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
tamaranim1 [39]
3 years ago
8

To find the extreme values of a function​ f(x,y) on a curve xequals​x(t), yequals​y(t), treat f as a function of the single vari

able t and use the chain rule to find where​ df/dt is zero. As in any other​ single-variable case, the extreme values of f are then found among the values at the critical points​ (points where​ df/dt is zero or fails to​ exist), and endpoints of the parameter domain. Find the absolute maximum and minimum values of the following function on the given curves. Use the parametric equations xequals2 cosine t​, yequals2 sine t.
Mathematics
1 answer:
pychu [463]3 years ago
7 0

Answer:

Absolute maximum is 2  

Absolute minimum at -2

Step-by-step explanation:

The given parametric functions are:

x=2\cos t,y=2\sin t

By the chain rule:

f'(t)=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }

\frac{df}{dt} =\frac{2 \cos t}{-2\sin t} =-\cot(t)

At fixed points, f'(t)=0

\implies -\cot (t)=0

This gives t=\frac{\pi}{2} ,\frac{3\pi}{2} on 0\le t\le 2\pi

This implies that the extreme points are (2\cos \frac{\pi}{2}, 2\sin \frac{\pi}{2})=(0,2) and (2\cos \frac{3\pi}{2}, 2\sin \frac{3\pi}{2})=(0,-2)

By eliminating the parameter, we have x^2+y^2=4

This is a circle with radius 2, centered at the origin.

Hence (0,2) is an absolute maximum ,at t=\frac{\pi}{2} and (0,-2) is an absolute minimum at  t=\frac{3\pi}{2}

You might be interested in
What is a possible value for the missing term of the geometric sequence ?
lesantik [10]
50 * 3 = 150  and 150 * 3 = 450

So the answer is b 150
3 0
3 years ago
Find the point slope equation of the line using the point (6,9) and slope of 3/2
Natali [406]

Answer:

y=1.5x

Step-by-step explanation:

Use the equation y-y1=m(x-x1)

y-9=1.5(x-6)

y-9=1.5x-9

y=1.5x

8 0
3 years ago
Mrs Hom bought 44 pizzas which consist of regular size and large size pizzas to be distributed equally to 96 workers. Each regul
tino4ka555 [31]

96÷8= 12

44-12=32

12 Large Pizzas & 32 Regular Pizzas

32×6=192 slices

192÷96=2

Each worker got 1 slice of the large pizza & 2 slices of the regular pizza

5 0
3 years ago
The key idea of the transformation called a reflection is the rotating of a plane about a fixed point. true or false
Dennis_Churaev [7]

Answer: The answer is true your welcome

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
This graph represents
hram777 [196]
It is C (2, 1) I think it is because they intersect
8 0
3 years ago
Other questions:
  • a principal of $700 is invested in an account at 6% per year compounded annually what is the total amount of money in the accoun
    9·2 answers
  • A given line has the equation 10x 2y -2.What is the equation, in slope-intercept form, of the line that is parallel to the given
    12·1 answer
  • How many grams 1.5 pounds equal to?
    14·2 answers
  • Ke onda alv dame los answers
    12·1 answer
  • Using the linear equation 3x+2y=6, express y in terms of x
    6·2 answers
  • Hey how would you put this in a system equation and using the Elimination method. Thank you❤
    5·2 answers
  • Point A(−5,8) is reflected across the line y = x. What are the coordinates of A′? Show your work and explain.
    14·2 answers
  • Write the sentence as an equation. Let the variable x represent the number. Seven less than 3 times a number gives 14. The given
    12·1 answer
  • Why did Kierra get this problem marked wrong and what should correct answer be? PLS HELP ILL MARK AS BRAINLESS
    15·1 answer
  • Find the unit rate for the following. REMEMBER, UNIT RATE IS HOW MUCH IS ONE OF SOMETHING.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!