A 10m tall lader rests against a house at an angle of 30 degrees from the ground. At what height does the ladder touch the house?
We know that the ladder, ground and house form a right triangle. The hypotenuse of the triangle is the ladder which is 10m. The trig function that will help us solve for the opposite side of the triangle is sin. Therefore, sin(30) = opposite/10. Rearrange and get 10sin(30) = opposite =5
Find the derivative of (2x+3)^3
Notice that (2x+3) is raised to the 3rd power. The chain rule will be used in this problem. Start by taking the derivative and pretend that 2x+3 is just an x for now. So you would have x^3. The derivative of that would be 3x^2. Bring the x out front and subtract the power by one. Now we must use the chain rule. The inside is 2x+3. You can take the derivative of that as well. It would be just 2. The chain rule says you must tack this on to the original. Therefore the answer would be 3*2(2x+3)^2 = 6(2x+3)^2
y = -8x +4 8x+4y = 0 Find the value of x and y
We need to get one equation in terms of just x or just y. By looking at the first equation, you know y = -8x +4. Plug that into the second equation and get: 8x + 4(-8x+4) = 0. Simplify: -24x+16=0 or 24x = 16. Next, solve for x. x x 16/24 = 2/3 Now we know x = 2/3. Plug this into the top equation and solve for y. y = -8(2/3) + 4 y = -16/24 + 4 y = 10/3 Therefore, x = 2/3, y = 10/3