Exam 1: Topics From Algebra

A stream of water moving at the rate of v feet per second can carry particles of size $0.03 \sqrt { v }$ inches. Find the size of the largest particle that can be carried by a stream flowing at the rate of $\frac { 7 } { 6 }$ foot per second. (Round your answer to three decimal places.) ​

Use inequality notation to describe the set. ​ q is at least 6 but less than 22 ​

Determine which number/s in the set is/are natural number/s. ​ {2.65, 0.669..., -2, 0.019937247..., 35, -20} ​

Do the operation and express the answer in a + bi form. ​ $\frac { - 9 } { i ^ { 12 } }$ ​

Factor the perfect square trinomial. ​ $x ^ { 2 } + 8 x + 16$ ​

Solve the inequality and graph the solution on the real number line. ​ $\frac { 1 } { x } \geq \frac { 1 } { x + 5 }$ ​

Evaluate the following expression. ​

Write the quotient in standard form. ​ $\frac { 7 } { 1 - i }$ ​

Find the distance between a and b. ​ a = 173, b = 57 ​

Plot the following real number on the real number line.

Solve the inequality and graph the solution on the real number line ​ $x ^ { 3 } + 6 x ^ { 2 } - 36 x - 216 \leq 0$ ​

Use the properties of radicals to simplify the following expression. ​ $\sqrt [ 5 ] { 160 x ^ { 5 } }$ ​

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. ​ $\sqrt { - 24 }$ ​

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. ​ $3 - 11 i$ ​