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A piece of rope there is 28 feet long is cut into two pieces. One is use to form a circle and others used to form a square. Write a function G representing the area of the square as a function of the radius of the circle R

Answers

Answer 1

Answer:

The function g representing the area of the square as a function of the radius of the circle r is given as:

$g(r) = 49 - 22r + (121r^2)/(49)$

Solution:

Given that,

length of rope = 28 feet

Let "c" be the circumference of circle

Let "p" be the perimeter of square

Therefore,

length of rope = circumference of circle + perimeter of square

c + p = 28 ------- eqn 1

The circumference of circle is given as:

$c = 2 \pi r$

Where, "r" is the radius of circle

Substitute the above circumference in eqn 1

$2 \pi r + p = 28$

$p = 28 - 2 \pi r$ ----------- eqn 2

If "a" is the length of each side of square, then the perimeter of sqaure is given as:

p = 4a

Substitute p = 4a in eqn 2

$4a = 28 - 2 \pi r\n\na = (28 - 2 \pi r)/(4)\n\na = 7 - ( \pi r)/(2)$

The area of square is given as:

$area = (side)^2\n\narea = a^2$

Substitute the value of "a" in above area expression

$area = (7 - ( \pi r)/(2))^2$ ------ eqn 3

We know that,

$(a - b)^2 = a^2 - 2ab + b^2$

Therefore eqn 3 becomes,

$area = 7^2 -2(7)((\pi r)/(2)) + (( \pi r)/(2))^2\n\narea = 49 - 7 \pi r + ( (\pi)^2 r^2 )/(4)$

$\text{ substitute } \pi = (22)/(7)$

$area = 49 - 7 * (22)/(7) * r + ((22)/(7))^2 * (r^2 )/(4)\n\narea = 49 - 22r + (121)/(49) * r^2\n\narea = 49 - 22r + (121r^2)/(49)$

Let g(r) represent the area of the square as a function of the radius of the circle r, then we get

$g(r) = 49 - 22r + (121r^2)/(49)$

Thus the function is found

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Solve the equation
log4x=2

Answers

Change it to exponential form:

log₄(x) = 2 ⇒ 4² = x = 16

Final answer: 16

Help me with this question pleasereee

Answers

Answer:

b=43 i think

Step-by-step explanation:

If this is a 1 attempt thing do not trust me but just know that is 180 degrees so a+b+c=180 will be your formula

Use cubic regression to find afunction that fits the following
points.
(1,-1), (2,-13), (3,-45),(-1,11)
y = [?]x3+[ ]x2+0 ]x+[ ]

Answers

The cubic regression function of the points (1,-1), (2,-13), (3,-45), (-1,11) is y = -2x³ + 2x² - 4x + 3

How to determine the function?

The points are given as:

(x,y) = (1,-1), (2,-13), (3,-45), (-1,11)

A cubic regression function is represented as:

y = ax³ + bx² + cx + d

Next, we determine the cubic function using a graphing calculator.

From the graphing calculator, we have the following coefficients:

a = -2
b = 2
c = -4
d = 3

Recall that:

y = ax³ + bx² + cx + d

So, we have:

y = -2x³ + 2x² - 4x + 3

Hence, the cubic regression function of the points is y = -2x³ + 2x² - 4x + 3

Read more about regression functions at:

brainly.com/question/25226042

#SPJ1

Solve for x 4 - (x + 2) < -3(x + 4)

Answers

Answer:

x<-7

Step-by-step explanation:

Use inverse operations to solve

4 - ( x + 2 ) < -3 ( x+ 4)

first distribute the (-) sign and the (-3)

4 -x -2 < -3x -12

simplify

2 -x < -3x -12

simplify again, with inverse operations

2 -x < -3x -12

+3x +3x

2 + 2x < -12

-2 -2

2x < -14

/2 /2

x<-7

in 4 - (x + 2) < -3(x + 4), x < -7

isolate the variable by dividing each side by factors that don't contain the variable.

Find the greatest factor of 6w^3 and 10a^4

Answers

Answer:2

Step-by-step explanation:

Greatest factor of 6w^4 10a^4

6w^4=2x3xw^4

10a^4=2x5xa^4

There greatest common factor is 2

In the first quadrant you start at (6, 10) and move 6 units right and 4 units down what point will you end up with

Answers

Answer:

(12,6)

Step-by-step explanation:

If you move 6 units right, you get to (12,10). Moving 4 units down takes you to (12,6).

It would be 12,6 I believe

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Adam is climbing up the stairs in a building. At a certain point, Adam starts counting the steps and when he reaches the last step, he has counted 56 steps. If he knows that there are a total of 100 steps in the building, how many steps did he climb before he started counting the steps?

Need help...,.......

What is the distance between -34 and 16

Determine whether the improper integral converges or diverges, and find the value of each that converges.∫^0_-[infinity] 5e^60x dx