A data collection probe is dropped from a stationary balloon, and it falls with a velocity (in m/s) given by $v(t)=9.8t$, neglecting air resistance. After 10 s, a chute deploys and the probe immediately slows to a constant speed of 10 m/s, which it maintains until it enters the ocean.

Graph the velocity function.

State whether each equation or function is a linear function. Write yes or no. Explain.

$$h(x)=6$$

Use the fact 6(−3) = −18 to write two equations showing that 6, −3, and −18 are related by division.

Solve each equation. Check your answer. 8x-2=3x+12.25

Determine all singular points of the given differential equation and classify them as regular or irregular singular points.

$$( x - 2 ) ^ { 2 } y ^ { \prime \prime } + ( x - 2 ) e ^ { x } y ^ { \prime } + \frac { 4 } { x } y = 0.$$

Calculate the indicated quantity. What percent of 25 is 45?

Using the graph of

$$f ( x ) = \sqrt { x }$$

as a guide, describe the transformation and graph the function.

$$j ( x ) = \sqrt { x + 4 } – 1$$

Write 750,000 in expanded notation.

Give formulas for the following complex ions. tetracarbonyldihydroxochromium(III) ion

a. If the tax that you pay when you purchase an item is 12% of the sale price, write an expression that gives the tax on the item with a price p. Write another expression that gives the total price of the item, including tax. b. What operations are involved in the expressions you wrote? c. Determine the total price, including tax, of an item that costs $75. d. Explain how the order of operations helped you solve this problem.

Solve. Identify all double roots.

$$( s - 1 ) ^ { 2 } ( s - 3 ) ^ { 2 } = 0$$

A complex number is given. Graph the complex number in the complex plane. $1+\sqrt{3} i$

Which statement describes the roots of $x^{4}-8 x^{4}-21 x^{2}+108$? A. 1 real root, 5 imaginary B. 3 real roots, 3 imaginary C. 4 real roots, 2 imaginary D. 5 real roots, 1 imaginary E. 6 real roots, 0 imaginary

A substance that has been genetically engineered into transgenic rice has the potential to treat a. cancer. b. high blood pressure. c. vitamin A deficiency. d. malaria.