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AlekseyPX
2 years ago
15

Given the functions, f(x) = x2 + 2 and g(x) = 4x - 1, perform the indicated operation. When applicable, state the domain restric

tion.
g(f(x))

4 x2 + 1
16 x2 + 3
4 x2 + 7
16 x2 - 8 x + 3
Mathematics
1 answer:
Naya [18.7K]2 years ago
5 0

Answer:

3rd option

Step-by-step explanation:

substitute x = f(x) into g(x)

g(f(x))

= g(x² + 2)

= 4(x² + 2) - 1

= 4x² + 8 - 1

= 4x² + 7

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3 years ago
Angle of the Sun A 96-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun
scoray [572]

Answer:

The angle of elevation of the sun is 39⁰

Step-by-step explanation:

Given;

height of the tree, h = 96 ft

length of the shadow, L = 120 ft

                                                   |

                                                   | 96ft

                                                   |

                                                   |

       θ------------------------------------

                    120ft

Completing this triangle to cut across the top of the tree gives you a right angled triangle with θ as the angle of elevation of the sun.

Apply trig-ratio to determine the angle of elevation of the sun;

tanθ = opposite side / adjacent side

tanθ = 96 / 120

tanθ = 0.8

θ = tan⁻¹(0.8)

θ = 38.7⁰

θ = 39⁰

Therefore, the angle of elevation of the sun is 39⁰

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