7. Newton's laws of cooling proposes that the rate of change of temperature is proportional to the temperature difference to the ambient (room) temperature. And can be modelled using the equation: \[ \frac{d T}{d t}=-k\left(T-T_{a}\right) \] This can also be written as: \[ \frac{d T}{T-T_{a}}=-k d t \] Where: \( T= \) Temperature of material \( T_{a}= \) Ambient (room) temperature \( k=A \) cooling constant a) Integrate both sides of the equation and show that the temperature difference is given by: ( \( \left.T-T_{a}\right)=C_{o} e^{-k t} \) [ \( C_{o} \) is a constant for this problem]

If \( f(x)=2\left(x^{2}+5\right) \), then \( f(-3)= \) a.) 28 a.t 23 b.) 23 c.) -13 d.) -8

1.4 Gegee: / Given: \( \frac{3}{2} ; 1 ; \frac{7}{10} ; \frac{9}{17} ; \ldots \) Skryf die \( n \) de term van die ry neer in die vorm \( T_{n}=\ldots \) Write down the \( n \)th term of the sequence in the form \( T_{n}= \)

Suppose an account pays \( 6 \% \) interest that is compounded annually. At the beginning of each year, \( \$ 2,000 \) is deposited into the account (including \( \$ 2,000 \) at the start of the first year). What is the value of the account after the tenth total deposit if no withdrawals or additional deposits are made?

What is the constant of proportionality in the equation \( y=2.5 x \) ? constant of proportionality \( =\square \)

Monthly income in Ksh Tax rate in each shilling(\%) \( 0-11421 \) \( 11422-20733 \) \( 20734-30045 \) \( 30046-39357 \) 39358 and above In that year, Leta earned a salary of Ksh 39000 per month. Calculate Leta's income tax per month given that a monthly tax relief of Ksh 868 was allowed.