Answer:
The third option (C) Yes, because there is enough water in the cooler for about 81 cups total.Step-by-step explanation:
Answer: $222.73
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Work Shown:
x = pre-GST price
10% of x = 0.10x = tax amount
x + 0.10x = 1.10x = post-GST price = 245
1.10x = 245
x = 245/1.10
x = 222.7272 approximately
x = 222.73 is the price before tax.
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Check:
10% of 222.73 = 0.10*222.73 = 22.273 = 22.27
The tax amount ($22.27) is added to the pre-GST price to get
22.27+222.73 = 245
which matches the post-GST price mentioned.
The answer is confirmed.
Or another way to confirm the answer is to calculate this
1.10*222.73 = 245.003 = 245
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.
The answer is true I believe
