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
8_murik_8 [283]
3 years ago
14

Find the first and second derivative of the function defined by the parametric equation.

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
6 0

Answer:

Step-by-step explanation:

Given two parametric equations x(t) and y(t), the first derivative can be found using the following equation:

\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}

In this problem, x(t) = 3e and y(t) = 3^{3t} - 1. Finding the derivative of each of these functions with respect to t gives us the following:

\frac{dx}{dt} = 0

\frac{dy}{dt} = 3^{3t + 1}\log{3}

Because \frac{dx}{dt} = 0, that means the function is a vertical line and has an infinite first derivative.

You might be interested in
A rock is dropped from the edge of a 550 foot cliff. It's position above the ground at any given time (t) is modeled by the func
Gemiola [76]
S(5) = -16*(5)*2 + 550 = 390

you just replace t with 5
3 0
3 years ago
Read 2 more answers
The table includes points on a quadratic function used to model the shape of a hole for one support beam at a new building site.
erastovalidia [21]

The hole is 8 feet deep at ground level ⇒ 3rd answer

Step-by-step explanation:

The form of the quadratic function is y = ax² + bx + c, where

  • a is the coefficient of x²
  • b is the coefficient of x
  • c is the y-intercept (at x = 0)

The vertex point of the quadratic is (h , k), where h=\frac{-b}{2a}

and k is the value of y when x = h

The table:

→  x  :  -2   ,  0  ,  2

→  y  :  -6   , -8  ,  -6

∵ x represents distance from hole's center in feet

∵ y represents the depth from level ground

∴ The quadratic function is y = ax² + bx + c

∵ c is the value of y at x = 0 ⇒ y-intercept

- From the table at x = 0 ⇒ y = -8

∴ c = -8

- Substitute its value in the function model

∴ y = ax² + bx - 8

- To find the values of a and b substitute x and y in the model by

   the coordinates of the point in the table

∵ x = -2 and y = -6

∴ -6 = a(-2)² + b(-2) - 8

∴ -6 = 4a - 2b - 8

- Add 8 to both sides

∴ 2 = 4a - 2b

- Switch the two sides

∴ 4a - 2b = 2 ⇒ (1)

∵ x = 2 and y = -6

∴ -6 = a(2)² + b(2) - 8

∴ -6 = 4a + 2b - 8

- Add 8 to both sides

∴ 2 = 4a + 2b

- Switch the two sides

∴ 4a + 2b = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equations(1) and (2) to eliminate b

∵ 8a = 4

- Divide both sides by 8

∴ a = 0.5

- Substitute value of a in equation (1) or to to find b

∵ 4(0.5) + 2b = 2

∴ 2 + 2b = 2

- Subtract 2 from both sides

∴ 2b = 0

- Divide both sides by 2

∴ b = 0

Substitute the values of a and b in the function model

∴ y = 0.5x² + (0)x - 8

∴ y = 0.5x² - 8

∵ y represents the depth from level ground

∵ The vertex of the function model is (h , k)

∴ The deep of the hole at ground level is the value of k

∵ h=\frac{-b}{2a}

∴ h=\frac{-(0)}{2(0.5)}

∴ h = 0

∵ k is the value of y when x = h

- From the table at x = 0 ⇒ y = -8

∴ k = -8

- Ignore the sign (-) because the k represents the depth of the

  hole in feet

∴ The deep of the hole at ground level is 8 feet

The hole is 8 feet deep at ground level

Learn more:

You can learn more about the quadratic function in brainly.com/question/1332667

#LearnwithBrainly

4 0
3 years ago
What is the value of X?<br><br> PLEASE HELP
GREYUIT [131]

Answer:

23

Step-by-step explanation:

19=x-4

x=23

3 0
3 years ago
Randy school requires that there are two adult chaperones for every 18 students when the students go on a field trip to the muse
Viktor [21]
Use a proportion.

2 adults to 18 students is as x adults to 99 students.

2/18 = x/99

18x = 2 * 99

18x = 198

x = 11

Answer: 11 adults
8 0
3 years ago
3(4x+2)-6x=5x-5(2+x) please solve show your work do not solve for x​
pshichka [43]

Answer:

  • simplifies to 6x+6=-10
  • x = -8/3 = -2 2/3

Step-by-step explanation:

3(4x+2)-6x=5x-5(2+x)

12x +6 -6x = 5x -10 -5x . . . . . eliminate parentheses using the distributive property

6x +6 = -10 . . . . . . . . . . . . . . . collect terms

x +1 = -10/6 . . . . . . . . . . . . . . . divide by 6

x = -1 - 5/3 . . . . . . . . . . . . . . . add -1

x = -8/3 . . . . . . . . . . . . . . . . . simplify

5 0
3 years ago
Other questions:
  • Tyree bought a book for $49.62. he sold it for $52.10 what is the percent change in the price of the book
    10·2 answers
  • 3) Malik deposited $1.050 in a savings account, and it earned $241.50 in
    11·1 answer
  • What is 6/12 plus 3/12
    9·2 answers
  • 54 is 120% of what number? Explain please!
    11·2 answers
  • Amy and two of her friends eat lunch at a restaurant. Their bill, including tax, comes to $27.63. They decide to split the bill
    11·1 answer
  • Find the approximate perimeter of ABC plotted below.
    10·1 answer
  • Please help!! I'm super confused:(
    15·1 answer
  • What two numbers that multiply to -115 but add to 10
    7·1 answer
  • Please help a-e I will rate and like response. Thank u
    6·1 answer
  • 2. Lisa can buy orange juice in 0.24-liter cartons or 0.48-liter cartons. Which is closest to the
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!