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arsen [322]
3 years ago
15

HELP ME PLEASE I WILL REWARD BRAINLIEST ANSWER Use the functions f(x) = 3x + 7 and g(x) = 4x − 2 to complete the function operat

ions listed below. Part A: Find (f + g)(x). Show your work. (3 points) Part B: Find (f ⋅ g)(x). Show your work. (3 points) Part C: Find f[g(x)]. Show your work. (4 points)
Mathematics
1 answer:
Elza [17]3 years ago
4 0
1. (f + g)(x) = f(x) + g(x)
  =  3x + 7 + 4x − 2
=7x+5

2.(f .g)(x) = f(x) x g(x)
(3x + 7) x (4x − 2)
12x²- 6x + 28x -14 =
12x²-34x -14

3. Substitute the x in the f function by the g function, like this:

3(4x − 2) + 7=
12x- 6 +7=
12x+1


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<u>Answer:</u>

a) 3.675 m  

b) 3.67m

<u>Explanation:</u>

We are given acceleration due to gravity on earth =9.8ms^-2

And on planet given = 2.0ms^-2

A) <u>Since the maximum</u><u> jump height</u><u> is given by the formula  </u>

\mathrm{H}=\frac{\left(\mathrm{v} 0^{2} \times \sin 2 \emptyset\right)}{2 \mathrm{g}}

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v0 = velocity of jump,  

Ø = angle of jump and  

g = acceleration due to gravity

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\frac{\mathrm{H} 1}{\mathrm{H} 2}=\frac{\mathrm{g} 2}{\mathrm{g} 1}

Where H1 = jump height on given planet,

H2 = jump height on earth = 0.75m (given)  

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g2 = 9.8ms^-2

Substituting these values we get H1 = 3.675m which is the required answer

B)<u> Formula to </u><u>find height</u><u> of ball thrown is given by  </u>

 \mathrm{h}=(\mathrm{v} 0 * \mathrm{t})+\frac{\mathrm{a} *\left(t^{2}\right)}{2}

which is due to projectile motion of ball  

Now h = max height,

v0 = initial velocity = 0,

t = time of motion,  

a = acceleration = g = acceleration due to gravity

Considering t = same on both places we can write  

\frac{\mathrm{H} 1}{\mathrm{H} 2}=\frac{\mathrm{g} 1}{\mathrm{g} 2}

where h1 and h2 are max heights ball reaches on planet and earth respectively and g1 and g2 are respective accelerations

substituting h2 = 18m, g1 = 2.0ms^-2  and g2 = 9.8ms^-2

We get h1 = 3.67m which is the required height

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3 years ago
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