<h3>The number of beads lina has is 31</h3><h3>
Laura made a mistake by adding the constant 7 and variable 4b</h3>
<em><u>Solution:</u></em>
Given that,
Laura wrote and solved the following expression to find the total number of beads Lina has
There are 6 beads in each packet
7+4b = 11b
= 11(6)
=66
From given,
Lina has a total of 7 + 4b beads
Given that, There are 6 beads in each packet
Substitute b = 6
7 + 4(6)
Simplify
7 + 24
Add
31
Thus, she has a total of 31 beads and not 66 beads
Laura made a mistake by adding the constant 7 and variable 4b
But a constant and variable cannot be added
(5x²+4)–(5+5x³)
25x+4–5+125x
150x–1
Answer:
520?
Step-by-step explanation:
I think
Answer:

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

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

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

Hope this helps
regards