Rates and variations questions | form three Basic Mathematics

Juma bought motor vehicle spare parts from Japan worth 5,900,000 Japanese Yen. When he arrived in Tanzania he was charged custom duty of 25% on the spare parts. If the exchange rates were as follows:

1 US dollar = 118 Japanese Yen

1 US dollar = 76 Tanzania Shillings

Calculate the duty he paid in Tanzania shillings.

The distance of the horizon d km varies as the square root of the height h m of the observer above sea level. an observer at a height of 100m above sea level sees the horizon at a distance of 35.7km.

Find ;

1. the distance of the horizon from an observer 70m above sea level.
2. an equation connecting d and h.

The value V of a diamond is proportional to the square of its weight W. It is known that a diamond  weighing 10grams is worth shs. 200,000/=.

1. Write down an expression which relates V and W.
2. Find the value of a diamond weighing 30 grams.
3. Find the weight of a diamond worth shs.5,000,000/=

A variable “a” varies directly as “b” and inversely as the square root of “c”. If a=0.2 when b=4 and c=100, find the value of a when b=16 and c=64.

If n*m=(a+m)²-m, find the value of (3*1)*2.

The operator * is defined as a*b=b²-a. Find the value of 1*(3*2).

If it is known that x:y=5:1, find the value of

Given that p varies directly proportional to q but inversely proportional to r and that, when p=35, q=7 and r=6. Find the value of p when q=2 and r=5.

If a*b= (a²-2b)b, find the :

1. 3*2
2. n if 4*n=0.

If y varies inversely as and x is multiplied by a. What is the ratio of the first y to the second y?.