Answer:
![V=61.66](https://tex.z-dn.net/?f=V%3D61.66)
Step-by-step explanation:
This problem can be solved by using the expression for the Volume of a solid with the washer method
![V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%20%5Climit_a%5Eb%5BR%28x%29%5E2-r%28x%29%5E2%5Ddx)
where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).
Before we have to compute the limits of the integral. We can do that by taking f=g, that is
![f(x)=g(x)\\ln(x)=\frac{1}{2}x-2](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29%5C%5Cln%28x%29%3D%5Cfrac%7B1%7D%7B2%7Dx-2)
there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)
x1=0.14
x2=8.21
and because the revolution is around y=-5 we have
![R=ln(x)-(-5)\\r=\frac{1}{2}x-2-(-5)\\](https://tex.z-dn.net/?f=R%3Dln%28x%29-%28-5%29%5C%5Cr%3D%5Cfrac%7B1%7D%7B2%7Dx-2-%28-5%29%5C%5C)
and by replacing in the integral we have
![V=\pi \int \limit_{x1}^{x2}[(lnx+5)^2-(\frac{1}{2}x+3)^2]dx\\](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%20%5Climit_%7Bx1%7D%5E%7Bx2%7D%5B%28lnx%2B5%29%5E2-%28%5Cfrac%7B1%7D%7B2%7Dx%2B3%29%5E2%5Ddx%5C%5C)
and by evaluating in the limits we have
![V=61.66](https://tex.z-dn.net/?f=V%3D61.66)
Hope this helps
regards
Answer:
The correct selling price = $10.02
The manager's likely error = $6.02
Step-by-step explanation:
Markup of 67% on all items
An item cost $6
The correct selling price = $6 + 67% of $6
= $6 + 0.67 × $6
= $6 + $4.02
= $10.02
The correct selling price = $10.02
The store manager's selling price is $4.
The manager's likely error = The correct spelling price - the manager's selling price
= $10.02 - $4
= $6.02
The manager's likely error = $6.02
Answer:
9 cupcakes and 64$
Step-by-step explanation:
try the math
I'm not sure what your mean by that??