The vector is first dilated by a factor of 2.5 and then rotated by radians. If the resulting vector is , then a =_ and b = _.

a = 10

b = 2.5

Step-by-step explanation:

The given vector is

<-1, 4>

Let represents <-1, 4>.

First, the dilation is done by a factor of 2.5.

If the dilation of a vector <, > is done by a factor k:

Then the resulting vector becomes:

The resulting as per above explanation:

Now, it is given that the vector is rotated by or .

The steps to find the resulting vector after the rotation of or , we can use the simple method:

Step 1:  Multiply the value with -1.

i.e. the vector now becomes <2.5, 10> (Negative sign of x value removed).

Step 2: Swap the values of and .

So, the resulting vector is:

<10, 2.5>

In other form, we can represent the above vector as:

Comparing with

a = 10

b = 2.5

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5