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HACTEHA [7]
3 years ago
9

An operator at the top of a lighthouse sights a sailboat. The point from which the sighting is made is 25 m above sea level. The

angle of depression of the sighting is 10 degrees. How far is the boat from the base of the lighthouse?
Mathematics
1 answer:
Aneli [31]3 years ago
4 0

Answer:

141.78 m

Step-by-step explanation:

Let d = distance of boat from the base of the lighthouse

Tan 10 = 25/d

d tan 10 = 25

d = 25/tan 10

d = 141.78 m

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Write each statement as a decimal to two decimal places.
Ad libitum [116K]

Step-by-step explanation:

The above given statements can be written as decimals by first writing both quantities in a statement in the same unit.

1. $6.00 to 95 cents:

This is same as $6.00 : 95 cents = \frac{6.00}{95}956.00

Convert $6 .00 to cents to make both quantities be in the same unit.

$1 = 100 cents

$6.00 = 6*100 = 600 cents

\frac{600}{95} = 6.3295600=6.32 (to 2 d.p)

2. 3 hours to 35 minutes:

Convert 3 hours to 35 mins

1 hr = 60 mins

3 hrs = 3*60 = 180 mins

180mins : 35 mins = \frac{180}{35} = 5.14180mins:35mins=35180=5.14 (2 d.p)

3. 42 inches to 2 feet:

Convert 2 ft to inches

1 ft = 12 inches

2ft = 2*12 = 24 inches

42 in:24 in = \frac{42}{24} = 1.7542in:24in=2442=1.75

5 0
2 years ago
Reduce to simplest form. - 3/5 + 1/3
Pani-rosa [81]

Answer: -4/15

Step-by-step explanation: To add these two fractions together,

we start by finding their <em>Least Common Denominator</em> (LCD).

Since our denominators of 5 and 3 have no factors in common,

our least common denominator is 5 · 3 or 15.

In order to get a denominator of 15 in each fraction,

we multiply top and bottom of the first fraction by 3

and top and bottom of the second fraction by 5.

That gives us -9/15 + 5/15 which simplifies to -4/15.

As your last step, make sure that the fraction

that you end up with doesn't reduce.

In this case, -4/15 does not reduce but watch out for this last step.

8 0
3 years ago
A circle circumference is 600 M. what is the good approximation of the circle area​
wlad13 [49]

Answer:

The area of the circle is 28662 M².

Step-by-step explanation:

Given:

Circumference of circle = 600 M.

Now, to find the area of the circle.

So, <em>to get the area we need to find the radius.</em>

By putting the formula of circumference we get the radius:

Let the radius be r.

Circumference = 2πr

600 = 2\times 3.14\times r (taking the value of π = 3.14.)

600=6.28r

Dividing both sides by 6.28 we get:

95.54=r

Now, <em>for getting the area we put the formula:</em>

Area = πr²

Area = 3.14\times 95.54^{2}

Area = 3.14\times 9127.89

Area = 28661.57

So, <u><em>approximately the area of  the circle = 28662 M²</em></u>.

Therefore, the area of the circle is 28662 M².

4 0
3 years ago
The number of households without a computer at home in 2009 was closest to A)801000 B)1153000 C)1737000 D)3433000 E)4017000
bagirrra123 [75]

Answer:

B) 1153000

Step-by-step explanation:

Given

See attachment

Required

Number of households without computer in 2009

From the attachment, we have:

n=5170000 --- survey

p = 22.3\% --- proportion without computer

So, the actual number is:

Number = p * n

Number = 22.3\% * 5170000

Number = 1152910

Number \approx 1153000

<em>Hence: (B) is correct</em>

7 0
3 years ago
What is the intermediate step in the form (x + a)2 = b as a result of completing the
Eddi Din [679]

Answer:

(x + 7)^2 = 64

Step-by-step explanation:

x^2 + 23x – 19 = 9x - 4

x^2 + 23x - 9x = -4 + 19

x^2 + 14x = 15 = 0

Completing the square:

(x + 14/2)^2 - (14/2)^2 = 15

(x + 7)^2 - 49 = 15

(x + 7)^2 = 64

8 0
3 years ago
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