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3 years ago

A ship leaves port at noon and travels at a bearing of 214°. The ship’s average rate of speed is 15 miles per hour.

Mathematics

1 answer:

Daniel [21]3 years ago

3 0

Answer: (-31.09 mi, -20.97 mi)

Step-by-step explanation:

If the noon is our initial time, then we have that 2:30 pm is t = 2.5 hours.

Now, the position (x, y) of the ship can be writen as:

(velocity*time*cos(angle), velocity*time*sin(angle))

or:

(15mph*t¨*cos(214°), 15mph*t*sin(214°))

then the position at t = 2.5 hours is:

(15mph*2.5h*cos(214°), 15mph*2.5h*sin(214°))

(-31.09 mi, -20.97 mi)

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Two buildings are facing each other on a road of width 12 metre . From the top of the first building, which is 10 metre high , t

Karo-lina-s [1.5K]

Answer:

$\displaystyle 10 + 12\sqrt{3}$ metres

Step-by-step explanation:

You are finding the height of the building with an angle of elevation, therefore we need to solve for EC to add it to BA [10 metres] and use TRIGONOMETRIC RATIOS to arrive at our conclusion. Just in case you have forgotten what they were, here they are:

$\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ$

We can now solve for EC:

$\displaystyle cot\:60 = \frac{12}{EC} → ECcot\:60 = 12 \\ \\ \frac{ECcot\:60}{cot\:60} = \frac{12}{cot\:60} → 12\sqrt{3} = EC$

OR

$\displaystyle tan\:60 = \frac{EC}{12} → 12tan\:60 = EC → 12\sqrt{3} = EC$

Now that you have solved for EC, you can now add it to your original 10 metres to get $\displaystyle 10 + 12\sqrt{3}$ metres. As a decimal, you would get $\displaystyle 30,78460969...$ metres. You can go ahead and round this off if necessary.

** The reason why the cotangent [or tangent] ratio was used was because EA is equivalent to DB by the definition of a rectangle. It has two pairs of parallel and congruent sides with four right angles. Plus, that is the adjacent side of the triangle, while EC is the opposite side of the triangle, so we knew our ratios were correct.

I am joyous to assist you at any time.

8 0

2 years ago

A waiter receives tips from each customer. On average, the tip is 15% of the customer’s bill. At this rate, which of the followi

Lelechka [254]

Answer:

C) $12.00

Step-by-step explanation:

Take the price of the bill

78.20

Find 10 %

78.20 * .1

7.82

Take half ( which is 5%)

3.91

Add the two amounts together

7.82+3.91

11.73

Rounding to the nearest dollar

12.00

Round the bill to 80.00

Take 15%

80 * .15

12.00

4 0

3 years ago

The sum of three numbers is 96. The third number is 6 less than the first. The second number is 3 times the third. What are the

11Alexandr11 [23.1K]

Let the first number be x.

Third number = x - 6

Second number = 3(x - 6) = 3x - 18

Sum of the numbers = 96

x + 3x - 18 + x - 6 = 96

5x -24 = 96

5x = 120

x = 24

Thus,

The first number is 24. The second number is 54. The third number is 18.

6 0

3 years ago

Which function is a linear function a. 1-3x^2 b. y+7=5x c. x^3 + 4 = y d. 9(x^2-y) = 3 e.y-x^3=8

FrozenT [24]

Answer:

b. y+7=5x

Step-by-step explanation:

a. 1-3x^2 is a quadratic

b. y+7=5x is a linear function: y = 5x - 7

c. x^3 + 4 = y is a cubic function

d. 9(x^2-y) = 3 is a quadratic function

e.y-x^3=8 is a cubic function

3 0

3 years ago

Find the value of x if B is the midpoint of AC, AB = 2x + 9 and BC = 37.

Leno4ka [110]

Answer:

Step-by-step explanation:

B is the midpoint of AC, in other words it is the halfway point.

So A to B should be equal to B to C

Our expression is:

2x + 9 = 37

Subtract 9

2x = 28

Divide by 2

x = 14

5 0

3 years ago

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