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3 years ago

Given that f(x) = 6x + 2 and g(x) =2x+4 over 5 solve for g(f(1))

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

6 0

F(1)=6(1)+2
= 6+2
=8

g(f(1))= 2x/5 +4/5
= 2(8)/5 +4/5
= 16/5 +4/5
= 20/5
=4

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A Ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the Ferris wheel makes one comp

Morgarella [4.7K]

Answer:

$y = 11 - 10cos(0.1\pi t)$

Step-by-step explanation:

Suppose at t = 0 the person is 1m above the ground and going up

Knowing that the wheel completes 1 revolution every 20s and 1 revolution = 2π rad in angle, we can calculate the angular speed

2π / 20 = 0.1π rad/s

The height above ground would be the sum of the vertical distance from the ground to the bottom of the wheel and the vertical distance from the bottom of the wheel to the person, which is the wheel radius subtracted by the vertical distance of the person to the center of the wheel.

$y = h_g + d_b = h_g + R - d_c$ (1)

where $h_g = 1$ is vertical distance from the ground to the bottom of the wheel, $d_b$ is the vertical distance from the bottom of the wheel to the person, R = 10 is the wheel radius, $d_c$ is the vertical distance of the person to the center of the wheel.

So solve for $d_c$ in term of t, we just need to find the cosine of angle θ it has swept after time t and multiply it with R

$d_c = Rcos(\theta(t)) = Rcos(\omega t) = 10cos(0.1\pi t)$

Note that $d_c$ is negative when angle θ gets between π/2 (90 degrees) and 3π/2 (270 degrees) but that is expected since it would mean adding the vertical distance to the wheel radius.

Therefore, if we plug this into equation (1) then

$y = h_g + R - d_c = 1 + 10 - 10cos(0.1\pi t) = 11 - 10cos(0.1\pi t)$

7 0

3 years ago

The population of a town has grown at an annual rate of 2.7%. How long does it take for it’s population of 18,450 people to doub

charle [14.2K]

It would take 26 years.

The equation will be in the form y = a(1+r)ˣ, where a is the initial population, r is the growth rate as a decimal number, and x is the amount of time. Using our information we have

y = 18450(1+0.027)ˣ = 18450(1.027)ˣ

We want the population to be doubled; 18450*2 = 36900:
36900 = 18450(1.027)ˣ

Divide both sides by 18450:
36900/18450 = 18450(1.027)ˣ/18450
2 = 1.027ˣ

Using logarithms, we have
$\log_{1.027}2=x
\\
\\x=26.017$

3 0

3 years ago

Solve the inequality- x+18 ≥ 8x+4 or 15x-15 ≤ 15x+5<br><br> I give Brainliest!

r-ruslan [8.4K]

Answer:

x ≥ 2

0 ≤ 20 (not quite sure if the question is right)

Step-by-step explanation:

x+18 ≥ 8x+4

x - 8x ≥ 4 - 18

-7x ≥ -14

x ≥ $\frac{-14}{-7}$

x ≥ 2

________________

15x-15 ≤ 15x+5

15x - 15x ≤ 5 + 15

0 ≤ 20

(I don't think this is the right question...cuz theres a 0)

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2 years ago

Question 3 of 10

Licemer1 [7]

Answer: D: Square Root Of 5

Step-by-step explanation: 30/6 is 5, now fill in the sqrt symbol. Hope this helped. (This problem was one of the simpler, friendlier numbers.)

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2 years ago

Provide a function that has both a vertical and horizontal asymptotes.

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X=3 and y=1 are the horizontal and vertical asymptotes of this function

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3 years ago