All categories

3 years ago

Which of the following is a parent function?

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

6 0

Answer:

$f(x) = e^x$

Step-by-step explanation:

Given

Options (a) to (d)

Required

Which is a parent function

A parent function is such that has a single term without coefficients

From the list of given options

$f(x) = e^x$ suits the above definition

Other options (b) to (d) either have coefficients, or have multiple terms

You might be interested in

Zia is building a plastic model rocket that has the combined shape of a cone and a cylinder as shown. additionally, the cylinder

scoray [572]

Answer:

226 cm^3

The mass of plastic used to make cylinder is greater

Step-by-step explanation:

Given:-

- The density of cone material, ρc = 1.4 g / cm^3

- The density of cylinder material, ρl = 0.8 g / cm^3

Solution:-

- To determine the volume of plastic that remains in the cylinder after gouging out a hemispherical amount of material.

- We will first consider a solid cylinder with length ( L = 10 cm ) and diameter ( d = 6 cm ). The volume of a cylinder is expressed as follows:

$V_L =\pi \frac{d^2}{4} * L$

- Determine the volume of complete cylindrical body as follows:

$V_L = \pi \frac{(6)^2}{4} * 10\\\\V_L = 90\pi cm^3\\$

- Where the volume of hemisphere with diameter ( d = 6 cm ) is given by:

$V_h = \frac{\pi }{12}*d^3$

- Determine the volume of hemisphere gouged out as follows:

$V_h = \frac{\pi }{12}*6^3\\\\V_h = 18\pi cm^3$

- Apply the principle of super-position and subtract the volume of hemisphere from the cylinder as follows to the nearest ( cm^3 ):

$V = V_L - V_h\\\\V = 90\pi - 18\pi \\\\V = 226 cm^3$

Answer: The amount of volume that remains in the cylinder is 226 cm^3

- The volume of cone with base diameter ( d = 6 cm ) and height ( h = 5 cm ) is expressed as follows:

$V_c = \frac{\pi }{12} *d^2 * h$

- Determine the volume of cone:

$V_c = \frac{\pi }{12} *6^2 * 5\\\\V_c = 15\pi cm^3$

- The mass of plastic for the cylinder and the cone can be evaluated using their respective densities and volumes as follows:

$m_i = p_i * V_i$

- The mass of plastic used to make the cylinder ( after removing hemispherical amount ) is:

$m_L = p_L * V\\\\m_L = 0.8 * 226\\\\m_L = 180.8 g$

- Similarly the mass of plastic used to make the cone would be:

$m_c = p_c * V_c\\\\m_c = 1.4 * 15\pi \\\\m_c = 65.973 g$

Answer: The total weight of the cylinder ( m_l = 180.8 g ) is greater than the total weight of the cone ( m_c = 66 g ).

8 0

3 years ago

Solve w 15= -3 {w - 2}

ryzh [129]

Answer: w= -3

Step-by-step explanation:

15= -3(w-2)

(Divide both sides by 3)

5=-(w-2)

(Remove the parentheses)

5=-(w+2)

(Move terms)

w=2-5

(Calculate)

w-3

4 0

3 years ago

Which equations are equivalent? Select all that apply.

elena-14-01-66 [18.8K]

3n+4+5n=52, 8n+4=52, and 4(2n+1)=52

7 0

3 years ago

A man invests a certain amount of money at 2% interest and $800 more than that amount in another account at 4% interest. At the

Alex777 [14]

112 dallors interest beca0.02x + 0.04(800) = 112 0.02x + 0.04(x + 800) = 112 0.04x + 0.02(x + 800) = 112 use

6 0

4 years ago

Read 2 more answers

in a canoe race, a team paddles downstream 480 m in 60 s. The same team makes the trip upstream in 80 s. Find the team's rate in

Vera_Pavlovna [14]

480=60(v+s)

480=60v+60s

8=v+s

s=8-v...

480=80(v-s) using s from above we get:

480=80(v-(8-v))

6=v-8+v

6=2v-8

2v=14

v=7, and since s=8-v, s=1

So the rate of the team is 7m/s while the rate of the stream is 1m/s

7 0

3 years ago