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A particle start from rest and moves in a straight Line on a smooth horizontal surface.The speed of the particle given that V=e^2-1/4 when t=1.Show that V=1/4(e^2t-1)

Forces F1,F3 and F3 act at points with position Vectors r1,r2 and r4 respectively where F1=(3i+5j)N,F2=(2i-4j)N,F3=(-5i-j)N, r1=(i-j)m,r2=(2i+j)m,r3=(-6i+j)m.Show that this system of forces form a couple giving the magnitude of the couple

Rose wants to buy a car on hire purchase for N$75,000.00 at the rate of 11% p.a. repayable using monthly installments for a period of 3 years and 10 months. (No deposit was required). Use the given information to calculate the:

a. Total amount of money expected to be paid to the Hire Purchase Company over the years. (5)

b. Monthly installment to be paid by Rose (5)

Emmerson invests N$100,000.00 on a monthly basis, at the end of each month at an interest rate of

8.5% compounded quarterly.

a) How much will he have after 3.5 years?


b) How much interest does he earn on a monthly basis? (Hint: Calculate the monthly average).(4)

If a closed map F is bijective then its inverse F-1 is a closed map.

If a closed map F is bijective then its inverse F -1 is a closed map.

Given the demand function


and the supply function


Calculate the producer surplus for the supply function.

Say True or False with proof

Q1. If 𝑓(π‘₯) = 2|π‘₯ βˆ’ 1| and 𝑔(π‘₯) = 3π‘₯ βˆ’ 10,

then π‘“π‘œπ‘”(1) = 12.

Q2. (√2, 1,1/2)∈ 𝑸 Γ— 𝒁 Γ— 𝑹.

Q3. The domain of the function f defined by 𝑓(π‘₯)

=√{(3-x)/(x-2)} is R-{2}.

Represent the rational functioο»Ώn f(x)=1/3x-1 using its table values and graph





Show that d is metric on x

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