1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Natasha_Volkova [10]
3 years ago
15

The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When

Mathematics
1 answer:
atroni [7]3 years ago
8 0

Answer:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

Step-by-step explanation:

The area for a rectangle is given by the formula:

A=w\ell

Where <em>w</em> is the width and <em>l</em> is the length.

We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.

First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>

\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]

By the Product Rule:

\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w

Since we know that dl/dt = 6 and that dw/dt = 5:

\displaystyle \frac{dA}{dt}=5\ell + 6w

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

You might be interested in
I need the help ASAP, please and thank you :)
SVEN [57.7K]

Answer: Im struggling to understand this one and im in highschool my brain is melting.

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
What is the solution to the equation 6t=144
Grace [21]
Isolate the variable by dividing both sides by 6:
t=144/6=24


The solution is t=24

Good luck!
8 0
3 years ago
Read 2 more answers
What is the third term in the expansion of (x+2)^3
maw [93]

Answer:

(x+2)^3=x^3-6x^2+12x-8

Step-by-step explanation:

6 0
3 years ago
If I put a different sticker on the 30th, 50th, and 60th pages will any of the first 600 pages have all 3 stickers?
icang [17]

Answer:

so the which page that will have the 3 sticker, we must solve the least common multiple of 30, 50, 60. A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, ....

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

so the least common multiple of 30, 50 and 60 is 300. so the page that will have 3 stickers is 300th page

Step-by-step explanation:

8 0
3 years ago
Can someone simply explain how to find the area of a triangular prism ? step by step ^^;
Vika [28.1K]
The formula:
A = bh + L (s1 + s2 + s3)

A: area
b: base
h: height
L: length
s1: side 1 (cross-sectional area)
s2: side 2 (cross-sectional area)
s3: side 3 (cross-sectional area)

Here’s an example (see attached image)

A = (4 x 6) + (12 x [7 + 7 + 4])
A = (24) + (12 x 18)
A = 24 + 216
A = 240cm^2

I hope this helped? Comment if you need more explanation or anything!

8 0
2 years ago
Other questions:
  • How many hours would someone who earns $7.50 per hour have to work to earn $116.25?
    7·2 answers
  • Huang buys 3 shirts that each cost the same amount, a pair of pants that cost $12, and he pays with a $100 bill. Which expressio
    7·2 answers
  • The functions f(x) and g(x) are shown below:
    10·2 answers
  • What is 16tons what pounds
    15·2 answers
  • After listing her expenses and income, Sara realizes that her actual expenses exceed her actual income. What can Sara do to elim
    5·1 answer
  • In circle N, KL ≅ ML.<br><br> What is the measure of ?<br> 77°<br> 90°<br> 132°<br> 154°
    13·2 answers
  • The price of bottles water at the concession stand was doubled. Scott says this is 50% increase, but David says it’s a 100% incr
    6·1 answer
  • 12 ly
    10·1 answer
  • Cans of tuna cost $1.59 for 6 oz. At that rate, how much would 25 oz of tuna cost?
    15·1 answer
  • Sue has 100 dimes and quarters. If the total value of the coins is &amp;21.40, how many of each kind of coin does she have?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!