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Juliette [100K]
3 years ago
8

A baseball is thrown upwards from a height of 5 feet with an initial speed of 64 feet per second, and its height h (in feet) fro

m the ground is given by h(t) = 5 + 64t – 16t2 where t is time in seconds. Using a graphing calculator, determine at what time the ball reaches its maximum height.

Mathematics
2 answers:
Juli2301 [7.4K]3 years ago
8 0

Answer:

2 seconds

Step-by-step explanation:

Given : A baseball is thrown upwards from a height of 5 feet with an initial speed of 64 feet per second, and its height h (in feet) from the ground is given by h(t) = 5 + 64t -16t^2 where t is time in seconds.

To Find: Using a graphing calculator, determine at what time the ball reaches its maximum height.

Solution:

Plot the graph of the given equation

Refer the attached graph

So, the given equation is a downward parabola

So, the y coordinate of vertex of the parabola will give its maximum height and x coordinate will given the time at which the ball is at maximum height

So, Vertex = (2,69)

Maximum height = 69 feet

Time to reach maximum height = 2 seconds

Hence it will take 2 seconds to reach its maximum height.

alexira [117]3 years ago
6 0
A graphing calculator shows the ball reaches its maximum height of 69 feet at t = 2 seconds.

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Irina18 [472]

Answer:

<u>TO FIND :-</u>

  • Length of all missing sides.

<u>FORMULAES TO KNOW BEFORE SOLVING :-</u>

  • \sin \theta = \frac{Side \: opposite \: to \: \theta}{Hypotenuse}
  • \cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}
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<u>SOLUTION :-</u>

1) θ = 16°

Length of side opposite to θ = 7

Hypotenuse = x

=> \sin 16 = \frac{7}{x}

=> \frac{7}{x} = 0.27563......

=> x = \frac{7}{0.27563....} = 25.39568..... ≈ 25.3

2) θ = 29°

Length of side opposite to θ = 6

Hypotenuse = x

=> \sin 29 = \frac{6}{x}

=> \frac{6}{x} = 0.48480......

=> x = \frac{6}{0.48480....} = 12.37599..... ≈ 12.3

3) θ = 30°

Length of side opposite to θ = x

Hypotenuse = 11

=> \sin 30 = \frac{x}{11}

=> \frac{x}{11} = 0.5

=> x = 0.5 \times 11 = 5.5

4) θ = 43°

Length of side adjacent to θ = x

Hypotenuse = 12

=> \cos 43 = \frac{x}{12}

=> \frac{x}{12} = 0.73135......

=> x = 12 \times 0.73135.... = 8.77624.... ≈ 8.8

5) θ = 55°

Length of side adjacent to θ = x

Hypotenuse = 6

=> \cos 55 = \frac{x}{6}

=> \frac{x}{6} = 0.57357......

=> x = 6 \times 0.57357.... = 3.44145.... ≈ 3.4

6) θ = 73°

Length of side adjacent to θ = 8

Hypotenuse = x

=> \cos 73 = \frac{8}{x}

=> \frac{8}{x} = 0.29237......

=> x = \frac{8}{0.29237.....} = 27.36242..... ≈ 27.3

7) θ = 69°

Length of side opposite to θ = 12

Length of side adjacent to θ = x

=> \tan 69 = \frac{12}{x}

=> \frac{12}{x} = 2.60508......

=> x = \frac{12}{2.60508....}  = 4.60636.... ≈ 4.6

8) θ = 20°

Length of side opposite to θ = 11

Length of side adjacent to θ = x

=> \tan 20 = \frac{11}{x}

=> \frac{11}{x} = 0.36397......

=> x = \frac{11}{0.36397....}  =30.22225.... ≈ 30.2

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Distance = Rate * Time where the asterisk represents multiplication

We can isolate the rate if we divide both sides by the time. So we'll end up with this formula
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The distance is measured in feet while the time is measured in minutes. The rate r is measured in feet per minute. If the speed was 10 feet per minute, then this would mean that the object travels 10 feet every minute. Or put another way, when one minute passes by, the object has traveled 10 feet.

How did I get "feet per minute" from the equation r = d/t? 
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So writing "d/t" would turn into "feet/minute" when we think of the units only (ignore the actual numbers). Then we rewrite "feet/minute" into "feet per minute" as they mean the same thing, just written different ways. 

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Step-by-step explanation:

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T=\dfrac{\pi}{3}

B. The period of the function y=6\sin 3x is

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C. The period of the function y=-4\cot \dfrac{x}{4} is

T=\dfrac{\pi}{\frac{1}{4}}=4\pi

D. The period of the function y=2\cos \dfrac{2x}{3} is

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