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Max/Min Rectangle Problem, Maximize the Area

Q: You have 128 feet of fencing to fence a rectangular area. Find the largest possible area to enclose this amount.

A: The perimeter of the space will be 128=2w+2L, where w=width and L=length

Isolate for L: L=64-w

The formula for the area of the rectangle is A=w*L. Substitute L=64-w into the area formula . . . → Read More: Max/Min Rectangle Problem, Maximize the Area

Max/Min Problem – Maximizing Revenue, Selling Calculators

Q: Calculators are sold to students for 20 dollars each. Three hundred students are willing to buy them at that price. For every 5 dollar increase in price, there are 30 fewer students willing to buy the calculator. What selling price will produce the maximum revenue and what will the maximum revenue be?

A: . . . → Read More: Max/Min Problem – Maximizing Revenue, Selling Calculators

Airplane with Tailwind and Headwind

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Q: An airplane flew 3 hours with a 40 mph head wind. The return trip with a tail wind of the same speed took 2 hours. Find the speed of the plane in still air.

A: When you have a headwind, you have to subtract the wind’s speed from the . . . → Read More: Airplane with Tailwind and Headwind

Radian Conversion

Q: What is a radian?

A: A radian is the angle measured between radii of a circle which are subtended by an arc which has the same length as the radii.

It may be easier to remember: a radian is just another measure of an angle, just like degrees.

1 radian = 57.2958 ° . . . → Read More: Radian Conversion

Exponent Laws

Q: What are the Exponent Laws?

A: There are 4 basic identities to remember:

Example: Example: Example: . . . → Read More: Exponent Laws

Negative and Zero Exponents

Q: What is a negative exponent?

A: A number raised to a negative exponent produces the reciprocal of that number. Recall that a reciprocal is just 1 divided by the number. It is very useful to memorize these identities:

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Q: How do I evaluate a zero exponent?

A: Any number raised . . . → Read More: Negative and Zero Exponents

Arithmetic Sequence

Q: What is an arithmetic sequence?

A: An arithmetic sequence is a sequence of numbers in which the difference between successive numbers is constant. The nth term of an arithmetic sequence is given by:

where a is the first term and d is the common difference.

Adding Radicals

Q: How do I add radicals like this: ?

A: = =

Note that this is analogous to 2x + 4x = 6x, where the terms act similar to the variable x.

Let’s look at some more examples:

= =

Adding Unlike Radicals

Q: What if I have to add radicals, but the radicals are different? I am trying to add .

A: You can’t add those, or simplify any further without a calculator. You just have to leave it as it is, because the square roots are different (3 and 5).

=

Let’s look at . . . → Read More: Adding Unlike Radicals

Subtracting Radicals

Q: How do I subtract radicals like this: ?

A: Subtracting radicals is very similar to adding radicals.

= =