Determine an expression for dy
dx given that x = sin3
(t)andy = cos3
(t)

Answers

Answer 1

Answer:

[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]

Step-by-step explanation:

Recall that using the chain rule we can state:

[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]

and therefore solve for dy/dx as long as dx/dt is different from zero.

Then we find dy/dt  and dx/dt,

Given that

[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]

And similarly:

[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]

Therefore, dy/dx can be determined by the quotient of the expressions we just found:

[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]

now notice that we can find   [tex]cos(t) = \sqrt[3]{y}[/tex]  from the expression for y,

and   [tex]sin(t) = \sqrt[3]{x}[/tex]  from its expression for x.

Therefore dy/dx can be written in terms of x and y as:

[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]


Related Questions

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2.25
What is the value of x?
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Enter your answer in the box.
с
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Answers

3 should be it......

Eighteen cups are equally packed into 6 boxes. Two boxes of cups break. How many cups are unbroken?

Answers

Answer:12

Step-by-step explanation:

18/6=3 cups in each box

3*2=6 cups broke=2 boxes

18-6=12 cups are unbroken

You start at (0, 8). You move up 1 unit and right 3 units. Where do you end?

Answers

Answer:

1.11

Step-by-step explanation:

you will end up at (3,9)


5
Subtract 27 from 43
14
21

Answers

Answer:

-0.4522

Step-by-step explanation:

it costs 13$ for admission to amusement park, plus 1.50$ for each ride.if you have a total of 35.50 to spend, what is the greatest number of rides you can go on

Answers

Answer:

Thus, the greatest number of rides I can go on is 15 rides

Step-by-step explanation:

I have $35.50 to spend for admission plus rides in the amusement park.

Admission costs $13. That leaves me with

$35.50 - $13 = $22.50

to spend on rides.

Considering each ride costs $1.50, we can find the maximum number of rides by dividing the remaining money by the cost per ride as follows:

$22.50 / $1.50 = 15

Thus, the greatest number of rides I can go on is 15 rides

What is 0.06% written as a decimal?

Answers

Answer:

0.0006

Step-by-step explanation:

The temperature drops from 7°F to -17°F. By how much did the temperature decrease?

Answers

Answer:

24 degrees

Step-by-step explanation:

If you use 0 as kind of a benchmark it is really useful, frist you subtract 7, because it is our positive number., then you subtract 17 from 0, making -17.

7+17=24

7 degree F minus -17 degree F
Is 24 degree F

True of False:the following polynomial is written in standard form
2x^4-x^3+5x^2+x-7

Answers

The following polynomial is not written in standard form so it is false

A theater sold 1,802 tickets for
their Saturday evening
performance. This was 635 more
than the number of tickets sold
for the matinee performance. If
tickets cost $75 each, find the
total ticket sales for two
performances.

Answers

Answer:

the answer would be 2,969 also i think the cost of tickets is pretty useless

Step-by-step explanation:

Answer:2,969

Step-by-step explanation:

Step 1:Choose the lowest common denominator

Find the sum of 1/5 and 7/10

The expression written in equation from with common denominator is______

The sum is___​

Answers

Answer:

-6/8 +5/8 and -1/8

Step-by-step explanation:

just got done doing it.

There are 24 female performers in a dance recital. The ratio of men to women is 7:8. How many men are in the dance recital?

Answers

I need help to I’m struggling at math

11. Find the product of (4x-5) and (2x+7) in simplest form.

Answers

8x^2 + 18x - 35


(4x - 5)(2x + 7)

8x^2 + 28x - 10x - 35

8x^2 + 18x - 35

Please find measure of angle s. PLEASE HELP FAST!!

Answers

Answer:

27

Step-by-step explanation:

15x-31 = 9x+11

6x-31 = 11

6x = 42

x = 7

15x -31 + 9x + 11 + s = 180

15(7) -31 + 9(7) + 11  + s = 180

105 - 31 + 63 + 11 + s = 180

153 + s = 180

s = 27

Which equation has the correct sign on the product?
A 45(-4)=180 B 13•3= -39
C (-8)(-8)= -64 D (-18)4 = -72​

Answers

answer:

the answer is a

Answer is D because (-18)4 equals -72.... it’s right.

Solve the following​

Answers

Answer:

Q1

|a-b| = b-a when a<b

Q2

104159/33000

Step-by-step explanation:

Q1

If a<b then a-b will always be negative.  To get the absolute value, we can take -(a-b) = -a+b = b-a.

Q2

Let x = 3.12789789789...

We isolate the repeating decimal to start after the decimal, so we multiply by 100.

100x = 312.789789789...

