Find the area first, then multiply the result with the price
dy/dx = y cos(x) dy/y = cos(x) dx ln y + const = sin(x) + const ln y = sin(x) + const ln 3 = sin(0) + const const = ln 3 ln y = sin(x) + ln 3 ln y - ln 3 = sin(x) ln (y/3) = sin(x) y/3 = e^sin(x) y = 3e^sin(x)
Assume that the perimeter is x x = 28 + (4/9)x + (2/5)x x(1 - 4/9 - 2/5) = 28 Solve the calculation above, and you'll get the answer
Assume that the distance travelled before turning 60 degrees is x The total distance travelled = x+10 Distance A-B in straight line = x + 6 Use the cosine rule: (x+6)^2 = x^2 + 100 - (2*x*10*cos(120)) Finish the calculation, you'll find x. Total distance travelled will be ...
Oh sorry. It should be: S sin(u) du
The first problem is correct. As for the second problem, take: u = ln x du = (1/x) dx So: S (ln u) du = ? Try it yourself
Cross multiple means: nominator of left side x denominator of right side = nominator of right side x denominator of left side So for this case: 9 * (x-3) = 4 * (x-7) 9x - 27 = 4x - 28 Now, let's collect the variable x on the left side, and the rest on the right side. 9x - ...
For |x|, we have 2 situations. |x| = x, for x >= 0 |x| = -x, for x < 0 So: ¤ for x>=0: d/dx (2(x^2 + 3x)) = ? ¤ for x<0: d/dx (2(x^2 - 3x)) = ?
A = l* w dA/dt = l*dw/dt + w*dl/dt Plug in the values and calculate