Question #160715

In a right-angled triangle the altitude to the hypotenuse is 8 cm high. The hypotenuse is 20 cm long. Find the lengths of the segements of the hypotenuse (Hint: let the length of the segment be x.)




In a right-angled triangle, the median to the hypotenuse is 6.4 cm. What is the length of the hypotenuse?




A bridge crosses a river at an angle of 60°. If the length of the bridge is 170 m, what is the width of the river?




If you deposit 6 500 FRW com-pounded monthly into an account paying 8% annual interest compounded monthly, how much money will be in the account after 7 years?




If you deposit 8 000 FRW into anaccount paying 7% annual interest compounded quarterly, how long will it take to have 12 400 FRW in the account?




A car hire company with 24 cars uses 2 940 litres of petrol in 5 days. How long would 4 116 litres of petrol last if the company had 28 cars and the consumption rate does not change?




A new car falls in value by 30% a year. After a year, it is worth 84 000 FRW. Find the price of the car when it was new.       



1
Expert's answer
2021-02-24T06:45:01-0500

Let x=x= the length of the first segement of the hypotenuse. Then the length of the second segement of the hypotenuse is 20x.20-x.


82=x(20x),0<x<208^2=x(20-x), 0<x<20

x220x+64=0x^2-20x+64=0

(x4)(x16)=0(x-4)(x-16)=0

x1=4,x2=16x_1=4, x_2=16

The length of the first segement of the hypotenuse is 4 cm.

The length of the second segement of the hypotenuse is 16 cm.



In a right-angled triangle the middle of the hypotenuse is the center of the the circumscribed circle. Then hypotenuse is twice the median to the hypotenuse


26.4=12.82\cdot6.4=12.8

 The length of the hypotenuse is 12.8 cm.



If a bridge crosses a river at an angle of 60° with the river bank, then


sin60°=widthlength\sin 60\degree=\dfrac{width}{length}

width=length32width=length\cdot\dfrac{\sqrt{3}}{2}

width=853 mwidth=85\sqrt{3}\ m



FV=P(1+rn)ntFV=P(1+\dfrac{r}{n})^{nt}

FV=6500(1+0.0812)12(7)=11358.24FV=6500(1+\dfrac{0.08}{12})^{12(7)}=11358.24

11358.24 FRW will be in the account after 7 years.




FV=P(1+rn)ntFV=P(1+\dfrac{r}{n})^{nt}

12400=8000(1+0.074)4(n)12400=8000(1+\dfrac{0.07}{4})^{4(n)}

(1.0175)4(n)=1.55(1.0175)^{4(n)}=1.55

4n=ln(1.55)ln(1.0175)4n=\dfrac{\ln(1.55)}{\ln(1.0175)}

4n=25.26164n=25.2616

n=6.3154n=6.3154

It will take 6.3154 years to have 12 400 FRW in the account.




2940245=24.5\dfrac{2940}{24\cdot5}=24.5

n=411624.528=6n=\dfrac{4116}{24.5\cdot28}=6

A car hire company with 28 cars uses 4 116 litres of petrol in 6 days.




8400010.3=120000\dfrac{84000}{1-0.3}=120000

The price of the car when it was new was 120 000 FRW.



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