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We are given ratios of side lengths and the total perimeter. The perimeter of the triangle is simply the sum of the side lengths. Imagine that the sides are made up of "units": 3 times a unit + ...

First, you need to make sure that each equation has a common denominator. You do this by multiplying the numerators of each equation with the denominators of the others. This allows you to form one algebr...

Multiply equation 1) by 2 : 12a+2b=32. There are alternate signs of b and so therefore add the equations together: 17a=51. Solve for a: a=3. Sub a into one of the equations to find b: 5*3-2b=19b=-2. The f...

First, we need to find the derivative f'(x) for all x, and then we will substitute x=2π into the function we find. To do this, we need to set up our limit:
f'(x) = lim [sin(3(x+h))-sin(3x)]/h as h-&...

Expand by multiplying out the brackets (using crab claws or similar method): 18x^2 + 30x - 12x -20Simplify by combining like terms: 18x^2 + 18x -20