(8) slope? y-intercept? (9) slope? y-intercept?

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

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.

5 0

2 years ago

Write 9,540,000 in expanded form using exponents to show powers of 10

krek1111 [17]

Answer:

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

Step-by-step explanation:

Given : 9,540,000

To find : Write 9,540,000 in expanded form using exponents to show powers of 10.

Solution : We have given 9,540,000

Here 9 is at million place 9000000

5 is at hundred thousand place = 500,000.

4 is at tens thousand place = 40,000

We expanded it as

9, 000,000 + 500,000+40,000.

In term of power of 10.

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

Therefore,

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

6 0

3 years ago

I need help pls help

Snezhnost [94]

Answer:

c.

Step-by-step explanation:

hope this helps

3 0

2 years ago

Read 2 more answers

Which of the following equations describes the graph shown above

andrey2020 [161]

Answer: D

Step-by-step explanation:

this is in y=Mx+ b form. M stands for the slope and b stands for the y intercept, or where the line intersects with the y-axis.

Going left to right, the line slopes downwards, therefore it is a negative Slope. This narrows down your answer to either a or d. the slope is -1 because you can only ever write x by itself if it means 1x. In this case it is negative so it would look like this: -x

for the y-intercept, simply look at where the line passes through the y-axis. In this case, it is positive 2.

your finished equation would be: y=-x+2

i hope this is helpful

8 0

2 years ago

In a recent baseball season, Ron was hit by pitches 21 times in 602 plate appearances during the regular season. Assume that the

ozzi

Answer:

the probability that Ron will get hit by a pitch exactly once is 36.71%

Step-by-step explanation:

The random variable X= number of times Ron is hits by pitches in 23 plate appearances follows ,a binomial distribution. Where

P(X=x) = n!/(x!*(n-x)!)*p^x*(1-p)^x

where

n= plate appearances =23

p= probability of being hit by pitches = 21/602

x= number of successes=1

then replacing values

P(X=1) = 0.3671 (36.71%)

8 0

3 years ago

(8)slope?y-intercept?(9)slope?y-intercept?​

(8)slope?y-intercept?(9)slope?y-intercept?