Answer:
The rate of change of the volume of the cylinder at that instant = 
Step-by-step explanation:
Given:
Rate of increase of base of radius of base of cylinder = 7 mm/hr
Height of cylinder = 1.5 mm
Radius at a certain instant = 12 mm
To find rate of change of volume of cylinder at that instant.
Solution:
Let
represent radius of base of cylinder at any instant.
Rate of increase of base of radius of base of cylinder can be given as:

Volume of cylinder is given by:

Finding derivative of the Volume with respect to time.

Plugging in the values given:


Using 

(Answer)
Thus rate of change of the volume of the cylinder at that instant = 
<u>Answer</u>
C. 4 + 6
D. 3.15151515.. + 4.6
E. √64 × √25
<u>Explanation</u>
A rational number is a number that can be expressed as a quotient or a fraction. That is it can be written as a/b.
π×6 = 6π ⇒ can not be written as a rational number.
√3 + √5 ⇒ the sum of two irrational numbers can not be rational.
4 + 6 = 10. Ten is a rational number. it can be written as 10/1
3.15151515.. + 4.6 = 104/33 + 23/5
= 1279/165
√64 × √25 = 8×5=40 This can be written as 40/1
Angle of taller building Tan 45° = opposite (height of the building)/
adjacent 50 feet (distance between Kathy and the taller building
Tan 45° = 1
Height of taller building from eye level = multiplying adjacent
50 feet * Angle (Tan 45°) 1 = 50 feet opposite
Angle of smaller building Tan 38° = 0.781
Height of smaller building from eye level = Angle * adjacent
50 feet = 39.06 feet
Difference of eye level from ground is 5 feet
Taller building height is 50 + 5
Total height of taller building is 55 feet.
Smaller building height is 39.06 + 5
Total height of smaller building is 44.06 feet
<span> </span>
y = -
x + 
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = 4x + 5 is in this form with slope m - 4
Given the slope of a line m, then the slope (
) of a line perpendicular to it is
= - (1 / m ) = - 
y = -
x + c is the partial equation of the perpendicular line
to find c, substitute ( 2, 7 ) into the partial equation
7 = -
+ c ⇒ c = 
y = -
x +
← equation of perp. line