91Ó°ÊÓ

Find a number \(d\) such that the line containing the points \((d, 4)\) and (-2,9) has slope -3 .

Find the asymptotes of the graph of the given function \(\mathrm{r}\). $$ r(x)=\frac{6 x^{6}-7 x^{3}+3}{3 x^{6}+5 x^{4}+x^{2}+1} $$

Use the following information: If an object is thrown straight up into the air from height H feet at time 0 with initial velocity \(V\) feet per second, then at time \(t\) seconds the height of the object is \(h(t)\) feet, where $$h(t)=-16.1 t^{2}+V t+H$$ This formula uses only gravitational force, ignoring air friction. It is valid only until the object hits the ground or some other object. Suppose a ball is tossed straight up into the air from height 4 feet. What should be the initial velocity to have the ball reach its maximum height after 2 seconds?

Evaluate the given expression. Do not use a calculator. $$ \left(\frac{5}{4}\right)^{-3} $$

Suppose the tuition per semester at Euphoria State University is $$\$ 525$$ plus $$\$ 200$$ for each unit taken. (a) What is the tuition for a semester in which a student is taking 10 units? (b) Find a linear function \(t\) such that \(t(u)\) is the tuition in dollars for a semester in which a student is taking \(u\) units. (c) Find the total tuition for a student who takes 12 semesters to accumulate the 120 units needed to graduate. (d) Find a linear function \(g\) such that \(g(s)\) is the total tuition for a student who takes \(s\) semesters to accumulate the 120 units needed to graduate.

Write the indicated expression as \(a\) polynomial. $$ (p(x))^{2} $$

Find the asymptotes of the graph of the given function \(\mathrm{r}\). $$ r(x)=\frac{9 x+5}{x^{2}-x-6} $$

The numbers are too large to be handled by a calculator. These exercises require an understanding of the concepts. Write \(9^{3000}\) as a power of 3 .

The numbers are too large to be handled by a calculator. These exercises require an understanding of the concepts. Write \(27^{4000}\) as a power of 3 .

Write the indicated expression as \(a\) polynomial. $$ (q(x))^{2} $$