Write a System of Linear Inequalities

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

pychu [463]

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 $t=\frac{3\pi}{2}$

7 0

2 years ago

PLEASE HELP ME SEE IF MY ANSWERS ARE CORRECT!!!!!!!

Lena [83]

So first one
'how many solutions does 2x-y=-5 and 2x+y=5 have?'
add and get
2x-y-5
plus
2x+y=5

equals
2x+2x+y-y=5-5
4x=0
x=0 always
solve for y
4(0)+y=5
y=5
the solution is (0,5)
only <u>ONE </u>solution

one way is to subsitute
just remember that it is in (x,y) form so
the pont (1,2) means that 1 solution is x=1 and y=2 so subsitute and find that
the first one is the answer you are correct

just look at the graph
the solution is the intersection
it seems to be at a point that is 3 units to the right and -6 units up (6 units down)
so the solution is (3,-6)
yo are corect

subsitution
y=y
therefor
the answe ris (-4,-14) if you did the math correctly

#8 is correct

# 9 is correct

# 10 the answe ris bananas=0.40 pears=0.60

the last one you got it wrong, remember to check your answer to the graph for commonsense
then answer is (-2,5) and (1,2)

8 0

2 years ago

What if the carrots were 50 cents less per pound how much Victoria pay for 8.5 pounds of carrots?

nikdorinn [45]

If you multiply 8.5 by 50 cents your answer will be 4.25

5 0

2 years ago

A sales representative for a baby food company wants to survey 300 random couples who are new parents to find out if their newbo

AleksAgata [21]

Answer:

A. Yes, because each of the two outcomes are equally likely.

Step-by-step explanation:

A sales representative for a baby food company wants to survey 300 random couples who are new parents to find out if their newborn child is a boy or a girl.

The representative uses a 1 for a girl and a 2 for a boy when running a simulation.

Yes, the simulation will be a fair representation of possible survey results.

A. Yes, because each of the two outcomes are equally likely.

5 0

2 years ago

What is the volume of a rectangle prism withe the base area of 24 and the height of 4

grandymaker [24]

Answer:

The answer to your question is Volume = 32 u³

Step-by-step explanation:

Data

The volume of a rectangular prism = ?

Area of the base = 24

height = 4

Process

1.- Write the formula to calculate the volume of a pyramid

Volume = 1/3 Area of the base x height

2.- Substitution

Volume = 1/3 (24)(4)

3.- Simplification

Volume = 96/3

4.- Result

Volume = 32 u³

5 0

2 years ago