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goblinko [34]
3 years ago
8

A man on the deck of a ship is 14 ft above water level. He observes that the angle of elevation of the top of a cliff is 40 degr

ees and the angle of depression of the base is 20 degrees. Find the distance of the cliff from the ship and the height of the cliff if the base of the cliff is at sea level.

Mathematics
1 answer:
topjm [15]3 years ago
4 0

Answer:

The distance of the ship from the cliff is 38.465 feet

The height of the cliff is 46.28 feet.

Step-by-step explanation:

As shown in the figure attached d is the distance from the ship to the cliff, and h is the height of the cliff from the ship.

From trigonometry

tan(20^o)=\frac{14}{d}

d=\frac{14}{tan(20^o)}=38.465\:feet.\\\\\boxed{d=38.465ft}

This is the distance to the cliff.

And we have

tan(40^o)=\frac{h}{d}

since d=38.465ft

h=d*tan(40^o)=38.465*tan(40^o)=32.28ft

Ad the height of the cliff is just 14+h or

32.28+14=46.28 ft\\\\\boxed{height=46.28ft}

Which is the height of the cliff.

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Answer:

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Step-by-step explanation:

<u>For the question a *</u> you need to find a polynomial of degree 3 with zeros in -3, 1 and 4.

This means that the polynomial P(x) must be zero when x = -3, x = 1 and x = 4.

Then write the polynomial in factored form.

P (x) = (x + 3) (x-1) (x-4)

Note that this polynomial has degree 3 and is zero at x = -3, x = 1 and x = 4.

<u>For question b, do the same procedure</u>.

Degree: 3

Zeros: -5/2, 4/5, 6.

The factors are

x = -\frac{5}{2}\\\\x +\frac{5}{2} = 0\\\\(2x +5) = 0

---------------------------------------

x =\frac{4}{5}\\\\x-\frac{4}{5} = 0\\\\(5x-4) = 0

--------------------------------------

x = 6\\\\(x-6) = 0

--------------------------------------

P (x) = (2x + 5) (5x - 4) (x-6)

<u>Finally for the question c we have</u>

Degree: 5

Zeros: -3, 1, 4, -1

Multiplicity 2 in -1

x = -3\\\\(x-3) = 0

--------------------------------------

x = 1\\\\(x-1) = 0

--------------------------------------

x = 4\\\\(x-4) = 0

----------------------------------------

x = -1\\\\(x + 1) = 0

-----------------------------------------

P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2

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Can someone help me with this math homework please!
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Answer:

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Step-by-step explanation:

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------------------------------------------------------------------------

From

4 - 6x + 1 = 36x ( add 6x to both sides )

5 = 42x ← option 6 will have the same solution set

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