Questions in mathematics

Questions in mathematics

📝 Answered - Find the arc length of the curve defined by the parametric equations [tex]x(t)=5 e^{2 t}[/tex] and [tex]y(t)=3 e^{3 t}[/tex] from [tex]0.7 \leq t \leq 1.5[/tex]. Round your answer to the nearest hundredth. [tex]s \approx \square[/tex]

📝 Answered - The formula for finding the volume of a pyramid is [tex]v=b h / 3[/tex]. What formula should you use to find the altitude [tex]h[/tex]? A. [tex]h=3 b / v[/tex] B. [tex]h=v / 3 b[/tex] C. [tex]h=3 b v[/tex] D. [tex]h=3 v / b[/tex]

📝 Answered - $\begin{array}{r}8 x+y=4 \\ -2 x-8=y\end{array}$

📝 Answered - Let [tex]$b_n$[/tex] be an infinite sequence of zeros and ones. What is the largest possible value of [tex]$x=\sum_{n=1}^{\infty} \frac{b_n}{2^n}$[/tex]?

📝 Answered - Convert the following mass into kilograms: a) 38475 Vg

📝 Answered - Rationalize the denominator and simplify: [tex]$\frac{4-\sqrt{3}}{\sqrt{5}}$[/tex]

📝 Answered - Simplify the expression below and write it as a single logarithm: $3 \log (x+4)+2 \log (x-7)-5 \log (x-2)-\log \left(x^2\right)$ A. $\log \left(\frac{(x+4)^3(x-2)^5}{(x-7)^2 x^2}\right)$ B. $\log \left(\frac{(x+4)^3(x-7)^2}{(x-2)^{-5} x^{-2}}\right)$ C. $\log \left(\frac{x^2(x+4)^3(x-7)^2}{(x-2)^5}\right)$ D. $\log \left(\frac{(x+4)^3(x-7)^2}{(x-2)^5 x^2}\right)$

📝 Answered - Which is the correct solution to the cubic equation, $\sqrt[3]{2 x-3}=-3$? A. 12 B. 6 C. -12 D. -6

📝 Answered - What are the solutions of the quadratic equation $(x-8)^2-13(x-8)+30=0$? Use $u$ substitution to solve. A. $x=-11$ and $x=-18$ B. $x=-2$ and $x=5$ C. $x=2$ and $x=-5$ D. $x=11$ and $x=18

📝 Answered - Simplify: [tex]2 \log _2 3+\log _2 x-3 \log ^2[/tex]