Answer: i'm pretty sure todd's score would be 19
39=2x-1
Missing fact is 13 seats are empty
<span>If </span><span /><span><span><span><span><span><span>x</span><span>≠</span><span><span><span>0</span></span></span></span><span /></span></span><span /></span><span>x≠0</span></span><span>, then </span><span /><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>x</span><span /></span><span><span>2</span><span /></span></span></span></span><span /></span><span><span><span><span>−</span><span /></span><span><span>−</span><span /></span></span><span /></span><span><span><span>√</span></span><span /></span></span></span><span /></span><span><span>x</span><span /></span><span><span /><span /></span></span></span><span>=</span></span><span /></span></span><span /></span><span>x2x=</span></span>
9514 1404 393
Answer:
90 miles
Step-by-step explanation:
Let d represent the distance to Grandma's house.
The speed going was ...
speed = distance/time
speed = d/2
The speed coming home was ...
speed = d/2.25
The difference of these speeds is 5 miles per hour:
d/2 -d/2.25 = 5
2.25d -2d = 5(4.50) . . . . . multiply by 4.50
0.25d = 22.5 . . . . . . . . . . .simplify
d = 90 . . . . . . . . . . . . . . . . multiply by 4
Grandma's house is 90 miles away.
You can either use the inverse function theorem or compute the general derivative using implicit differentiation. The first method is slightly faster.
The IFT goes like this: if f(x) is invertible and f(a) = b, then finv(b) = a (where "finv" means "inverse of f").
By definition of inverse functions, we have
f(finv(x)) = finv(f(x)) = x
Differentiating both sides of the second equality with respect to x using the chain rule gives
finv'(f(x)) * f'(x) = 1
When x = a, we get
finv'(b) * f'(a) = 1
or
finv'(b) = 1/f'(a)
Now let f(x) = sin(x), which is invertible over the interval -π/2 ≤ x ≤ π/2. In the interval, we have sin(x) = √3/2 when x = π/3. We also have f'(x) = cos(x).
So we take a = π/3 and b = √3/2. Then
arcsin'(√3/2) = 1/cos(π/3) = 1/(1/2) = 2
