91Ó°ÊÓ

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

Suppose \(p(x)=x^{2}+5 x+2\) \(q(x)=2 x^{3}-3 x+1, \quad s(x)=4 x^{3}-2\) Write the indicated expression as a polynomial. $$ (p s)(x) $$

For Exercises \(5-8\), find the asymptotes of the graph of the given function \(r .\) $$ r(x)=\frac{6 x^{6}-7 x^{3}+3}{3 x^{6}+5 x^{4}+x^{2}+1} $$

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 .

For Exercises \(5-8\), find the asymptotes of the graph of the given function \(r .\) $$ r(x)=\frac{3 x+1}{x^{2}+x-2} $$

For Exercises 1-12, 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 5 feet. What should be the initial velocity to have the ball reach a height of 50 feet?

Suppose \(p(x)=x^{2}+5 x+2\) \(q(x)=2 x^{3}-3 x+1, \quad s(x)=4 x^{3}-2\) Write the indicated expression as a polynomial. $$ (p(x))^{2} $$

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.

For Exercises 1-12, 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. S 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 a height of 70 feet?

Suppose \(p(x)=x^{2}+5 x+2\) \(q(x)=2 x^{3}-3 x+1, \quad s(x)=4 x^{3}-2\) Write the indicated expression as a polynomial. $$ (q(x))^{2} $$