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solmaris [256]
3 years ago
13

A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept f

ocused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight
Mathematics
1 answer:
krek1111 [17]3 years ago
6 0

Answer:

0.128rad/sec

Step-by-step explanation:

Let x represent the between the man and the point on the path

θ = the angle

dx/dt = 4 ft/s

dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight

tan θ = x/20 ft

Cross Multiply

20tan θ = x

dx/dt = 20sec² θ dθ/dt

dθ/dt = 1/20 × cos² θ dx/dt

dθ/dt= 1/20 × cos² θ × 4

dθ/dt = 1/5 × cos² θ

Note : cos θ = 4/5

dθ/dt = 1/5 × (4/5)²

dθ/dt = 16/125

dθ/dt = 0.128rad/sec

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denis-greek [22]

How about this?

(x - 6) x (x + 2)


8 0
3 years ago
What is the solution of 6x= 15 <br>​
balandron [24]

Answer:

2.5

Step-by-step explanation:

When a variable is next to a number (coefficient) it means you need to multiply. In this equation 6x are next to eachother.

Because we don't know what x is, we have to work backwards.

The opposite of multiplying is dividing, so here we can do...

15/6  and that equals 2.5

To check you replace x with 2.5 like so,

6(2.5)= 15 and it is true!

Hope this helps and have a great day!

6 0
3 years ago
Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can?
Naddika [18.5K]
Check the picture below.

so, a cone, that fits inside the cylinder, will have the same height "h" and radius "r".  Thus


\bf \textit{volume of a cylinder}\\\\&#10;V=\pi r^2 h\qquad \boxed{\pi r^2 h}=15&#10;\\\\\\&#10;\textit{volume of a cone}\\\\&#10;V=\cfrac{\pi r^2 h}{3}\implies V=\cfrac{\boxed{15}}{3}

8 0
2 years ago
Write and solve and equation to find how many movies they have time to show.
GalinKa [24]

Answer:

Equation 0.5 + 1.75(x) = 4

x = 2movies

Step-by-step explanation:

Given that,

movie night will last for 4 hours

each movie take 1.75 hours

time for eating popcorn 0.5 hours

To find,

number of movies which can be watched

<h2>Equation</h2><h2>0.5 + 1.75(x) = 4</h2><h2>Solve for x</h2><h3>1.75(x) = 4 - 0.5</h3><h3>1.75(x) = 3.5</h3><h3>x = 3.5/1.75</h3><h3>x = 2  </h3>

So, total number of movies which could be watched in 4hr = 2

<h3 /><h3 /><h3 /><h3 /><h3 /><h3 /><h3 />

7 0
3 years ago
In a random sample of 70 people, it was found that 44 of them were fans of the New York Yankees. What is the margin of error for
Veronika [31]
The general formula for the margin of error would be:

z * √[p (1-p) ÷ n]

where:
z = values for selected confidence level
p = sample proportion
n = sample size

Since the confidence level is not given, we can only solve for the 
<span>√[p (1-p) ÷ n]  part.
</span>
p = 44/70
n = 70

√[44/70 (1 - (44/70) ÷ 70]

√[0.6286 (0.3714)] ÷ 70

√0.2335 ÷ 70

√0.0033357 = 0.05775 or 0.058 Choice B.



7 0
3 years ago
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