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mafiozo [28]
3 years ago
5

Two ships leave a harbor at the same time. One ship travels on a bearing Upper S 14 degrees Upper W at 15 miles per hour. The ot

her ship travels on a bearing Upper N 75 degrees Upper E at 12 miles per hour. How far apart will the ships be after 3 ​hours?
Mathematics
1 answer:
jekas [21]3 years ago
4 0

Answer:

69.94 miles

Step-by-step explanation:

The distance d₁ the first ship moves after 3 hours is 3 hours × 15 miles per hours = 45 miles

The distance d₂ the second ship moves after 3 hours is 3 hours × 12 miles per hours = 36 miles.

The angle the first ship's direction makes in the North-East direction is 90° - 75° = 15°

The angle the second ship's direction makes in the South-West direction  = 14°

The distance moved by the two ships form the side of a triangle. The angle,  θ between the two ship directions is 14° + 90° + 15° = 119°

Using the cosine rule, we find the distance d between the two ships

d = √(d₁² + d₂² -2d₁d₂cosθ)

= √(45² + 36² -2×45×36cos119°)

= √(2025 + 1296- (-1570.78))

= √(3321 + 1570.78)

= √4891.78

= 69.94 miles

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Slav-nsk [51]

Step-by-step explanation:

Let grandson's age be x.

Let grandpa's age be y {equation : y = 8+5x}

so,

x + y = 88

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or, 6x + 8 =88

or, 6x = 88-8

or, 6x = 80

or, x = 80/6

so, x = 13.33

so grandson's age = 13.33

grandpa's age = 8 + 5x = 8 + (5×13.33) = 74.65 yrs

7 0
3 years ago
What is the ratio in which the point P(3/4,5/12) decides the line segment joining points A(1/2,3/2) and B(2,-5)
timama [110]

Given:

The point P\left(\dfrac{3}{4},\dfrac{5}{12}\right) divides the line segment joining points A\left(\dfrac{1}{2},\dfrac{3}{2}\right) and B(2,-5).

To find:

The ratio in which he point P divides the segment AB.

Solution:

Section formula: If a point divides a segment in m:n, then the coordinates of that point are,

Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)

Let point P divides the segment AB in m:n. Then by using the section formula, we get

\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)

\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)

On comparing both sides, we get

\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}

\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}

Multiply both sides by 4.

3(m+n)=2(4m+n)

3m+3n=8m+2n

3n-2n=8m-3m

n=5m

It can be written as

\dfrac{1}{5}=\dfrac{m}{n}

1:5=m:n

Therefore, the point P divides the line segment AB in 1:5.

6 0
3 years ago
All triangle angles have 60 degree angles. What are the side lengths?
Alex_Xolod [135]
If all the angles are 60 degrees, this is an equilateral triangle. This means that all the sides have the same lengths. Whatever length side a is, b and c have the same length. 

Hope this helps :)
3 0
3 years ago
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If there were 48 alligators and 5/6 were sleeping, how many are asleep?
Sergio039 [100]

5/6

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3 years ago
A rectangle measures 6 cm by 4 cm. Another rectangle with adjacent sides 8 cm and x cm is geometrically similar to it. Find the
Elis [28]

Answer:

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Step-by-step explanation:

to find the scale factor, you must divide the two equal sides.

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Now, the way to get the value of x is to divide 4 by 3/4 0r 0.75

\frac{4}{0.75}

Which equals

5.333 repeating or 5 1/3

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

6 0
3 years ago
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