Answer:
hob
Step-by-step explanation:
jbibou
a) (0.17 ac)×(126 min/ac) = 21.42 min
b) I can mow 1/126 ac/min; you can mow 1/117 ac/min. Together, we can mow at a rate that is the sum of these:
... (1/126 + 1/117) ac/min = (117 + 126)/(126×117) = 243/14,742 ac/min
Then it will take 14,742/243 min/ac × 0.17 ac/lawn ≈ 10.31 min/lawn
Answer:
C
Step-by-step explanation:
Since the difference between 0 and -10 is 10, this means that the difference between the diving board and the pool also has to be 10. Therefore, the diving board is 10 feet above the water since 0+10 is 10.
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
Let 
. Compute the inverse:
![f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20%5Csqrt%7B1%20%2B%20f%5E%7B-1%7D%28x%29%5E3%7D%20%3D%20x%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2-1%7D)
and we immediately notice that ![f^{-1}(x+1)=\sqrt[3]{x^2+2x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%2B1%29%3D%5Csqrt%5B3%5D%7Bx%5E2%2B2x%7D)
.
So, we can write the given integral as
Splitting up terms and replacing 
in the first integral, we get
<span>x^2 + 15x + 56.25 = 105.25
"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.
Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?"
Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25
Now take the square root of each side
(x+7.5) = sqrt(105.25)
And let's use both the positive and negative square roots.
So
x+7.5 = 10.25914226
and
x+7.5 = -10.25914226
And let's find X.
x+7.5 = 10.25914226
x = 2.759142264
x+7.5 = -10.25914226
x = -17.75914226
So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>
