91Ó°ÊÓ

Simplify the given expressions. Express results with positive exponents only. $$\left(\frac{2 b^{2}}{-y^{5}}\right)^{-2}$$

Solve the given problems.See Exercise 45. Write the following numbers in engineering \(\begin{array}{lll}\text { notation. (a) } 8,090,000 & \text { (b) } 809,000 & \text { (c) } 0.0809\end{array}\).

Perform the indicated divisions. By division show that \(\frac{x^{5}+y^{3}}{x+y}\) is not equal to \(x^{2}+y^{2}.\)

In Exercises \(5-48,\) simplify the given expressions. Express results with positive exponents only. $$\left(\frac{2 b^{2}}{-y^{5}}\right)^{-2}$$

find the indicated values. The efficiency \(E\) of a computer multiprocessor compilation is given by \(E=\frac{1}{q+p(1-q)},\) where \(p\) is the number of processors and \(q\) is the fraction of the compilation that can be performed by the available parallel processors. Find \(p\) for \(E=0.66\) and \(q=0.83\)

Solve the given problems. The resistance in an amplifier circuit is found by evaluating \(\sqrt{Z^{2}-X^{2}}\). Find the resistance for \(Z=5.362 \Omega\) and \(\bar{X}=2.875 \Omega\).

For numbers a and \(b,\) determine which of the following expressions equals the given expression. (a) \(a+b\) (b) \(a-b\) (c) \(b-a \quad\) (d) \(-a-b\) $$-b-(-a)$$

Solve the given problems. To find the amount of a certain investment of \(x\) dollars, it is necessary to solve the equation \(0.03 x+0.06(2000-x)=96\) Solve for \(x\).

Solve the given problems. The speed (in \(\mathrm{m} / \mathrm{s}\) ) of sound in seawater is found by evaluating \(\sqrt{B / d}\) for \(B=2.18 \times 10^{9} \mathrm{Pa}\) and \(d=1.03 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} .\) Find this speed, which is important in locating underwater objects using sonar.

Perform the indicated divisions. Find \(k\) such that the remainder of the division $$\left(6 x^{3}-x^{2}-14 x+k\right) \div(3 x-2) \text { is }-2.$$