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slega [8]
2 years ago
12

Gwen is two years older than her cousin Julie. Aunt Jess is twice as old as uncle Mark. Julie’s age is 26 less than the sum of a

unt Jess and uncle Mark’s ages. The twins are 2 years younger than one-third Gwen’s age. Mark celebrated his 8th birthday at the reunion 10 years ago
Mathematics
1 answer:
Keith_Richards [23]2 years ago
3 0
If mark celebrated his 8th birthday 10 years ago then mark is 18 years old. Jess is twice as old as mark so Jess is 36 years old. Julie is 26 less than mark and jess combined so Julie is 28 years old. Gwen is two years older than Julie so Gwen is 30 years old. The twins are 2 less than 1/3 of gwen so the twins are 8 years old
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8 0
3 years ago
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
Zigmanuir [339]

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.

7 0
3 years ago
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stepan [7]
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8 0
3 years ago
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irina1246 [14]

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Step-by-step explanation:

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Answer:

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