Find the c in the following problem: -c +12 = -4c
Firstly, we have to group all the variable with the same in one side. 12 = -3c Next, in order to solve for c we have to divide 12 by the number in front of c (-3) so c can end up alone. 12/-3=c If asked, we can simplify it to just simply -4=c
Take the antiderivative of the following problem ∫x^3(9-x^2)^1/2dx.
So we cannot just simply use u- substitution in this case. So, we take 9-x^2 and we equal it to 3^2-x^2 because we need the number (a) to be squared. The form would be (a^2 - x^2) and that and (3^2-x^2) fulfills that requirement. x= asin(theta) and then we put in the form - a^2 -a^2sin^2(theta) so that would just simplify to a^2(1-sin^2(theta)) now we figure out the derivative: x=3sin(theta) dx= 3cos(theta) d(theta) Take the integral of ((27sin^3(theta) (9-9sin^2(theta))^1/2*3cos(theta)d(theta) (9-9sin^2theta)^1/2 becomes 3cos(theta) Next, theres 243 ∫sin^3(theta)cos^2(theta) d(theta) 243∫sin^2(theta)cos^2(theta)sin(theta) d(theta) 243∫(1-cos^2(theta))cos^2(theta)sin(theta)d(theta) u=cos(theta) du=-sin(theta) d(theta) -243∫(1-u^2)(u^2)du -243∫(u^2-u^4)du -243(u^3/3 -u^5/5)+C
Why does the American government have three branches?
The Constitution - the law of the country - created by the founding fathers (the people that wrote our government). The three branches - legislative, executive, and judicial - were created so they would keep each other in check and not give too much power to each branch (checks and balances). Most of Europe for example has a parliament that includes most of the government while here it is divided in three.