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Liula [17]
3 years ago
5

the domain of a function f(x) is x > 1, and the range is y < -2. What are the domain and range of its inverse function, f^

-1(x)?
Mathematics
1 answer:
Marianna [84]3 years ago
8 0

9514 1404 393

Answer:

  • domain: x < -2
  • range: y > 1

Step-by-step explanation:

Domain and range of the inverse function are swapped: the domain of the function is the range of its inverse, and vice versa.

__

The graph shows an example of a function and its inverse with the given domain and range. The function is red; its inverse is blue.

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Find the surface area of a water tower that is 40 feet tall and has a diameter of 20 feet.
Ganezh [65]

Answer:

The surface area is 3140 feet².

What is Surface Area?

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given that:

Diameter = 20 feet

radius =  20 ÷ 2 = 10 feet

Now, Surface area  will be,

=2πr²+ 2πrh

= 2 × 3.14 × (10)² + 2 × 3.14 × 10 × 40

= 6.28  × 100  + 6.28  × 400

= 628 + 25.12  × 100

= 628+ 2512

= 3140 feet²

hence, the surface area is 3140 feet².

Step-by-step explanation:

6 0
1 year ago
Which of the following equations have a solution of y = -22 ? Select all that apply.
nevsk [136]

Answer:

Where are the equations?

7 0
3 years ago
X+y+z=12<br> 6x-2y+z=16<br> 3x+4y+2z=28<br> What does x, y, and z equal?
lianna [129]

Answer:

x = 20/13 , y = 16/13 , z = 120/13

Step-by-step explanation:

Solve the following system:

{x + y + z = 12 | (equation 1)

6 x - 2 y + z = 16 | (equation 2)

3 x + 4 y + 2 z = 28 | (equation 3)

Swap equation 1 with equation 2:

{6 x - 2 y + z = 16 | (equation 1)

x + y + z = 12 | (equation 2)

3 x + 4 y + 2 z = 28 | (equation 3)

Subtract 1/6 × (equation 1) from equation 2:

{6 x - 2 y + z = 16 | (equation 1)

0 x+(4 y)/3 + (5 z)/6 = 28/3 | (equation 2)

3 x + 4 y + 2 z = 28 | (equation 3)

Multiply equation 2 by 6:

{6 x - 2 y + z = 16 | (equation 1)

0 x+8 y + 5 z = 56 | (equation 2)

3 x + 4 y + 2 z = 28 | (equation 3)

Subtract 1/2 × (equation 1) from equation 3:

{6 x - 2 y + z = 16 | (equation 1)

0 x+8 y + 5 z = 56 | (equation 2)

0 x+5 y + (3 z)/2 = 20 | (equation 3)

Multiply equation 3 by 2:

{6 x - 2 y + z = 16 | (equation 1)

0 x+8 y + 5 z = 56 | (equation 2)

0 x+10 y + 3 z = 40 | (equation 3)

Swap equation 2 with equation 3:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y + 3 z = 40 | (equation 2)

0 x+8 y + 5 z = 56 | (equation 3)

Subtract 4/5 × (equation 2) from equation 3:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y + 3 z = 40 | (equation 2)

0 x+0 y+(13 z)/5 = 24 | (equation 3)

Multiply equation 3 by 5:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y + 3 z = 40 | (equation 2)

0 x+0 y+13 z = 120 | (equation 3)

Divide equation 3 by 13:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y + 3 z = 40 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Subtract 3 × (equation 3) from equation 2:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y+0 z = 160/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Divide equation 2 by 10:

{6 x - 2 y + z = 16 | (equation 1)

0 x+y+0 z = 16/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Add 2 × (equation 2) to equation 1:

{6 x + 0 y+z = 240/13 | (equation 1)

0 x+y+0 z = 16/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Subtract equation 3 from equation 1:

{6 x+0 y+0 z = 120/13 | (equation 1)

0 x+y+0 z = 16/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Divide equation 1 by 6:

{x+0 y+0 z = 20/13 | (equation 1)

0 x+y+0 z = 16/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Collect results:

Answer:  {x = 20/13 , y = 16/13 , z = 120/13

8 0
3 years ago
Bonsoir vous pouvez m’aider alors : A la masse x (en g) d’un objet suspendu , on associe la longueur (en mm) d’un ressort . Cett
natita [175]

Answer:

50 g = 95mm

60 g = 98 mm

0 g = 98/60 = 1.63 mm Step-by-step                                                      explanation:hope this help y'all

8 0
2 years ago
A grapefruit has a peel that is 1cm thick and a total diameter of 12cm. What percentage of volume of the grapefruit is the peel?
ira [324]

Answer:

0.3056 or 30.56%

Step-by-step explanation:

The volume of the grapefruit with the peel is:

V_p=\frac{4 \pi (d/2)^2}{3}\\V_p=\frac{4 \pi (12/2)^2}{3}\\V_p=48 \pi

When removing the peel, the grapefruit diameter becomes 10 cm (take out 1 cm of peel from each side). The volume of the grapefruit without the peel is:

V_n=\frac{4 \pi (d/2)^2}{3}\\V_n=\frac{4 \pi (10/2)^2}{3}\\V_n=33.333 \pi

The percentage of the volume correspondent to the peel is given by the difference between both volumes, divided by the total volume:

\%P = \frac{48\pi - 33.333\pi}{48\pi}\\ \%P =0.3056 = 30.56\%

30.56% of volume of the grapefruit is the peel.

4 0
3 years ago
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