Answer:
The angle is
.
Step-by-step explanation:
The building is 35 feet tall, and the rope is 400 feet long.Applying the trigonometric function, we have;
Sin θ = ![\frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
The height of the building represents the opposite side, while the length of the rope represents the hypotenuse. Thus;
Sin θ = ![\frac{35}{400}](https://tex.z-dn.net/?f=%5Cfrac%7B35%7D%7B400%7D)
Sin θ = 0.0875
θ =
0.0875
= ![5.02^{0}](https://tex.z-dn.net/?f=5.02%5E%7B0%7D)
The angle made by the rope with respect to the ground is approximately
.
Given that the equation to find the height of the firework is
h(t) = at² + vt + h₀
with a = -16 ft/s² and v = 128 ft/s. In addition, since the firework starts from the ground, then the initial height, h₀, is equal to 0. Substituting these values, we have
h(t) = -16t² + 128t + 0 = -16t² + 128t
Seeing that h(t) is a quadratic function, then it forms a parabola. To find its maximum height, we can compute for the parabola's vertex.
To find the vertex's x-coordinate, we can use
t = -b/2a = (-128)/(2 · -16) = -128/-32 = 4
Since, it takes 4 seconds for the firework to reach its maximum height, then the maximum height it reaches is equal to h(4). Hence, we have
h(4) = -16(4)² + 128(4) = -16(16) + 512 = 256
Hence, the highest that the firework can reach is equal to 256 ft.
Answer: A. 256 ft
Answer: 10.2 meters per hour; or, write as: 10 ⅕ meters per hour.
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Explanation:
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Note: "h" = time in "hour(s)" ;
"cm" = length in "centimeter(s)" ;
"min" = time in "minute(s)";
"m" = length in "meter(s)"
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Note these EXACT conversions:
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100 cm = 1 m ;
60 min = 1 h ;
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To solve:
Given: 17 cm / min ; convert to: ________ m / h
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(17 cm / min)* (1 m /100cm) * (60 min / 1 h) = _______ m / h
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The "cm" units cancel to "1"; the "min" units cancel to "1" and we are left with units of "m/h" {"meters per hour"}.
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We are left with (17 *1 m * 60) / (100 * 1 h) = [(17 * 60) m] / [100 h]
= [(17 *60) / 100 ] meters per hour.
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To simply: (17 * 60) / 100 ;
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Method 1): To simplify: (17 * 60) / 100 ;
→Rewrite as: (17*60) / 100 = (17*20*3)/(20*5) ;
→Cancel out the "20's "; and rewrite as:
→ (17*60) / 100 = (17*3)/5 = 51/5
= 10.2 meters per hour; or, write as: 10 ⅕ meters per hour.
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Method 2) To simplify: (17 * 60) / 100 ; Use calculator (or by hand):
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→ (17 * 60) / 100 = 1,020 /100
= 10.2 meters per hour; or, write as: 10 ⅕ meters per hour.
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Method 3) To simplify: (17 * 60) / 100 ;
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→ (17 * 60) / 100 = ? ;
→ Divide BOTH the "100" AND the "60" by "10";
→ 60÷10 = 6 ; 100÷10 =10; and rewrite—replace the "60" with a "6"; and replace the "100" with a "10" ;
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→ (17*60)/100 = (17*6)/10 = 102/10
= 10.2 meters per hours; or, write as: 10 ⅕ meters per hour.
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-7.2 is your answer. I would show the work but I can't take pictures at the moment.