Which of the following has an exact cube root?<br> a. 125<br> b. 49<br> C. 24

A ship leaves port at noon and has a bearing of S29oW. The ship sails at 20 knots. How many nautical miles south and how many na

ira [324]

Answer:

Approximately $58.2\; \text{nautical miles}$ (assuming that the bearing is ${\rm S$29^{\circ}$W}$ .)

Step-by-step explanation:

Let $v$ denote the speed of the ship, and let $t$ denote the duration of the trip. The magnitude of the displacement of this ship would be $v\, t$ .

Refer to the diagram attached. The direction ${\rm S$29^{\circ}$W}$ means $29^{\circ}$ west of south. Thus, start with the south direction and turn towards west (clockwise) by $29^{\circ}$ to find the direction of the displacement of the ship.

The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of $v\, t$ . The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly $29^{\circ}$ .

Since the hypotenuse is of length $v\, t$ , the dashed line segment opposite to the $\theta = 29^{\circ}$ vertex would have a length of:

$\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}$ .

Substitute in $\begin{aligned} v &= 20\; \frac{\text{nautical mile}}{\text{hour}}\end{aligned}$ and $t = 6\; \text{hour}$ :

$\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}$ .

7 0

2 years ago

Which is a factor of 91 multiple choice 7 20 4 or 12

ki77a [65]

Answer:

7

Step-by-step explanation:

Recall that a factor is a number that can divide a number and return a whole number as the quotient.

In this case, 91 / 7 = 13

So 7 is a factor

4 0

3 years ago

Can u help me plz and say how u done it :)

puteri [66]

Answer:

3(2x+7)

=21x+21

this is the answer hope you like it

5 0

3 years ago

Plz can you help me, thank you :)

Pepsi [2]

Answer:

A

c= s^3 AJ / km^2

Step-by-step explanation:

If you plug in this answer in the equation, you cancel out the km^2 and AJ, leaving s^3 = s^3

5 0

3 years ago

a runner is 7/8 mile from the finsh line. she can travel 3/8 mile per minute,how long will it take her to finsh the race

Simora [160]

I hope this helps you

if 3/8 miles per a hour

7/8 miles ? hour

?.3/8=7/8.1

?=7/3

?=2,3333... hour

4 0

3 years ago

Which of the following has an exact cube root? a. 125 b. 49 C. 24