Let
![I = \displaystyle \int e^{-2x} \cos(2x) \, dx[/]texIntegrate by parts:[tex]\displaystyle \int u \, dv = uv - \int v \, du](https://tex.z-dn.net/?f=I%20%3D%20%5Cdisplaystyle%20%5Cint%20e%5E%7B-2x%7D%20%5Ccos%282x%29%20%5C%2C%20dx%5B%2F%5Dtex%3C%2Fp%3E%3Cp%3EIntegrate%20by%20parts%3A%3C%2Fp%3E%3Cp%3E%5Btex%5D%5Cdisplaystyle%20%5Cint%20u%20%5C%2C%20dv%20%3D%20uv%20-%20%5Cint%20v%20%5C%2C%20du)
with
Then
Integrate by parts again, this time with
so that
Simplify just means put together everything into one big thing. In this case that is just adding. To add a fraction and a decimal we have to convert the fraction into a decimal as well. The decimal form of 1/4 is 0.25, and as such, 3/4 is .75. This means we have -0.75+1.5. Adding a positive to a negative is the same thing as simply subtracting the first number from the second, or 1.5-0.75. This is .75. The answer is C.
Answer:
11
Step-by-step explanation:
Let e represent the number of students with blue eyes. Then the number of students with blond hair is 2e. The total number of students is ...
3 + e + 2e -6 = 30
We subtracted 6 because the expressions e and 2e cause the 6 students with both blond hair and blue eyes to be counted twice.
3e = 33 . . . . add 3 and simplify
e = 11
11 students have blue eyes.
A square has 4 equal sides
use pythagroeas theorem since a square has 4 right angles
a^2+b^2=c^2
a=b because the sides are equal (11)
11^2+11^2=c^2
242=c^2
square root both sides
11√2=c
the diagonal legnth is 11√2 centimiters
