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3 years ago

Can someone help me with this question? Thank you!

Mathematics

1 answer:

Natali [406]3 years ago

3 0

Answer:

Step-by-step explanation:

22 is the largest number you are given in this diagram. 0 is the smallest. that would be your first step.

Next think about it as if you already know your midpoint, as in, midpoint being half of your ending value.

Lastly, you want to divide 22 in half, since midpoint is half of your line segment, and then answer you get is 11

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Step-by-step explanation:

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A lighthouse is located on a small island 2 km away from the nearest point P on a straight shoreline and its light makes four re

ddd [48]

Answer:

62.8 km per min

Step-by-step explanation:

Let the diagram of this situation is shown below,

In which $\theta$ is the angle made by light to the straight line joining the lighthouse and P,

∵ Light makes 4 revolutions per minute.

Also, 1 revolution = $2\pi$ radians

So, the change in angle with respect to t ( time ),

$\frac{d\theta}{dt}=8\pi\text{ radians per min}$

Let x be the distance of beam from P,

$\implies \tan \theta = \frac{x}{2}$

Differentiating with respect to x,

$\sec^2 \theta \frac{d\theta}{dt}=\frac{1}{2}\frac{dx}{dt}$

$(1+\tan^2 \theta) (8\pi) = \frac{1}{2}\frac{dx}{dt}$

$(1+\frac{x^2}{2^2})(8\pi) = \frac{1}{2}\frac{dx}{dt}$

If x = 1 km,

$(1+\frac{1}{4})8\pi =\frac{1}{2}\frac{dx}{dt}$

$\frac{5}{4}8\pi = \frac{1}{2}\frac{dx}{dt}$

$\implies \frac{dx}{dt}=\frac{80\pi}{4}= 20\pi\approx 62.8\text{ km per min}$

Hence, the beam of light moving along the shoreline with the speed of 62.8 km per min

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4 years ago

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nikitadnepr [17]

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Vlad1618 [11]

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Step-by-step explanation:

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Can someone help me with this question? Thank you! ​

Can someone help me with this question? Thank you!