All categories

3 years ago

Bearings Problem Solving Question:

Mathematics

1 answer:

Lynna [10]3 years ago

7 0

9514 1404 393

Answer:

a) 123.4°

b) 3.3 km

Step-by-step explanation:

In (N, E) coordinates, Boat 1 is located relative to the lighthouse at ...

2(cos(60°), sin(60°)) = (1.0, 1.732) . . . . . km

Boat 2 is located at ...

3(cost(340°), sin(340°)) = (2.819, -1.026) . . . . . km

So, relative to Boat 2, Boat 1 is located at ...

(1, 1.732) -(2.819, -1.026) = (-1.819, 2.758) . . . . . km

This is at a bearing of ...

arctan(2.758/-1.819) = 123.4°

and a distance of ...

√(1.819² +2.758²) ≈ 3.304 . . . . . km

a) Boat 2 would need to travel on a bearing of 123.4°.

b) Boat 2 would need to travel 3.3 km.

_____

Additional comment

We use (North, East) coordinates so we don't have to do the mental gyrations necessary to translate to and from (E, N) coordinates. The latter would correctly orient a map relative to the X-Y Cartesian plane. The former are equivalent to flipping the map over and looking at it from the back side. This is a "rigid transformation", so angles and distances remain unchanged.

You might be interested in

Helen had $330 in her savings account when Vince opened a savings account with zero dollars.

Nastasia [14]

I think the answer is 30x+330>50x

Step-by-step explanation:

for the option A it was slightly changed,

cause the $30 was deposited by helen not Vince.

so check that well

4 0

3 years ago

What is the solution set for this inequality?

olasank [31]

Step-by-step explanation:

-9x+18<-27
-9x+18-18<-27-18
-9x<-45
x>-45/-9
x>5

6 0

2 years ago

On Monday Godswill ate some grapes. On Tuesday he

garri49 [273]

Answer: He ate 8 grapes on Monday.

Step-by-step explanation:

Let be "x" the number of grapes Godswill ate on Monday.

You know that he ate 6 more grapes than he had on Monday. This can be expressed with:

$x+6$

Since each day that week, he ate 6 more grapes than the day before and he realized on Friday he had eaten a total of 100 grapes this week, you can write the following expression and solve for "x":

$x+(x+6)+(x+12)+(x+18)+(x+24)=100\\\\5x+60=100\\\\x=\frac{40}{5}\\\\x=8$

5 0

3 years ago

Read 2 more answers

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college

hammer [34]

Answer:

$s^2_p = \frac{9*0.3^2 +9*0.4^2}{10+10-2}=0.125$

$s_p =\sqrt{0.125}=0.354$

$(2.7 -2.4) - 2.1*0.354\sqrt{\frac{1}{10}+\frac{1}{10}}=-0.032$

$(2.7 -2.4)+ 2.1*0.354\sqrt{\frac{1}{10}+\frac{1}{10}}=0.632$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data given

$\bar X_M = 2.7$ represent the sample mean for men