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At 8:15 Bonita left her house to the airport at an average speed of R65km/h. At 9:00 her boyfriend Bernard left Bonita's house and followed her path at an average speed of 104km/h. Bonita and Bernard arrived at the airport at exactly the same time. A linear relationship exist between the time and the distance travelled. The time is dependent on the number of kilometers travelled. Determine the time they arrived at the airport

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Using Laplace transformers solve du/dt=d²u/dx², x>0 ,t>0 with the condition U(0,t)=1,u(x,0)=0

Using the method Laplace of separation of variables, solve du /dt=d²u/dx², u(0,t)=0, u(4,t)=0, u(x,0)=sin3x

A piece of lead falls from a height of 100 meters on a fixed non _ conducting slad which brings it to rest. Show that it is temperature immediately 7.5°c, knowing that the specific heat of lead is 0.13 J/g°c.)

2) The extent to which an individual can exercise power can be viewed as a function of the dependency relationship that exists between parties. If B depends on A (for knowledge, income resources, material resources, information e.t.c) then A is in a position to exercise influence over B. Represent this mathematically?

The Fernandos bought a 55” LED Television. It had a cash prize of Php 98,700. They agreed to pay for it in six (6) months with monthly payments. If the carrying charge was Php 7,800 what was their installment payment?

A cart travels continuously around a circular track with a constant acceleration. The track has a length of 10km.

At a specific time, t = 0, its position is measured.

It takes half an hour for the cart to complete one full lap of the track.

It takes two hours (from time t = 0) for the cart to complete ten full laps of the track. The following formula describes this situation

s = u0t + a t^2 /2

   where

• s is the displacement, measured in km

• u0 is the velocity of the cart when t = 0, measured in kmh-1

• t is the time taken, measured in hours

• a is the acceleration of the cart, measured in kmh-2

a) Use the information about the position of the cart after half an hour to write a formula linking u0 and a.

b) Use the information about the position of the cart after two hours to write another formula linking u0 and a.

c) Use your equations to find the initial velocity of the cart and its acceleration.

9 Water flows through a pipe AB 1.2m diameter at 3m/s and then passes through a pipe BC of diameter 1.5m. At C, the pipe branches. Branch CD is 0.8m in diameter and carries one third of the flow in AB. The flow velocity in branch CE is 2.5m/s. find the volume rate of flow in AB, the velocity in BC, the velocity in CD and diameter of CE

An inductance of L Henrys and a resistance of 8 ohms are connected in 

series with EMF of 100 Volts. If the current is initially zero and is equal to 18

amperes after 1 second. Find L and find the current after 0.2 s.