Show by substitution that u(x,t)=cos(απx)e^−α^2π^2t is a solution of the heat equation ut=uxx on any interval [0, L].

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)?

How to expand and simplify ${\displaystyle 2(3x+4)-3(4x-5)}$?

Find an equation equivalent to $x^2-y^2=4$ in polar coordinates.

How to graph ${\displaystyle r=5\sin \theta }$?

How to find the length of a curve in calculus?

When two straight lines are parallel their slopes are equal.
A)True;
B)False

Integration of 1/sinx-sin2x dx

Converting percentage into a decimal. $8.5\%$

Arrange the following in the correct order of increasing density.
Air
Oil
Water
Brick

What is the exact length of the spiraling polar curve ${\displaystyle r=5e^{2\theta }}$ from 0 to ${\displaystyle 2\pi }$?

What is ${\displaystyle \frac{\sqrt{7}}{\sqrt{11}}}$ in simplest radical form?

What is the slope of the tangent line of ${\displaystyle r=-2\sin \left(3\theta \right)-12\cos \left(\frac{\theta }{2}\right)}$ at ${\displaystyle \theta =\frac{-\pi }{3}}$?

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

Use the summation formulas to rewrite the expression ${\displaystyle \Sigma \frac{2i+1}{n^2}}$ as i=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000.

How to calculate the right hand and left hand riemann sum using 4 sub intervals of f(x)= 3x on the interval [1,5]?