What is the answer to g(3b)=x^2-x

Find the absolute maximum and minimum values of the following function in the closed region bounded by the triangle with vertice

alukav5142 [94]

$f(x,y)=2x^2-8x+y^2-8y+2$

$f_x(x,y)=4x-8=0\implies x=2$

$f_y(x,y)=2y-8=0\implies y=4$

There is one critical point at (2, 4), but this point happens to fall on one of the boundaries of the region. We'll get to that point in a moment.

Along the boundary $x=0$ , we have

$f(0,y)=y^2-8y+2=(y-4)^2-14$

which attains a maximum value of

$f(0,4)=-14$

Along $y=44$ , we have

$f(x,44)=2x^2-8x+1586=2(x-2)^2+1578$

which attains a maximum of

$f(2,44)=1578$

Along $y=2x$ , we have

$f(x,2x)=6x^2-24x+2=6(x-2)^2-22$

which attains a maximum of

$f(2,4)=-22$

So over the given region, the absolute maximum of $f(x,y)$ is 1578 at (2, 44).

8 0

3 years ago

jose invests money in two simple interests account. he invests twice as much in an account paying 13% as he does in an account p

d1i1m1o1n [39]

Answer:

He invested altogether $900

Step-by-step explanation:

* Lets explain how to solve the problem

- Jose invests money in two simple interests account

- He invests twice as much in an account paying 13% as he does in

an account paying 5%

- That means the amount he invested in the account paying 13% is

twice the amount he invested in the account paying 5%

- He earns $93.00 in interest in one year from both accounts combined

- We need to find how much he invested in each account

- Assume that he invested $x in the account paying 5%

∵ He invested twice as much in an account paying 13% as he does in

an account paying 5%

∴ He invested $2x in the account paying 13%

- The simple interest I = PRT, where P is the money invested, R is the

rate of interest in decimal and t is the time of investment

# Account paying 13%

∵ P = 2x , R = 13/100 = 0.13 , T = 1

∴ I = 2x(0.13)(1)

∴ I = 0.26 x ⇒ (1)

# Account paying 5%

∵ P = x , R = 5/100 = 0.05 , T = 1

∴ I = x(0.05)(1)

∴ I = 0.05 x ⇒ (2)

∵ He earns $93.00 in interest in one year from both accounts

- Add (1) and (2) and equate the sum by 93.00

∴ 0.26 x + 0.05 x = 93.00

- Add like terms in the left hand side

∴ 0.31 x = 93.00

- Divide both sides by 0.31

∴ x = 300

∴ 2x = 2(300)

∴ 2x = 600

∵ x represents the amount of money invested in the account paying 5%

∴ The amount of money invested in the account of 5% is $300

∴ The amount of money invested in the account of 13% is $600

- The total amount of money he invested is the sum of the money

he invested in each account [$300 + $600 = $900]

∴ He invested altogether $900

7 0

3 years ago

The parent function f(x) = x2 is translated such that the function g(x) = –x2 + 6x – 5 represents the new function. What is true

andrew11 [14]

G(x)=-(x^2-6x+5)
=-(x-6x+9-9+5)
=-(x-3)²+4
It is reflected across the a axis, shifted 3 units to the right, shifted 4 units up, and It has an axis of symmetry at x=3

8 0

3 years ago

Read 2 more answers

A spool of ribbon holds 6.75 meters.A craft club buys 21 spools. What is the total cost if the ribbon sells for $2 per month

dangina [55]

6.75 x 21 = 141.75

141.75 x $2 = $283.50

6 0

3 years ago

Which of the following are properties of the circumcenter of a triangle? Check all that apply.

kakasveta [241]

Answer:

A) The circumcenter of a right triangle falls on the side opposite the right angle

B) The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides

D.) The circumcenter is equidistant from (Apex)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers