Tutor profile: Kevin V.
Subject: Basic Math
If 5% of a number is 25, what is that number?
The easiest way to imagine this question is to translate the words into math terms. "Of a number" means "a number" is being multiplied. That means "a number" times 5% is 25. If you want to find the number, you have to do "the opposite" of multiplication -- that would be division. 5% is 0.05. So you will have to divide the 25 by 0.05 to find the number: this calculates to 500. So 5% of 500 is 25.
How do you determine the area between three graphs?
The first step is to figure out where the enclosed area is, and if you want to take horizontal (dy) or vertical slices (dx). The first is important because this will tell you where the graphs intersect, so you can figure out where it ends and it begins. The second is also important, because this will be what you are integrating in terms of; depending on what variable it is (either x or y, in most cases), you will have to rewrite the equations to make it easier to integrate. Graphing the equations is highly suggested, because you will create a helpful visual to see what you will be integrating. Once you have these basics set up and you've figured out how you want to integrate, you can set up your integral. Area = integral[ (top graph) - (bottom graph)], taken from the first end point to the last end point. When you set up this integral, it is important to know that you can split up the graph into multiple integrals in case either of the graphs change. The summation of the integrals will represent the total enclosed area. You can use geometry and the graphs you've drawn to help figure out the different integral you might need to write. After setting up all your definite integrals, you can integrate and add to find your answer.
Solve for x: -0.25x^2 + 1.5 = -10.75
First, write the equation. \\ -0.25x^2 + 1.5 = -10.75 Next, get the term with the variable by itself. Subtract the 1.5 from both sides. \\ -0.25x^2 + 1.5 - 1.5 = -10.75 - 1.5 -0.25x^2 = -12.25 Now, we can divide both sides by the -0.25 to get the x^2 by itself. \\ (-0.25x^2) / (-0.25) = (-12.25) / (-0.25) x^2 = 49 Finally, we can get rid of the squared by using a square root. \\ sqrt( x^2 ) = sqrt( 49 ) Don't forget when you do a square root, you will have either a positive or negative answer! \\ x = +/- 7
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