If A=kr² and V=kr³, find the percentage increase in A and V if r is increased by 20%

The percentage increase in A is 44%. The percentage increase in V is 72.8%.

Step-by-step explanation:

The easiest way to go about solving this problem is to pick your own numbers and plug them into the given equations.

For example, let's say that k = 5 and that r = 10.

 ⇒

⇒

The question is asking, what is the percentage increase if r is increased by 20%. Our chosen k-value will stay the same but our r-value is going to increase. To find the new value of r, we multiply 10, our current value of r, by 1.2. This gives us a new value for r, which is 12.

Now, we are going to plug in our new r-value and our k-value into the given equations. k = 5; new r = 12

⇒

⇒

Next, we have to calculate the percentage increase in our values of A and V. To do this, we use the following formula:

Percentage Increase for A

Initial value: 500

Final Value: 720

Percentage Increase for V

Initial value: 5000

Final Value: 8640

The percentage increase for A is 44% and the percentage increase for V is 72.8%.

Hope this helps!

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

the answer is c.

step-by-step explanation: