Can I get helpppp plzz...also give steps

Mathematics

2 answers:

sammy [17]2 years ago

7 0

Answer:

3 inches

Step-by-step explanation:

Volume of a hemisphere = $\frac{2}{3}$ π $r^{3}$

=> 18π = $\frac{2}{3}$ π $r^{3}$

=> 18 = $\frac{2}{3}$ $r^{3}$

=> $r^{3}$ = 18 × $\frac{3}{2}$

=> $r^{3}$ = 27

=> r = $\sqrt[3]{27}$

=> r = 3 inches

Therefore, the radius of the hemisphere in inches is 3 inches.

Hope it helps :)

Please mark my answer as the brainliest

kramer2 years ago

3 0

3 inches I really do hope that helps

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Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, proj,u

11Alexandr11 [23.1K]

Answer:

Take $b = \frac{-17}{25}(7,1)$ as the projection of u onto v and $w \frac{1}{25}(-31,217)$ as the vector such that b+w =u

Step-by-step explanation:

The formula of projection of a vector u onto a vector v is given by

$\frac{u\cdot v}{v\cdot v}v$ , where $cdot$ is the dot product between vectors.

First, let b ve the projection of u onto v. Then

$b = \frac{u\cdot v}{v\cdot v}v= \frac{-6\cdot 7+8\cdot 1}{7\cdot 7+1\cdot 1}(7,1) = \frac{-34}{50}(7,1) = \frac{-17}{25}(7,1)$

We want a vector w, that is orthogonal to b and that b+w = u. From this equation we have that w = u-b = (-6,8)-\frac{-17}{25}(7,1)= \frac{1}{25}(-31,217)[/tex]

By construction, we have that w+b=u. We need to check that they are orthogonal. To do so, the dot product between w and b must be zero. Recall that if we have vectors a,b that are orthogonal then for every non-zero escalar r,k the vector ra and kb are also orthogonal. Then, we can check if w and b are orthogonal by checking if the vectors (7,1) and (-31, 217) are orthogonal.

We have that $(7,1)\cdot(-31,217) = 7\cdot -31 + 217 \cdot 1 = -217+217 =0$ . Then this vectors are orthogonal, and thus, w and b are orthogonal.