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
marusya05 [52]
2 years ago
11

assume x and y are both differentiable functions of t. find dx/dt given x=-1 and dy/dt=8 for the relation: 4x^2+3y^3=28

Mathematics
1 answer:
melomori [17]2 years ago
6 0

Given:

x and y are both differentiable functions of t.

4x^2+3y^3=28

x=-1\text{ and }\dfrac{dy}{dt}=8

To find:

The value of \dfrac{dx}{dt}.

Solution:

We have,

4x^2+3y^3=28       ...(i)

At x=-1,

4(-1)^2+3y^3=28

4+3y^3=28

3y^3=28-4

3y^3=24

Divide both sides by 3.

y^3=8

Taking cube root on both sides.

y=2

So, y=2 at x=-1.

Differentiate (i) with respect to t.

4(2x\dfrac{dx}{dt})+3(3y^2\dfrac{dy}{dt})=0

Putting x=-1, y=2 and \dfrac{dy}{dt}=8, we get

4(2(-1)\dfrac{dx}{dt})+3(3(2)^28)=0

-8\dfrac{dx}{dt}+9(4)(8)=0

-8(\dfrac{dx}{dt}-9(4))=0

Divide both sides by -8.

\dfrac{dx}{dt}-36=0

\dfrac{dx}{dt}=36

Therefore, the value of 4x^2+3y^3=28 is 36.

You might be interested in
Mr. A is 30 years old and Mr. B is 40 years old. Calculate thier year of birth :)​
ryzh [129]
Just subtract the year we’re in now. 2021-30=1991
2021-40=1981
Mr. A- 1991
Mr. B- 1981
8 0
3 years ago
32% is about the same as 1/4, 1/3, 3/5, 3/2.
Vlad1618 [11]
1/3 I do believe because it’s really close
6 0
3 years ago
I NEED HELP WITH 2 QUESTIONSS
ryzh [129]
1. 75

2. Between 87 and 88
6 0
2 years ago
18. A rectangular tables has a
Sauron [17]
Area = 7x + 3
Perimeter = 14x + 6
8 0
2 years ago
Read 2 more answers
4/7m = 2/7( 2m+1 )<br> What is M?<br> Check Solution
aev [14]
4/7m = 2/7(2m + 1)
4/7m = 4/7m + 2/7
4/7m - 4/7m = 2/7
0 = 2/7 (incorrect)

no solution
5 0
3 years ago
Read 2 more answers
Other questions:
  • Tai used a coupon and bought a sweater for $32. The full retail price of the sweater was $40. What percent did Tai save with her
    8·1 answer
  • A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string
    5·1 answer
  • In the equation,y=5x -12, what is the slope
    5·1 answer
  • Can someone simplify this please <br><br><br> (x+6)+(3x+5)
    11·1 answer
  • 30 is what percent of 64....
    14·1 answer
  • 350 people went to movies on saturday. fewer people went to the movie on sunday. about 600 people went to the movies in all. how
    12·2 answers
  • Numbers between 231 and 239
    15·2 answers
  • 35-284+4578567-32eye
    7·2 answers
  • I need help and fast I was supposed to turn this in last week
    13·1 answer
  • What are the first three common multiples of 2 and 7
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!