If you have a triangle that does not have a right angle but you have the length for each side, how do you find each angle for the triangle.
When looking at the triangle arbitrarily name one angle A,B,C then name each side opposite of that specific angle with the same letter a,b,c. You will then use the law of cosines to find each angle. Not going into the proof of the law, you will use c^2=a^2 + b^2 - abcosC . using simple algebra you will find that cos C = (c^2 -a^2 - b^2)/-ab where you will then take the inverse cosine also known as arccos to find angle C. You will repeat each step 2 more times or you can repeat the step 1 more time then with your two known angles subtract those from 180 degrees being that you know each angle added together in a triangle has to equal 180 degrees
How do you find that area under the curve of function between two certain points, for instance f(x)= x^2 between 0 and 1
To find the area under the curve you will integrate the function between those points. an easy way to remember integrating a simple function like x^2 is to add 1 to the exponent and divide the entire part by the number in the exponent plus 1. This means the integration would look like (1/3)x^3 from 0 to 1. Now to find the actual area you will take this integrated function from 0 to 1 which will look like [(1/3)(1^3)]-[(1/3)(0^3)] which will equal the area under the curve.
x^2 +4x +4 solve for x
when solving this type of problem you basically work it as backwards FOIL. If you were never taught the acronym FOIL it stands for: first, outside, inside, last. This is used when simplifying something like this, (x+2)(x+4). When solving the problem above you will start by knowing that if there is nothing in front of the x^2 the problem will look like (x+_)(x+_) then looking at the last two parts (4x and 4). You are looking for something that multiples together to = 4 and something that adds together to equal the 4. After thinking of simple math you come to find is (2+2) and (2*2). You will use this to plug into your first equation, (x+_)(x+_) which will be (x+2)(x+2). Then you will set each of those to 0 and find what x is equal to. To check yourself to make sure you found the simple equations correctly you can FOIL them out to make sure they match up. (x+2)(x+2) = x^2+2x+2x+4