Answer: D: 3.
Step-by-step explanation:
Ok, vamos a contar los dígitos de derecha a izquierda.
El dígito que ocupa el lugar de la centena de millón va a ser el 9. (o el primero contando de izquierda a derecha).
en el numero 341,427,538 el noveno dígito es un 3.
Entonces el numero que esta en el lugar de la centena de millón es un 3
La opción correcta es D
Answer:
Step-by-step explanation:
The volume of the cylinder from the rectangle is the size of the cylinder
The rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
<h3>How to determine the rectangle</h3>
Let the dimension of the rectangle be x and y.
So, the perimeter (P) is:
![P = 2 * (x + y)](https://tex.z-dn.net/?f=P%20%3D%202%20%2A%20%28x%20%2B%20y%29)
The perimeter is given as 18.
So, we have:
![2 * (x + y) = 18](https://tex.z-dn.net/?f=2%20%2A%20%28x%20%2B%20y%29%20%3D%2018)
Divide both sides by 2
![x + y = 9](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%209)
Make y the subject
![y = 9 - x](https://tex.z-dn.net/?f=y%20%3D%209%20-%20x)
The volume of a cylinder is:
![V = \pi r^2h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E2h)
So, we have:
![V = \pi x^2(9 -x)](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20x%5E2%289%20-x%29)
Expand
![V = \pi(9x^2 -x^3)](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%289x%5E2%20-x%5E3%29)
Differentiate
![V' = \pi(18x -3x^2)](https://tex.z-dn.net/?f=V%27%20%3D%20%5Cpi%2818x%20-3x%5E2%29)
Set to 0
![\pi(18x -3x^2) = 0](https://tex.z-dn.net/?f=%5Cpi%2818x%20-3x%5E2%29%20%3D%200)
Divide both sides by ![\pi](https://tex.z-dn.net/?f=%5Cpi)
![18x -3x^2 = 0](https://tex.z-dn.net/?f=18x%20-3x%5E2%20%3D%200)
Divide both sides by 3x
![6 -x = 0](https://tex.z-dn.net/?f=6%20-x%20%3D%200)
Make x the subject
![x = 6](https://tex.z-dn.net/?f=x%20%3D%206)
Recall that:
![y = 9 - x](https://tex.z-dn.net/?f=y%20%3D%209%20-%20x)
So, we have:
![y = 9 - 6](https://tex.z-dn.net/?f=y%20%3D%209%20-%206)
![y = 3](https://tex.z-dn.net/?f=y%20%3D%203)
Hence, the rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
Read more about volumes at:
brainly.com/question/10171109
Answer:
$80
Step-by-step explanation:
To solve this question you must first make an equation.
30 times however many sessions she has plus the $20 fee
Then $35 times however many sessions it is plus the $10 fee
you would then need to graph both to find where they meet.
$30(1)+20=50
$30(2)+20=80
$35(1)+10=45
$35(2)+10=80