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Naya [18.7K]
3 years ago
13

an aircraft flies from its base 200 km on a bearing 162 degree, then 350km on a bearing 260 degree and then returns directly to

base. Calculate the length and bearing of the return journey

Mathematics
1 answer:
Allushta [10]3 years ago
4 0
Solution is attached

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Plz help!!<br> Consider the given right triangle.
aalyn [17]

Answer:

b = 8

c = 16

Step-by-step explanation:

From the given right triangle,

a = 8\sqrt{3}, m(∠B) = 30°

By applying sine rule in the given triangle,

cos(B) = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

cos(B) = \frac{BC}{AB}

cos(30°) = \frac{8\sqrt{3}}{c}

\frac{\sqrt{3} }{2}= \frac{8\sqrt{3} }{c}

c = 16

Further we apply tangent rule,

tan(B) = \frac{\text{Opposite side}}{\text{Adjacent side}}

tan(30°) = \frac{b}{a}

\frac{1}{\sqrt{3}}=\frac{b}{8\sqrt{3} }

b = 8

4 0
2 years ago
Jane is is charge of making a banner for the basketball game this Saturday. She measures how long the banner is before painting
RSB [31]

Answer:

The measurement which Jane finds to be 10 meters is the length of the banner.

Step-by-step explanation:

The measurement of 10 meters which Jane found after measuring how long the banner is before painting is the LENGTH of the banner.

This is clear from the unit of what she finds (meters). It only indicates the measurement of one part of the banner, even though a banner has two parts, the length and width.

It is possible to find the AREA, or PERIMETER, or LENGTH.

But what she finds is the LENGTH of the banner. If it was Area or Perimeter, the unit would have been square meters.

7 0
3 years ago
A small country had a population of 2,254,000 people in the year 2012. If the population grows steadily
Anuta_ua [19.1K]

Step-by-step explanation:

year 2012 population = 2,254,000*3.5%

= 78.89

each year up to 2020

so 2020 - 2012 =8

78.89*8 = 631

total population at end of 2020 =2,254,000 + 631

= 2,254631

6 0
2 years ago
Write 0.452 as a percent. Round to the nearest whole number.
makkiz [27]

Answer:

45%

Step-by-step explanation:

8 0
3 years ago
Use mathematical induction to show that 4^n ≡ 3n+1 (mod 9) for all n equal to or greater than 0
cestrela7 [59]
When n=0, you have

4^0=1\equiv3(0)+1=1\mod9

Now assume this is true for n=k, i.e.

4^k\equiv3k+1\mod9

and under this hypothesis show that it's also true for n=k+1. You have

4^k\equiv3k+1\mod9
4\equiv4\mod9
\implies 4\times4^k\equiv4(3k+1)\mod9
\implies 4^{k+1}\equiv12k+4\mod9

In other words, there exists M such that

4^{k+1}=9M+12k+4

Rewriting, you have

4^{k+1}=9M+9k+3k+4
4^{k+1}=9(M+k)+3k+3+1
4^{k+1}=9(M+k)+3(k+1)+1

and this is equivalent to 3(k+1)+1 modulo 9, as desired.

3 0
3 years ago
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