Find the lateral (side) surface area of the cone generated by revolving the line segment \( y=\frac{9}{2} x, 0 \leq x \leq 3 \), about the \( x \)-axis. Check your answer with the following geometry formula. Lateral surface area \( =\frac{1}{2} \times \) base circumference \( \times \) slant height Set up the integral that gives the surface area of the cone. S \( =\int_{0} \mathrm{dx} \) (Type exact answers, using \( \pi \) as needed.) The lateral surface area is \( \square \). (Type an exact answer, using \( \pi \) as needed.)

Use synthetic division to find the result when \( x^{4}-x^{3}-4 x^{2}-5 x-3 \) is divided by \( x+1 \). If there is a remainder, express the result in the form \( q(x)+\frac{r(x)}{b(x)} \).

Choose the correct equation below which is set up such that the values of \( a, b \), and A. \( 6 x^{2}-29 x-5=0 \) \( x^{2}+x=2 \) C. \( (5 x+6)^{2}=7 \) \( (6 x-1)(x-2)=0 \) Dolve the equation found in the previous step. The solution set is \( \{ \). (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use inte

Question Find the equation of a line parallel to \( y=2 \) that contains the point \( (4,1) \). Write the equation in slope-intercept form. Provide your answer below: \[ y=\square \]

Find the equation of the line with slope \( \frac{1}{2} \) and \( y \)-intercept \( (0,2) \). Provide your answer below: \[ y=\square \]

A. Calcium nitrate-make an evidence based argument for why acid rain would cause the calcium carbonate in the marble to slowly break down and wash away over time when calcium nitrate is produced.