D. Use FOIL and guess and check to factor the equation
Answer:
no solution exists:
Step-by-step explanation:
x²−1x+10=0
Step 1: Simplify both sides of the equation.
x²−x+10=0
Step 2: Subtract 10 from both sides.
x²−x+10−10=0−10
x²−x=−10
Step 3: The coefficient of -x is -1. Let b=-1.
Then we need to add (b/2)^2=1/4 to both sides to complete the square.
Add 1/4 to both sides.
x²−x+
1/4=−10+
1/4
x²−x+
1/4=−39
/4
Step 4: Factor left side.
(x -1/2)² = −39
/4
Step 5: Take square root.
x −1
/2 =±√
−39
/4
Step 6: Add 1/2 to both sides.
x =−1/2 + 1/2 = 1/2 ±√
-39/4
x = 1/2 ±√
-39/4
No real solutions.
153.9 inches is the correct answer
Answer:
its 5 and 1/2
Step-by-step explanation:
Split up the integration interval into 4 subintervals:
![\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac%5Cpi8%5Cright%5D%2C%5Cleft%5B%5Cdfrac%5Cpi8%2C%5Cdfrac%5Cpi4%5Cright%5D%2C%5Cleft%5B%5Cdfrac%5Cpi4%2C%5Cdfrac%7B3%5Cpi%7D8%5Cright%5D%2C%5Cleft%5B%5Cdfrac%7B3%5Cpi%7D8%2C%5Cdfrac%5Cpi2%5Cright%5D)
The left and right endpoints of the 
-th subinterval, respectively, are
for 
, and the respective midpoints are
We approximate the (signed) area under the curve over each subinterval by
so that
We approximate the area for each subinterval by
so that
We first interpolate the integrand over each subinterval by a quadratic polynomial 
, where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
