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c. \( 4,3 x+12=33-5,7 x \)
Algebra Dec 20, 2024
Choose one correct answer to each question. An object causes a strong force of gravity. What must the large size large mass small size small mass Which of these objects has the largest mass in the Solar System? Earth Jupiter Sun Neptune
Physics Dec 14, 2024
Solve for \( x \) : (a) \( 10^{x} \cdot 9^{x}=1000 \) (b) \( 10^{x} \cdot 9^{2 x}=1000 \)
Algebra Dec 14, 2024
The function \( y(t) \) is given by \( y=\mathrm{e}^{t} \) (a) Calculate values of \( t \) such that \( y \) is (i) 1 , (ii) 2 , (iii) 4 , (iv) 8 . (b) Show that if \( t \) is increased by \( \ln 2 \) then the value of \( y \) doubles. (c) A function \( z(t) \) is given by \[ z=\mathrm{e}^{t} \quad k>0 \] Find the increase in the value of \( t \) which will result in the value of \( z \) doublin
Calculus Dec 14, 2024
The function \( y(t) \) is given by \( y=\mathrm{e}^{t} \) (a) Calculate values of \( t \) such that \( y \) is (i) 1 , (ii) 2 , (iii) 4 , (iv) 8 . (b) Show that if \( t \) is increased by \( \ln 2 \) then the value of \( y \) doubles. (c) A function \( z(t) \) is given by
Calculus Dec 14, 2024
Plot the graph of each of the following functions and determine their domains and ranges: (a) \( f(x)=2 x^{2}-8 \) (b) \( g(x)=3 x+5,-1<x \leq 4 \) (c) \( h(x)=\left\{\begin{array}{ll}x^{2} & x>0 \\ 2, & x=0 \\ 1-x, & x<0\end{array}\right. \)
Pre Calculus Dec 13, 2024
The lowest common multiple (LCM) of 4 and 6 is 12 .
Arithmetic Dec 13, 2024
Q8. Graphically, approximate the solutions of (a) \( e^{\frac{x}{3}}=2 e^{-x}, \quad \) (b) \( 4-\ln (2 x)=e^{x} \). [The End]
Pre Calculus Dec 13, 2024
Growth of a bacteria population \( B(t) \) (in millions), at time \( t \) (hours), follows the logisic growth \[ B(t)=\frac{4}{1+7 e^{-t}}, \quad t \geq 0 \] (a) Sketch the graph of the bacteria population verses time, for the first eight hours. (b) What is the initial population size? (d) What value does the bacteria population approach after large time?
Biology Dec 13, 2024
Write \( A=-2 \sqrt{27}+4 \sqrt{12}-\sqrt{3^{3}} \) in the formof a \( \sqrt{b} \) where \( a \) and \( b \) are natural numbers:
Pre Algebra Dec 10, 2024
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