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
Which equation shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation
olchik [2.2K]

Answer: x= 1

Step-by-step explanation: solve for  x  by simplifying both sides of the equation, then isolating the variable.

7 0
3 years ago
Hi can someone pls help it’s urgenttt
SVEN [57.7K]

Step-by-step explanation:

dont stress just move onto the next question :)

6 0
3 years ago
Read 2 more answers
Please help me:(:(:(:(
motikmotik

Answer:

1. 30/14

2. -26.775

3. 0.1668

4. -44/7 which can be simplified into -6 and -2/7

5. $10.96

5 0
2 years ago
Rachel saved money to buy art supplies. She used 13 of her savings to buy brushes. She used 35 of her savings to buy paint. What
vekshin1

Given:

Rachel used \dfrac{1}{3} of her savings to buy brushes.

She used \dfrac{3}{5} of her savings to buy paint.

To find:

The fraction for remaining savings.

Solution:

Fraction that Rachel used of her savings to buy brushes and paint is

\text{Fraction for used amount}=\dfrac{1}{3}+\dfrac{3}{5}

                                    =\dfrac{5+9}{15}

                                    =\dfrac{14}{15}

Now,

\text{Fraction for remaining savings}=1-\text{Fraction for used amount}

\text{Fraction for remaining savings}=1-\dfrac{14}{15}

\text{Fraction for remaining savings}=\dfrac{1}{15}

Therefore, \dfrac{1}{15} of her savings is remaining.

6 0
2 years ago
O 14,000 16) How many zeros will be in the product of 4 x 500?*​
SVETLANKA909090 [29]

Answer:

3 zeros

Step-by-step explanation:

4*500=2000

4 0
2 years ago
Other questions:
  • Five less than twice a number is equal to one half the difference of three times the number and 13.
    9·2 answers
  • The Body for Life gym charges $15 a month membership fee and a $2 per day usage fee. What does the ordered pair (13, 41) mean?
    15·1 answer
  • A barkers is having a sale on cupcakes. At 11am the bakery has sold 123 cupcakes. By 2pm the bakery has sold 470 cupcakes. What
    15·1 answer
  • Nine more than four times a number is the same as one less than twice the number.find the number.
    6·1 answer
  • Please I need help ASAP <br> Please give me the right answer not sure what the answer is
    14·1 answer
  • How does using an angle of rotation to find the length of the arc on a circle intercepted by the angle differ
    5·1 answer
  • WILL GIVE BRAINLIEST!!
    11·2 answers
  • Please help, I don't want any links​
    9·1 answer
  • HELP AM ABOUT TO GET AND F!!!
    5·1 answer
  • Find the solutions of the quadratic equation –9x2 + 49 = 0.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!