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salantis [7]
3 years ago
9

There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

B, 7 miles away. What is the bearing needed to navigate from island B to C? Round to the nearest degree
Mathematics
1 answer:
Nostrana [21]3 years ago
8 0

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta (1)

Where:

AC - The distance from A to C, measured in miles.

AB - The distance from A to B, measured in miles.

BC - The distance from B to C, measured in miles.

\theta - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta

\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}

\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right) (2)

If we know that BC = 7\,mi, AB = 8\,mi, AC = 5\,mi, then the bearing from island B to island C:

\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]

\theta \approx 38.213^{\circ}

The bearing needed to navigate from island B to island C is approximately 38.213º.

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If a person bikes 6 miles in 15 minutes, how far can she bike in 1.5 hours?
Natalka [10]

Answer:

36\:miles

Step-by-step explanation:

There is <em>one-and-a-half</em> <em>hour</em> in <em>ninety</em><em> </em><em>minutes</em>,<em> </em>so multiply 6 by 15 to get 90, then whatever is done to the bottom is also done to the top, so you <em>square</em> 6 to get 36.

I am joyous to assist you anytime.

8 0
3 years ago
What is the value of x?<br><br> Enter your answer, as a decimal, in the box.
Katarina [22]

Answer:

x=50.6cm

Step-by-step explanation:

Triangle MAB is similar to triangle MNP

Since the triangles are similar, the corresponding ratios are in the same proportion.

Therefore we can write the relation;

\frac{|MB|}{|MP|}=\frac{|MA|}{|MN|}


\frac{x}{72.6}=\frac{46.2-14}{46.2}


This implies that;

\frac{x}{72.6}=\frac{32.2}{46.2}


We multiply both sides by 72.6 to get


\frac{x}{72.6}\times 72.6=\frac{32.2}{46.2}\times72.6


\Rightarrow x=50.6


Hence the value of x is 50.6 cm



8 0
3 years ago
Read 2 more answers
1. A football team gains 2 yards on the first play,
Ilya [14]

Option C

The football team had a overall loss of 2 yards

<em><u>Solution:</u></em>

When the team gains yards we use a positive value, and when the team loses yards we use a negative value.

<em><u>Given that, football team gains 2 yards on the first play</u></em>

First play = +2

<em><u>Given that football team loses 5 yards on the second play</u></em>

Second play = -5

<em><u>Given that football team loses 3 yards  on the third play</u></em>

Third play = -3

<em><u>Given that football team gains 4 yards on the fourth play</u></em>

Fourth play = +4

Put the yards from four plays together, we get

⇒ 2 -5 -3 + 4

Let us simplify

⇒ -3 -3 + 4 = -6 + 4 = -2

So, -2 represents loss of two yards (since negative value indicates loss)

3 0
3 years ago
What is the inverse of the function f(x) = 2x – 10?
Nadusha1986 [10]

Answer:

f⁻¹(x) = (1/2)x +5

Step-by-step explanation:

In y = f(x), swap the variables, then solve for y. The expression you get is f⁻¹(x).

... y = 2x -10

... x = 2y -10 . . . . . . swapped variables

... x +10 = 2y . . . . . add 10

... (1/2)x + 5 = y . . . . divide by 2

... f⁻¹(x) = (1/2)x + 5 . . . . . . rewrite using function notation

6 0
3 years ago
Find the volume of the<br> triangular prism.<br> 3.6 cm<br> 5.4 cm<br> 9 cm
MrMuchimi

Answer:

174.96cm2

Step-by-step explanation:

V=lbh

=3.6×5.4×9

=174.96cm2

I don't knowif you want it in milliliters or litres so here are both of them

milliliters = 174.96

litres = 0.17496

6 0
2 years ago
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