Find the equation of the line tangent to the curve y=4x^3 +2x +1 at the point (1, 2).
Answer: y = 14x + 11 Step 1: Find the derivative of the curve. Step 2: Plug in your x-coordinate to the derivative to get slope. Step 3: Use point-slope for to find equation of the line using the coordinate pair and the slope. Get y alone if you want to get it in slope-intercept form.
There are 38 slots in a wheel. 2 are green, 18 are red, and 18 are black. A ball will land in a slot when the wheel is spun, and the ball has an equal chance of landing in any slot. What is the probability that the ball does NOT land in a red slot two spins in a row?
The answer is .2770. The probability that the ball doesn't land in red for one spin is P(black)+P(green) = 2/38 + 18/38 = 20/38. We want to know the probability of that happening for TWO spins. The two spins are independent (not disjoint), so we MULTIPLY 20/38 by 20/38.
The area of a rectangle is 3x^2 +5x +2. What are the dimension of this rectangle?
The dimensions (length and width) of this rectangle are 3x+2 and x+1. All we had to do were find the factors of the quadratic stated in the problem!