Question

3 mark for review if $sqrt{s}-3 = 9$, which of the following is a possible value of s? a 12 b 36 c 81 d 144 4 mark for review which of the following is equivalent to the expression $x^{6}y^{-3}z^{\frac{1}{2}}$? a $\frac{x^{6}sqrt{z}}{3y}$ b $\frac{x^{6}sqrt{2z}}{y^{3}}$ c $\frac{6xsqrt{z}}{y^{3}}$ d $\frac{x^{6}sqrt{z}}{y^{3}}$ 5 mark for review the function $f(x)=k^{0.3x}$, where k is a constant, can also be expressed as $f(x)=k^{\frac{bx}{9}}$ for what value of b? a 2.7 b 9.3 c 27 d 30 6 mark for review $sqrt{m^{2}+39}=8$ in the equation above, what is a possible value of m? a 3 b 4 c 5 d 6

Explanation:

3.

Step1: Isolate the square - root term

Given $\sqrt{s}-3 = 9$, add 3 to both sides of the equation: $\sqrt{s}=9 + 3=12$.

Step2: Solve for s

Square both sides of the equation $\sqrt{s}=12$ to get $s=12^{2}=144$.

Recall the negative - exponent rule $a^{-n}=\frac{1}{a^{n}}$ and the fractional - exponent rule $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. So, $x^{6}y^{-3}z^{\frac{1}{2}}=\frac{x^{6}\sqrt{z}}{y^{3}}$.

Since $f(x)=k^{0.3x}=k^{\frac{Bx}{9}}$, then by the property of exponential functions (if $a^{m}=a^{n}$, then $m = n$), we set $0.3x=\frac{Bx}{9}$. Since $x
eq0$ (if $x = 0$, the function is just a constant and we are looking at the general form of the exponential function), we can cancel out $x$ from both sides of the equation. We get $0.3=\frac{B}{9}$. Cross - multiply: $B=0.3\times9 = 2.7$.

Answer:

D. 144

4.