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svetoff [14.1K]
3 years ago
13

The height of a rectangle is increasing at a rate of 3 centimeters per hour and the width of the rectangle is decreasing at a ra

te of 4 centimeters per hour. At a certain instant, the height is 5 centimeters and the width is 9 centimeters. What is the rate of change of the area of the rectangle at that instant (in square centimeters per hour)?
Mathematics
1 answer:
n200080 [17]3 years ago
5 0

Answer:

Rate of change of the area of the rectangle at that instant = 7 cm²/hr.

Step-by-step explanation:

Area of rectangle = Height x Width

A = hw

The height of a rectangle is increasing at a rate of 3 centimeters per hour and the width of the rectangle is decreasing at a rate of 4 centimeters per hour.

\texttt{Rate of change of height = }\frac{dh}{dt}=3cm/hr\\\\\texttt{Rate of change of width = }\frac{dw}{dt}=-4cm/hr

Differentiating area with respect to time,

            \frac{dA}{dt}=h\frac{dw}{dt}+w\frac{dh}{dt}

We need to find rate of change of area when the height is 5 centimeters and the width is 9 centimeters.

          \frac{dA}{dt}=h\frac{dw}{dt}+w\frac{dh}{dt}\\\\\frac{dA}{dt}=5\times (-4)+9\times 3=-20+27=7cm^2/hr

Rate of change of the area of the rectangle at that instant = 7 cm²/hr.

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What is the quotient of 1,854/18?
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5 0
3 years ago
Help and show explanation please
Dennis_Churaev [7]
The picture can be divided into 2 same triangles and one rectangular.

The triangle areas is {1/2 *base * height}*2 (because 2 same triangles)

and you need to sum rectangular area (width * base).
The result will be area of 2 triangle +area of rectangular.
=2(1/2*base of triangle* height)+ (base of rectangular * height)
= (base of triangle* height)+(base of rectangular * height)
=(base of triangle +base of rectangular)*height

b1 is top length
b2 is bottom length, and so

Base of triangle =(b1-b2/2)
Base of rectangular =b2
Height =h
Thus A ={(b1-b2/2)+b2 }*h
A= [(b1+b2)/2]*h
8 0
1 year ago
(25 points) PLEASE HELP MY MOM AND I CANT UNDERSTAND HOW TO DO THIS, I KNOW THE ANSWERS BUT I DONT KNOW HOW TO GET IT, PLEASE HE
LuckyWell [14K]
A. Since the rectangle can hold about three of those circles on the side, the area is 5x12=60. And since it gives you have the area of the circle, multiply by 2 so it would be 8. Therefore, 8+8+60=76, so it is 76 cm in total.
B. Since the rectangle can hold about three circles on the side the area is 6x3=18. And since it gives you the area of half the circle, multiply it by 2 so it would be 4. Therefore, 4+4+18=26 cm in total.
C. Since the rectangle can hold about three circles on the side the area is 6x6=36. And since it gives you the area of half the circle, multiply it by 2 so it would be 4. Therefore, 4+4+36=44 cm in total

Finally, A. Since in the beginning you multiply 4 by 3. Therfore your answer which is 72 must be multiplied by 2. So the answer is 144.

B.Since in the beginning you multiply 2 by 3. Therfore your answer which is 26 must be multiplied by 2. So the answer is 52.

C.Since in the beginning you multiply 2 by 3. Therfore your answer which is 44 must be multiplied by 2. So the answer is 88.

In the Final analysis, A. 144 cm, B. 52 cm, and C. 88cm
8 0
3 years ago
Read 2 more answers
Find the average rate of change of the function defined by the following table
prohojiy [21]
In short, the average rate of change is plainly the slope of the set, so we can pick any two points off there, say 2, 35 and 10, 115,

\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{35})\qquad 
(\stackrel{x_2}{10}~,~\stackrel{y_2}{115})
\\\\\\
% slope  = m
slope =  m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{115-35}{10-2}\implies \cfrac{80}{8}\implies 10
4 0
3 years ago
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