We want to multiply by 10 for each digit that repeats (in this case 3), to get the repeating part to the left of the decimal.

100000x = 312789.789789

Subtracting the two...

x(100000-100) = 312789.789789 - 312.789789

99900x = 312477

x = 312477/99000 = 104159/33000

What is a mutual fund’s

Answers

A pool of money where investors buy shares and a fund manager invests them and gives the investor the return; the way that most Americans invest their money because of the ease. hope that helps!

Which ordered pair is a solution to the equation below? 3x + 2y = 10
Question 1 options:

(4, 0)

(6, -4)

(-1, 4)

Answers

Answer:

(6,-4)

Step-by-step explanation:

I have tried replacing each option with x, y in the equation.

Let's replace (6, -4) with x and y

3x+2y=10

3(6)+2(-4)=10

3(6)= 18 2(-4)= -8

18+(-8)=10

in other words:

18-8=10

The statement is true, so the correct answer is:

(6, -4)

These reverse processes are both part of

Answers

Answer:

you forgot the picture

Step-by-step explanation:

Please put a picture

romona has $800 in her bank account

Answers

Um not sure what you're asking for bud you didn't finish.

Answer:

Okay?????? I don't think you finished

select all equations that are equivalent to 5x+(x+6)+3x

Answers

Whoops! It looks like your question was not part of an academic assignment. Since Brainly is only intended for homework questions, we had to remove it. Please keep the question feed clear of personal questions so other users can get the help they need. Thanks! ߷

Danny bought 8 rolls of paper towels. He has 204.8 meters of paper towels in all. How many meters of paper towels are on each roll? A) 21.52 B) 25.12 C) 25.60 D) 26.52​

Answers

Answer:C) 25.60

Step-by-step explanation:204.8÷8=25.60

Answer:

:C) 25.60

Step-by-step explanation:

.
Determine the value of each of the following expressions

a.
25+310


b.
56−13


c.
45×78


d.
67÷34

Answers

a. 515
b. 43
c. 3510
d. 1.9705

#13 Easton is planning on buying a new pair of cowboy boots. When he
went to Eastern Outfitters last week they costs $60 on the black Friday
sale. This week, they aren't on sale anymore and they cost $85. What is the
percent of change on the boots? *
O 25%
O 45%
O 55%
75%

Answers

It will be 25%

Step-by-step explanation:

22. Find the slope and Y intercept of the line 3x+4y-9=0​

Answers

hi there! here's my answer for you...

Answer:

slope:

m = -3/4

y-intercept:

y = −3x/4 + 9/4

hope this helped. have a good one!

If 1 inch represents 10 miles on a map then how many inches will represent 120 miles ?

Answers

Answer:

12 inches

Step-by-step explanation:

We can write this as a proportion:

inches/miles = inches/miles

1/10 = x/120

Solving for x, we get 12 inches.


Find 2 consecutive positive odd integers such that 4 times the larger is 29 more
than three times the smaller?

Answers

Answer:

21 and 23

Step-by-step explanation:

Two integers are:

x  and x + 2

The equation and solution:

4(x + 2) = 3x + 294x + 8 = 3x + 294x - 3x = 29 - 8x = 21

And

x + 2 = 23

simplify (3x+2) (y-2) - (7y+3) (y-3)

Answers

Answer:

3 x y − 7 y 2 − 6 x + 20 y + 5

Step-by-step explanation:

Lara created a 15-pound platter of three different types of cookies for a banquet. The peanut butter cookies sell for $2 per pound, the sugar cookies sell for $3 and the chocolate chip cookies sell for $3.60 per pound. The entire platter is worth $40. The quantity of peanut butter cookies was 3 more than chocolate chips. How many pounds of each cookie was there. Answered with a chart.

Answers

Answer:

i need a bad bleep

Step-by-step explanation:

addison rae

Which of the following equations demonstrates the Identity Property of One? A. 3 - 2 = 1 B. 4 • 1 = 14 C. 1 • b = b D. 0 + 1 = 1

Answers

Answer: C

The identity property of 1 is that any number multiplied but it remains the same.

Hence

1 x b = b

a leaky faucet is losing water and it is filling a 5 gallon bucket every 12 hours. At the rate, how many gallons of water will the faucet leak 48 hours

Answers

Answer:

20 gallons

Step-by-step explanation:

First start off by dividing 48 by 12 to see how many times 12 goes into 48.

48 / 12 = 4

now that you know that 12 goes into 48 4 times, multiply 4 by 5 to see how many gallons the leaky faucet will fill in 48 hours.

4 x 5 = 20

therefore the answer is 20 gallons

I hope this helps ^^

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