The height of a rectangle is increasing at a rate of 11 centimeters per hour and the width of the rectangle is decreasing at a rate of 9 centimeters per hour. At a certain instant, the height is 3 centimeters and the width is 8 centimeters. What is the rate of change of change of the area of the rectangle at that instant?

-39 cm²/h

Step-by-step explanation:

The area of the rectangle is A = hw where h = height and w = width.

So the rate of change of area with respect to time is

dA/dt = d(hw)/dt

dA/dt = hdw/dt + wdh/dt

Given that at an instant h = 3cm, w = 8 cm and dh/dt = + 11 cm/h and dw/dt = -9 cm/h(negative since it is decreasing)

So, dA/dt = hdw/dt + wdh/dt

dA/dt = 3 cm × (+11 cm/h) + 8 cm × (-9 cm/h)

dA/dt = 33 cm²/h - 72 cm²/h

dA/dt = -39 cm²/h

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The answer is in the image 

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image 

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

tip=18% of 75.45

     =18/100 * 75.45 = $13.581

Tip = $13.581