A rectangle has width w inches and height h, where the width is twice the height. Both w and h are functions of time, t, measured in seconds. If A represents the area of the rectangle, what is the rate of change of A with respect to t at the instant where the width is 4 inches and the height is increasing at the rate of 2 inches per second?

dA/dt = 16 square inches per second

Step-by-step explanation:

Width of rectangle is w

Height of rectangle is h

width = twice height

w = 2h

Area = wh = (2h)*h

A = 2h^2

Differentiating the equation with respect to time

dA/dt = 2+2h dh/dt

dA/dt = 4h dh/dt

According to the given situation when width is 4 inches

h = w/2

h = 2

Rate of change of A is  

dA/dt = wh dh/dt

dA/dt = 4(2)(2)

dA/dt = 16 square inches per second

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!