방정식과 부등식 전체 문제

Suppose that an equation is given $p=-2{x}^{2}+280x-1000,$ where $x$ represents the number of items sold at an auction and $p$ is the profit made by the business that ran the auction. How many items sold would make this profit a maximum? Solve this by graphing the expression in your graphing utility and finding the maximum using 2^nd CALC maximum. To obtain a good window for the curve, set $x$ [0,200] and $y$ [0,10000].

A formula for the normal systolic blood pressure for a man age $A,$ measured in mmHg, is given as $P=0.006{A}^{2}-0.02A+120.$ Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.

The cost function for a certain company is $C=60x+300$ and the revenue is given by $R=100x-0.5{x}^{2}.$ Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $300.

A falling object travels a distance given by the formula $d=5t+16{t}^{2}$ ft, where $t$ is measured in seconds. How long will it take for the object to travel 74 ft?

A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 378 ft². Find the width of the walkway if the garden is 12 ft. wide by 15 ft. long.

An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, $P$, who contracted the flu $t$ days after it broke out is given by the model $P=-{t}^{2}+13t+130,$ where $1\le t\le 6.$ Find the day that 160 students had the flu. Recall that the restriction on $t$ is at most 6.

In a radical equation, what does it mean if a number is an extraneous solution?

Explain why possible solutions must be checked in radical equations.

Your friend tries to calculate the value $-{9}^{\frac{3}{2}}$ and keeps getting an ERROR message. What mistake are they probably making?

Explain why $|2x+5|=-7$ has no solutions.

Explain how to change a rational exponent into the correct radical expression.

For the following exercises, solve the rational exponent equation. Use factoring where necessary.

${x}^{\frac{2}{3}}=16$

For the following exercises, solve the rational exponent equation. Use factoring where necessary.

${x}^{\frac{3}{4}}=27$

For the following exercises, solve the rational exponent equation. Use factoring where necessary.

$2{x}^{\frac{1}{2}}-{x}^{\frac{1}{4}}=0$

For the following exercises, solve the rational exponent equation. Use factoring where necessary.

${(x-1)}^{\frac{3}{4}}=8$

For the following exercises, solve the rational exponent equation. Use factoring where necessary.

${(x+1)}^{\frac{2}{3}}=4$

For the following exercises, solve the rational exponent equation. Use factoring where necessary.

${x}^{\frac{2}{3}}-5{x}^{\frac{1}{3}}+6=0$

For the following exercises, solve the rational exponent equation. Use factoring where necessary.

${x}^{\frac{7}{3}}-3{x}^{\frac{4}{3}}-4{x}^{\frac{1}{3}}=0$

For the following exercises, solve the following polynomial equations by grouping and factoring.

${x}^{3}+2{x}^{2}-x-2=0$

For the following exercises, solve the following polynomial equations by grouping and factoring.

$3{x}^{3}-6{x}^{2}-27x+54=0$