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Questions in mathematics

[Jawaban] $f(x)=x$ $g(x)=1$ What is the domain of $\left(\frac{g}{f}\right)(x) ?$ A. $x \neq 0$ B. $x \neq-1$ C. All real numbers

[Jawaban] If [tex]f(x)=x+2[/tex] and [tex]g(x)=x^2-3[/tex], find: i) [tex]f(g(x))[/tex] ii) [tex]g(f(x))[/tex]

[Jawaban] If two solids have equal cross-sectional areas at every level parallel to the respective bases, then the two solids have equal volume. The two shared solids both have a height of [tex]$2 r$[/tex] units. At every level, the areas of the cross sections of both solids equal [tex]$\pi(r^2-b^2)$[/tex]. Cross-section area [tex]$=\pi r^2-\pi b^2 =\pi(r^2-b^2)$[/tex] Which of the following can be derived by writing an expression that represents the volume of: A. one cone within the cylinder. B. the two cones within the cylinder. C. the solid between the two cones and the cylinder. D. the cylinder.

[Jawaban] The third term of a linear sequence is 16 and its fifth term is 34. Find the second term.

[Jawaban] Given the numbers 113.79, 115, 117.79, 37.66, and 86.79, arrange them in ascending and descending order.

[Jawaban] Find the value of the remaining trigonometry functions if sec θ = 3/7 and θ ∈ IV.

[Jawaban] Use pen and paper to work out the answer to $124.62+13.81$

[Jawaban] The function $c(n)$ below relates the number of bushels of apples picked at a pick-your-own orchard to the final cost for the apples. It takes as input the number of bushels of apples picked after paying an entry fee to an orchard, and it returns as output the cost of the apples (in dollars). $c(n)=10 n+20$ Which equation below represents the inverse function $n(c)$, which takes the cost of the apples as input and returns the number of bushels picked as output? A. $n(c)=\frac{c-20}{10}$ B. $n(c)=\frac{c+20}{10}$ C. $n(c)=\frac{c+10}{20}$ D. $n(c)=\frac{c-10}{20}$

[Jawaban] If [tex]$f(x)=6 x-1$[/tex] and [tex]$g(x)=\frac{x+1}{6}$[/tex], which expressions can be used to verify [tex]$g(x)$[/tex] is the inverse of [tex]$f(x)$[/tex]? Check all that apply. [tex]$6(6 x-1)-1$[/tex] [tex]$\frac{(6 x-1)+1}{6}$[/tex] [tex]$6\left(\frac{x+1}{6}\right)-1$[/tex] [tex]$\frac{\left(\frac{x+1}{6}\right)+1}{6}$[/tex] [tex]$\frac{x+1}{6}+6 x-1$[/tex]

[Jawaban] Which is the graph of $y=5 \log (x+3)$?