The trick is to exploit the difference of squares formula,

Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:

Whatever you do to the denominator, you have to do to the numerator too. So

Expand the numerator:






So we have

But √12 = √(3•4) = 2√3, so

For find f(-2) of f(x)=7x+3, plug in -2 for x.
7(-2)+3=y
-14+3=y
y=-11
To find the rate, or the slope, you divide x/y. So 2/6 is 1/3. 3 over 9 is also 1/3. So the rate is 1/3. In rates you always divide, you don't mulitply or subtract or add to find the rate.
Answer: 70
Step-by-step explanation:
Antoine's elevation when he is halfway to the top is 70. You cut the diameter (120) in half which gets you 60 and you add the height of the stand holding the wheel (10) which gets you 70.
Tangent always meets radius at 90° angle.
Angle ABC = 90° so Pythagoras' theorem applies.
r² + 4² = (r+2)²
r² + 16 = r² + 4r + 4
12 = 4r
r = 3