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Furkat [3]
3 years ago
7

Use your calculator to evaluate the trigonometric expression to the nearest hundredth.

Mathematics
1 answer:
Viefleur [7K]3 years ago
3 0

Answer:

Sin(17) = 0.29

Cosine (78) = 0.21

Step-by-step explanation:

This problem bothers on the trigonometry.

Here we are presented with two trigonometric numbers

Sine (17) and cosine (78)

1.Let us begin by using our calculator to find Sine (17).

Remember to set your calculator in degrees

Sin(17) =0.2923

To the nearest hundredth we have

Sin(17) = 0.29

2. We can do likewise for cosine(78) setting our calculator in degrees

Cosine (78) = 0.2079

To the nearest hundredth we have

Cosine (78) = 0.21

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Given, the equation that represents the height of an object:

y(t)=100t-16t^2

First, we will find the velocity of the object which is the first derivative of the height using the method of the limits

\frac{dy}{dt}=\lim_{h\to a}\frac{y(3+h)-y(3)}{(3+h)-(3)}

We will find the value of the function y(t) when t = 3, and when t = 3+h

\begin{gathered} y(3+h)=100(3+h)-16(3+h)^2 \\ y(3+h)=300+300h-16(9+6h+h^2) \\ y(3+h)=300+300h-144-96h-16h^2 \\ y(3+h)=156+4h-16h^2 \\ y(3)=100(3)-16(3)^2=156 \end{gathered}

Substitute y(3+h) and y(3) into the expression of the limit

\begin{gathered} \frac{dy}{dt}|_{t=3}=\lim_{h\to a}\frac{156+4h-16h^2-156}{3+h-3}=\lim_{h\to a}\frac{4h-16h^2}{h} \\  \\ \frac{dy}{dt}|_{t=3}=\lim_{h\to a}(4-16h) \end{gathered}

Where a = 0

d) compute the instantaneous velocity at t = 3

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So, the answer will be:

\begin{gathered} \frac{dy}{dt}|_{t=3}=\lim_{h\to a}(4-16h) \\ a=0 \\  \\ \frac{dy}{dt}|_{t=3}=4\text{  ft/sec} \end{gathered}

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