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belka [17]
3 years ago
13

An aeroplane X whose average speed is 50°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then

changes its course and flies on a bearing 1200 to an airstrip A. Another aeroplane Y leaves kano airport at 10.00am and flies on a straight course to the airstrip A. both planes arrives at the airstrip A at 11.30am. calculate the average speed of Y to three significant figures. the direction of flight Y to the nearest degree

Mathematics
1 answer:
Zigmanuir [339]3 years ago
7 0

Answer:

(a)123 km/hr

(b)39 degrees

Step-by-step explanation:

Plane X with an average speed of 50km/hr travels for 2 hours from P (Kano Airport) to point Q in the diagram.

Distance = Speed X Time

Therefore: PQ =50km/hr X 2 hr =100 km

It moves from Point Q at 9.00 am and arrives at the airstrip A by 11.30am.

Distance, QA=50km/hr X 2.5 hr =125 km

Using alternate angles in the diagram:

\angle Q=110^\circ

(a)First, we calculate the distance traveled, PA by plane Y.

Using Cosine rule

q^2=p^2+a^2-2pa\cos Q\\q^2=100^2+125^2-2(100)(125)\cos 110^\circ\\q^2=34175.50\\q=184.87$ km

SInce aeroplane Y leaves kano airport at 10.00am and arrives at 11.30am

Time taken =1.5 hour

Therefore:

Average Speed of Y

=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)

(b)Flight Direction of Y

Using Law of Sines

\dfrac{p}{\sin P} =\dfrac{q}{\sin Q}\\\dfrac{125}{\sin P} =\dfrac{184.87}{\sin 110}\\123 \times \sin P=125 \times \sin 110\\\sin P=(125 \times \sin 110) \div 184.87\\P=\arcsin [(125 \times \sin 110) \div 184.87]\\P=39^\circ $ (to the nearest degree)

The direction of flight Y to the nearest degree is 39 degrees.

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We know that

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(x – 3)² = 7²--------> <span>will take the square root of each side
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then

x-3=7--------> x=10
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6 0
3 years ago
7. If F(x) = f(g(x)), where f(-2) = 8, f'(-2) = 4, f'(5) = 3, g(5)=-2, gʻ(5) = 6.. Find F'(5) <br>​
serious [3.7K]

Answer:

I'm going to lay this out in a chart so it's a little easier to see:

F(x) = f(g(x))

x | f (x) | f ' (x) | g (x) | g ' (x)

--------------------------------------

-2 | 8 | 4 |

5 | | 3 | -2 | 6

Remember the chain rule, which says

(f (g (x))) ' = g ' (x) f ' (g (x))

When they ask for F ' (5), they are asking for (f (g (x))) ' when x = 5.

Using the chain rule, that's

F ' (5) = g ' (5) f ' (g (5))

We can simplify using the numbers provided.

F ' (5) = (6) f ' (-2)

F ' (5) = (6) (4)

F ' (5) = 24

I hope that helps!

by jannat <33

7 0
2 years ago
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Which expression is equivalent to ? Assume.
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Answer:

2. -2x^{8}y^{18}  

Step-by-step explanation:  

We have been given an expression \frac{10x^{6}y^{12}}{-5x^{-2}y^{-6}} and we are asked to find equivalent expression to our given expression.

Using fraction rule \frac{a}{-b} =-\frac{a}{b} we can write our expression as: -\frac{10x^{6}y^{12}}{5x^{-2}y^{-6}}. 

Upon dividing 10 by 5 we will get,

-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}      

Upon using exponent property for quotient (\frac{a^{m}}{a^{n}} =a^{(m-n)}) we will get,  

-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}=-2x^{(6--2)}y^{(12--6)}    

-2x^{(6+2)}y^{(12+6)}

-2x^{8}y^{18}        

Therefore, our expression simplifies as -2x^{8}y^{18} and 2nd option is the correct choice.



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3 years ago
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Please help asap
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A cotton candy vendor has 10 cones of blue cotton candy to sell. If the blue cotton candy is 25% of the total number of cones, h
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Answer: 40 cones


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10 = 25%
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