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Westkost [7]
1 year ago
8

A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the

Mathematics
1 answer:
Novay_Z [31]1 year ago
5 0

The horizontal distance between light house and boat is 1588.78 feet approximately.

The figure is given by,

Here, AB  = height of the lighthouse bacon light above the water = 139 feet

Now angle ACB = 5 degree

Let the horizontal distance of light house from the boat = BC = x feet

So by trigonometric function we get,

tan 5 = AB/BC

tan 5 = 139/x

x = 139/tan 5 = 1588.78 (approximately)

Hence the horizontal distance between light house and boat is 1588.78 feet approximately.  

To know more about Trigonometric Function refer to:

brainly.com/question/1143565

#SPJ9

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Flauer [41]

Answer:

3

Step-by-step explanation:

slope = (y2-y1)/(x2-x1)

(-4-2)/(-4--2)

-6/-2

3

7 0
2 years ago
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Using exact values (e.g. 10+4π), find the area of the following composite shape:
Angelina_Jolie [31]

Answer:

12 - (⅛)π cm²

Step-by-step explanation:

Rectangle + circle - semicircle

(4 × 3) + (pi × 1²) - ½(pi × 1.5²)

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12 - (⅛)π

3 0
2 years ago
Solve the following pairs of simultaneous equations.
Sergeeva-Olga [200]

Answer and step-by-step explanation:

a) -4x + 5y = -9 (2)

2x + 3y = 21

Multiply the second equation by 2, you will get:

4x + 6y = 42 (1)

Use (1) plus with (2), you will get:

4x + (-4x) + 6y + 5y = -9 + 42

11y = 33

y = 33/11

y = 3

4x + 18 = 42

4x = 24

x = 6

b) 2x + 5y = -6

3x + 2y = 2

Multiply first equation by 3, you will get:

6x + 15y = -18 (1)

Multiply the second equation by 2 and you will get:

6x + 4y = 4 (2)

Subtract (1) by (2), we got:

6x -6x + 15y - 4y = -18 - 4

11y = -22

y = -22/11

y = -2

6x + 4y = 4

6x -8 = 4

6x = 12

x = 2

c) 2x - 2y = -4

5x + 4y = 17 (2)

Multiply the first euation by 2, we got:

4x - 4y = -4 (3)

Use (3) minus for (2), we get:

4x - 5x -4y + 4y = -4 - 17

-x = -21

x = 21

4x - 4y = -4

84 - 4y = -4

-4y = -4 + 84

-4y = 80

y = 80 / -4

y = -20

d) 2x - 3y = 6

4x - 5y = 9 (1)

Multiply the first equation by 2, we got:

4x - 6y = 12 (2)

Use (1) minus for (2), we got:

4x -4x - 5y - 6y = 9 -12

-11y = -3

y = -3/-11

y = 3/11

2x - 3y = 6

2x - 9/11 = 6

2x = 66/11 + 9/ 11

2x = 75/11

x = 75/11 * 1/2

x = 75 / 22

e) x/2 + y/3 = 2

x/4 + y/3 = 4

Use the first equation subtract the second equation, we got:

x/2 - x/4 + y/3 - y/3 = 2 - 4

2x/4 -x/4 = -2

x/ 4 = -2

x = -2 * 4

x = -8

x/2 + y/3 = 2

-8 / 2 + y/3 = 2

y / 3 = 2 + 4

y/3 = 6

y = 6*3

y = 18

f) x/3 + y/2 = 3/2 (1)

x/2 + y/5 = -1/2 (2)

I don't know how to solve this, sr

Hope this helped :3

3 0
3 years ago
Find the directional derivative of g(x, y) = xey − yex , 2x x − y at the point (1, 0) in the direction v = 3i + 4j
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no rurio greob tryo yeu

7 0
3 years ago
A store owner uses a selling price of 125% of the cost of an item. If a pair of jeans has a sales price of $52.50, what cost doe
IgorC [24]

Answer:

The cost store owner pay for the pair of jeans is <u>$42</u>.

Step-by-step explanation:

Given:

A store owner uses a selling price of 125% of the cost of an item.

If a pair of jeans has a sales price of $52.50.

Now, to find the cost price of the store owner pay for the pair of jeans.

Let the cost price of jeans be x.

Sell price of jeans = \$52.50.

Now, to get the cost price of store owner pay for the pair of jeans:

<em>As given the</em><em> </em><em>store owner uses a selling price of 125% of the cost of an item.</em>

According to question:

125\%\ of\ x=52.50

\frac{125}{100} \times x=52.50

1.25x=52.50

<em>Dividing both sides by 1.25 we get:</em>

x=42.

<em>The cost price of jeans = $42.</em>

Therefore, the cost store owner pay for the pair of jeans is $42.

6 0
2 years ago
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