact ans

amm1812

Ma $k\mathbf u+\mathbf v=k(-1,1,1)+(-7,6,15)=(-k-7,k+6,k+15)$

Recall that for a vector $\mathbf x\in\mathbb R^n$ , we have $\|\mathbf x\|=\sqrt{\mathbf x\cdot\mathbf x}$ . So we have

$\|k\mathbf u+\mathbf v\|=\sqrt{(k\mathbf u+\mathbf v)(k\mathbf u+\mathbf v)}=7$
$\implies k^2\mathbf u\cdot\mathbf u+2k\mathbf u\cdot\mathbf v+\mathbf v\cdot\mathbf v=49$
$\implies3k^2+56k+261=0$
$\implies k=-9,-\dfrac{29}3$