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
VARVARA [1.3K]
3 years ago
11

A hypothetical square grows so that the length of it's diagonals are increasing at a rate of 8 m/min. How fast is the area of th

e square increasing when the diagonals are 4m each?
Mathematics
1 answer:
guapka [62]3 years ago
5 0

Answer:

32m^{2}/min

Step-by-step explanation:

We let the length of the square be l, the diagonal be z and the area be A.

Then by Pythagoras theorem;

l^{2}+l^{2}=z^{2}\\2l^{2}=z^{2}

The are of a square of length l is given as;

A=l^{2}

Combining these two equations yields;

z^{2}=2A

A=\frac{z^{2} }{2}

Next, we have been given;

\frac{dz}{dt}=8

We are required to find;

\frac{dA}{dt} when z = 4

By chain rule;

\frac{dA}{dt}=\frac{dA}{dz}*\frac{dz}{dt}

Differentiating A=\frac{z^{2} }{2} with respect to z yields;

\frac{dA}{dz}=z

Therefore,

\frac{dA}{dt}=\frac{dA}{dz}*\frac{dz}{dt} = 8z

When z is 4m the area of the square will be increasing at a rate of;

8m/min * 4m = 32m^{2}/min

You might be interested in
The hypotenuse of a 45°-45°-90° triangle measures 7√2 units. what is the length of one leg of the triangle
Leto [7]
7 because a(one side)= 1/sqrt2 * hypotenuse (7*sqrt2) THis equals 7
8 0
3 years ago
Read 2 more answers
What is the answer A, B, C, or D
adell [148]

The answer would have to be

D


7 0
3 years ago
How many edges does a rectangle prism have?
creativ13 [48]

the answer to your question there would be 12

4 0
3 years ago
Read 2 more answers
Plss show the work<br> –4z + 8 = –2z
IceJOKER [234]

Answer:

z=-4/3

Step-by-step explanation:

8=-6z

z=-8/6

z=-4/3

4 0
2 years ago
Raleigh went to a gaming arcade for his birthday. His parents gave him $55 to spend. He purchased $14.25 in
amid [387]

Answer:

23 games

Step-by-step explanation:

40.75 divide by 1.25 comes out 23.28

8 0
3 years ago
Read 2 more answers
Other questions:
  • Find the arc length of the semicircle. Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a d
    9·1 answer
  • Can somebody please help me with 1 and 2 and explain why that’s the answer thanks
    11·1 answer
  • Prime factorization of 64 inexponential form
    14·1 answer
  • Last year there were k pies baked in the bake sale. This year, there were 187 pies baked. Using k, write an expression of the to
    13·1 answer
  • A potato chip company makes potato chips in two flavors, Regular and Salt &amp; Vinegar. Riley is a production manager for the c
    15·1 answer
  • Help me please I will really appreciate it
    8·1 answer
  • Someone pls help me I’ll give u brainliest :((((
    11·1 answer
  • A cone has a height of 5 cm, and the radius is 2 cm. Calculate the volume.
    12·2 answers
  • PLEASE HELP ASAP I WILL GIVE BRAINLIEST AND 100pts!!!!!!!!!!!!!!!!!!!!!!!!!!
    7·2 answers
  • A rectangular room has an area of 120 square feet. a. The length of the room is 15 feet. Find the perimeter of the room. The per
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!