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A point particle is travelling in a circular path with variable speed. If its



velocity at time t seconds is v = (2t + 1)θˆ:



a. What is the tangential component of acceleration at any time t ?



b. What is the centripetal acceleration at any time t ?



c. What the acceleration of the particle at any time t? Your answer should



look like a = acentriˆr + atan ˆθ, where acentri and atan are scalars which



represent the centripetal and tangential components, respectively, of



the total acceleration a.

The present capital structure is as follows;







2 000 000 ordinary shares with a par value of R1.00 per share. These shares are







currently trading at R2.50 per share and the latest dividend paid is 40 cents. An







average dividend growth of 9% is maintained.







1 500 000 8% R2.00 preference shares, with a market value of R1.80 per shareR10 000 000 non- distributable reserves R2 000 000 7% debentures due in 6 years time and the current yield to maturity is


10%, and R1 000 000 15% bank loan.


Additional information:


The company has a beta of 2.1 a risk free rate of 7% and a return of market of 16%.


The company tax rate is 30%.


Required



3.1Calculate the adjusted weighted average cost of capital using capital asset pricing model as the cost of equity.(13 marks)

Find the limit f(x),if it exists.sketch the graph of f(x).

Limit x approaching zero f(x),where f(x)=2-x,x less than or equal zero,. x+2, x>0


Explain the usefulness of central limit theorem in solving problems involving sampling

Three lottery tickets for first, second, and third prizes


Two of the five (5) foreign automobiles from an overseas shipment have slight paint blemishes. If an agency receives three (3) of these automobiles at random, list the elements of the sample space 𝑆 using the letters B and N for “blemished” and “non-blemished”, respectively. For each sample point, assign a value 𝑥 of the random variable 𝑋 representing the number of automobiles purchased by the agency with paint blemishes.


Three lottery tickets for first, second, and third prizes are drawn from a group of 45 tickets

the mean weight of baggage of 25 passengers from USA bound for the Philippines is 31.8 kilos with a variance of 16. test the claim that the population mean baggage weight is equal to 30 kilos at 0.01 level of significance. Assume that the population is normally distributed. The t value is 2.492






paul is standing at the top of an escalator and lily is standing at the bottom. Their vertical distance is 4.5 m and the angle of elevation of paul from lily is 20 degrees. Find the horizontal distance between them


The Boxing Fund must pay Daniel an old boxer, R18 000 every three months indefinitely as compensation.Money is worth 11,4% per year, compounded quarterly.

The opening balance of this fund is approximately


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