The area of a circle of radius r is given by and its circumference is given by C = 2πr. At a certain point in time, the radius of the circle is r = 8 inches and the area of the circle is changing at a rate of inches per second. How fast is the radius of the circle changing at this time?

the radius of the circle is changing at that time.

Step-by-step explanation:

Given:

Area of Circle

Radius

We need to find the radius of the circle changing at this time .

Solution:

To find the rate at which the radius of the circle is changing with respect to time we will apply derivative on Area of the circle.

Now we know that;

Applying derivative we get;

Now substituting the given value we get;

Hence the radius of the circle is changing at that time.

answer:  

123455421

step-by-step explanation: easy

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12