Find all values of the scalar k for which the two vectors are orthogonal:

u = (2,3) and v= (k+1, k-1)

Step-by-step explanation:

Two vectors are said to be orthogonal if their dot product is zero.

Dot product:

Suppose we have two vectors, a and b.

a = (1,2)

b = (2,3)

Their dot product is:

a.b = (1,2).(2,3) = 1*2 + 2*3 = 8

In this problem:

u = (2,3)

v = (k + 1, k - 1)

So

u.v = (2,3).(k + 1, k - 1) = 2(k + 1) + 3(k - 1) = 2k + 2 + 3k - 3 = 5k - 1

For the vectors to be orthogonal, the dot product has to be 0. So:

it's

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: