Find the inverse of each function1) g (x)= 3+(x-1)^3
4) f (x)=x^3+2
5) f (n)= 5 square root of (-n+1/2)

Answers

Answer 1

Answer: to find the inverse
1. replace f(x) or g(x) or f(n) with y
2. switch places of x and y
3. solve for y
4. replace y with f⁻¹(x) or g⁻¹(x) or f⁻¹(n)

1.
g(x)=3+(x-1)^3
replace
y=3+(x-1)^3
switch
x=3+(y-1)^3
solve
x=3+(y-1)^3
subtract 3
x-3=(y-1)^3
cube root both sides
$\sqrt[3]{x-3}$ =y-1
add 1
$\sqrt[3]{x-3}$ +1=y
switch y with g⁻¹(x)
g⁻¹(x)= $\sqrt[3]{x-3}$ +1

4. f(x)=x^3+2
replace with y
y=x^3+2
switch x and y
x=y^3+2
solve for y
x=y^3+2
subtract 2
x-2=y^3
cube roo both sides
$\sqrt[3]{x-2}$ =y
replace with f⁻¹(x)
f⁻¹(x)= $\sqrt[3]{x-2}$

5.
f(n)=5 $√(-n+1/2)$
replace
y=5 $√(-n+1/2)$
switch n and y
n=5 $√(-y+1/2)$
solve for y
n=5 $√(-y+1/2)$
divide both sides by 5
n/5=n= $√(-y+1/2)$
square both sides
$(n^2)/(25)$ =-y+1/2
subtract 1/2 from both sides
$(n^2)/(25)$ - $(1)/(2)$ =-y
multiply both sides by -1
- $(n^2)/(25)$ + $(1)/(2)$ =y
replace with f⁻¹(n)
f⁻¹(n)=- $(n^2)/(25)$ + $(1)/(2)$

1. g⁻¹(x)= $\sqrt[3]{x-3}$ +1
4. f⁻¹(x)= $\sqrt[3]{x-2}$
5. f⁻¹(n)=- $(n^2)/(25)$ + $(1)/(2)$

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15 POINTS. What is the area of the circle segment/shaded area? Picture included please help. Please answer in a way that will fill in the blanks, explanation preferred.

The formula for the area A of a trapezoid is A=1/2(b1+b2)h, where b1 and b2 represents the lengths of the bases and h represents the height. Which equation can be used to find the height of a trapezoid?A. h=2A-b1-b2
B. h=2A/b1+b2
C. h=A(b1+b2)/2
D. h=A-2/b1-b2

Answers

The answer: [B]: h = 2A / (b1 + b2) .
__________________________________________________________
Explanation:

Given: A = (½) * (b1 + b2) * h ;
________________________________
→Multiply EACH side of the equation by "2", to get rid of the fraction, "½";
____________________________________________________________
→ 2*A = 2 * (½) * (b1 + b2) * h ;

→ 2* A = 1 * (b1 + b2) * h ;

→ 2A = (b1 + b2) * h ;
____________________________
→ Now, divide EACH side of the equation by: "(b1 + b2)" ; to isolate "h" on one side of the equation;
__________________________________________________________
→ 2A / (b1 + b2) = [(b1 + b2) * h] / (b1 + b2) ;

→ 2A / (b1 + b2) = h ; ↔ h = 2A / (b1 + b2) ; which corresponds to:
"Answer choice: [B]" .
_____________________________________________________________

Answer:

Step-by-step explanation:

h=2a/b1+b2

Casey is reading a book for a book report. At 3:30 P.M., he started reading where he had left off the day before. At 5:30 P.M. he was on page 160. At 8:00 P.M. he was on page 280. If reading the book is modeled by a linear function, what page did Casey start on at 3:30 P.M.?

Answers

To find the time Casey read today, 5:30 from 8:00.
8:00 - 5:30 = 2:30
Casey

To find the number of pages Casey read today subtract the page number he started reading on to the page he stopped on.
280 - 160 = 120
Casey read 120 pages today.

Now you need to find how many pages Casey read in one hour.

If Casey read 120 pages in 2.5 hours, you can find how many pages he read in one hour by dividing 120 by 2.5.
120 ÷ 2.5 = 48.
Casey read 48 pages in one hour.

Casey was on page 160 at 5:30, and you need to find what page he was on at 3:30. Since Casey read for 2 hours before he reached page 160, you need to subtract 2 hours worth of reading from that number.

160 - (2×48)
160 - 96
64

Casey was on page 64 at 3:30 pm today.

if he started reading from where he left off, and it's 5:30 and he is at page 160, and then he got to page 280 by 8:00, that is 2 hours and 30 minutes. so bring the reading time down into easier numbers so that 5-> 30 minute terms, then find out how many pages he read in 30 minutes. The difference between 160 pages and 280 pages is 120 pages. 120 divided by 30 equals 4. the amount of time between 3:30 and 5:30 is 2 hours which is 4-> 30 minute terms. So if it takes 30 minutes to read 4 pages then multiply 4 with 4 which equals 16, and finally subtract 16 from 160 and that's going to equal 144 pages.

(Sorry about the paragraph but i figured ide give you my reasoning and work just in case if i was wrong, ide like to know what i did if i am wrong. And if I'm right then that's how you show your work!)

PLEASE HURRY AND ANSWER ASAP :)
THIS IS DUE IN 10 MIN

Answers

Answer:

23.2/20

Step-by-step explanation:

i looked it up

Matilda is filling a circular section of her porch with colorful pebbles. She knows the diameter of the circular section is 15ft, and each bag of pebbles covers 10ft. How many bags of pebbles will Matilda need? A. 15 bags B. 16 bags C. 17 bags D. 18 bags

Answers

Answer:

D. 18 bags

Step-by-step explanation:

Given:

Matilda is filling a circular section of her porch with colorful pebbles.

Diameter of circular section = 15 feet.

Each bag of pebbles covers 10 square feet.

Question asked:

How many bags of pebbles will Matilda need?

Solution:

Diameter of circular section = 15 feet

Radius, r = $(Diameter)/(2)=(15)/(2) =7.5\ feet$

$Area\ of\ circular\ section=\pi r^(2)$

$=(22)/(7) *7.5*7.5=(1237.5)/(7)=176.78} \ square\ feet$

10 square feet is covered by number of bag of pebbles = 1

1 square feet is covered by number of bag of pebbles = $(1)/(10)$

176.78 square feet is covered by number of bags of pebbles =

$(1)/(10)*176.78=17.67$

We found up to 17 bags of pebbles there is still some place left to fill the section:-

Thus, Matilda need about 18 bags of pebbles to fill the circular section of her porch.

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air at an initial velocity of 7 feet per second. The equation h = -2t^(2) + 7t + 4 models the toy's height h in feet from the ground at t seconds after he threw it. a) How high is the toy after 0-4 seconds?

Answers

Step-by-step explanation:

The height attained by the toy as a function of time t is given by :

$h = -2t^2 + 7t + 4$

h is in feet and t is in seconds

Height of the toy at t = 0

$h = -29(0)^2 + 7(0) + 4=4\ ft$

Height of the toy at t = 4 seconds is :

$h=-2(4)^2 + 7(4)+ 4=0$

So, between 0 to 4 seconds, height of the toy is 4 feets.

Final answer:

The toy's height after 0-4 seconds can be found by substituting different values of t into the given equation.

Explanation:

The equation given to model the toy's height is h = -2t^2 + 7t + 4, where h is the height in feet and t is the time in seconds. To find the height of the toy after 0-4 seconds, we substitute different values of t into the equation.

For t = 0, h = -2(0)^2 + 7(0) + 4 = 4 feet.

For t = 1, h = -2(1)^2 + 7(1) + 4 = 9 feet.

For t = 2, h = -2(2)^2 + 7(2) + 4 = 12 feet.

For t = 3, h = -2(3)^2 + 7(3) + 4 = 11 feet.

For t = 4, h = -2(4)^2 + 7(4) + 4 = 4 feet.

Learn more about Projectile motion here:

brainly.com/question/29545516

#SPJ3

A dartboard consists of two concentric circles. The probability of hitting the inner circle is64%. If the outer circle has a diameter of 20 inches, what is the radius of the inner circle?

2 inches
4 inches
8 inches
16 inch

Answers

Given:
Diameter of outer circle = 20 inches.

We need to find the Area of the outer circle to get the radius of the inner circle.

Area = πr²

Outer circle Area = 3.14 * (10in)² = 314 in²

314 in² * 64% probability = 200.96 in² Area of the inner circle.

200.96 in² = 3.14 * r²
200.96 in² / 3.14 = r²
64 in² = r²
√64 in² = √r²
8 in = r

radius of inner circle is 8 inches.

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