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Alexxandr [17]
3 years ago
7

A 400 foot rope is extended from the ground to the top of a building. The building is 35 ft tall. What is the angle made by the

rope with respect to the ground?
Mathematics
1 answer:
velikii [3]3 years ago
3 0

Answer:

The angle is 5.0^{0}.

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}

The height of the building represents the opposite side, while the length of the rope represents the hypotenuse. Thus;

Sin θ = \frac{35}{400}

Sin θ = 0.0875

θ = Sin^{-1} 0.0875

  = 5.02^{0}

The angle made by the rope with respect to the ground is approximately 5.0^{0}.

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Monthly sales of an SUV model are expected to increase at the rate of S′1t2 = -24t 1&gt;3 SUVs per month, where t is time in mon
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The company will continue to manufacture this model for 19 months.

The question is ill-formatted. The understandable format is given below.

An SUV model's monthly sales are anticipated to rise at a rate of

S'(t)=-24^{1/3} SUVs each month, where "t" denotes the number of months and "S(t)" denotes the monthly sales of SUVs. When monthly sales of 300 SUVs are reached, the business intends to discontinue producing this model.

Find S if monthly sales of SUVs are 1,200 at time t=0 (t). How long will the business keep making this model?

Given S'(t)=-24^{1/3} ... ... (1)

Condition (1) at t=0; s(t) =1200

We find S(t)=300 then t=?

a) We find S(t)

from S'(t)=-24^{1/3}

\implies \frac{dS(t)}{dt}=-24t^{1/3} ~~[\because X'(t)=\frac{dX}{dt} \\\implies dS(t) = -24t^{1/3}dt\\

On Integrating both sides

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Now, at t=0 then S(t)=1200

So, from (2)

1200=0+c

⇒c=1200

\thereforefrom eq (2)

S(t)=-18t^{4/3}+1200 ~...~...~(3)

b) Considering that the firm intends to cease production of this model once monthly sales exceed 300 SUVs.

So, take S(t)=300

from eq (2) 300=-18t^{4/3}+1200

t^{4/3}=\frac{1200-300}{18}\\=\frac{900}{18}=50\\\implies t=50^{3/4}\\\implies t=18.8030

Hence the company will continue 18.8020 months.

Learn more about integration here-

brainly.com/question/18125359

#SPJ10

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