The volume that is inside the larger cylinder shown but outside the cylinder with the
smaller radius, r, can be found with the formula below.
V = 250 - 10x²2
V is the volume inside the larger cylinder but outside the smaller cylinder in cubic
centimeters.
r is the radius of the smaller cylinder in centimeters.
Which equation and solution gives the radius of the smaller cylinder if the volume
inside the larger cylinder but outside the smaller cylinder is 160xz centimeters"?
160x250x- 10²
r=2
V = 250x - 10x(4)²
V = 90x
160x250x-102²
r=3
V =
250 - 10(4)²
V = 90
5 cm
CLEAR
10 cm
CHECK
The correct equation and solution is:
160x = 250 - 10r²
160x + 10r² = 250
10r² = 250 - 160x
r² = (250 - 160x) / 10
r = √[(250 - 160x) / 10]
Therefore, the correct equation and solution for the radius of the smaller cylinder is:
r = √[(250 - 160x) / 10]
which details from the text best supports the idea that the narrator is cautious in his new setting select two options
Based on the given text, there is no specific information provided about the narrator being cautious in his new setting. It solely mentions equations and calculations related to the volume of cylinders. Therefore, none of the details from the text can be used to support the idea that the narrator is cautious in his new setting.
To find the equation and solution for the radius of the smaller cylinder, we can equate the given volume, 160xz cm³, with the formula for the volume, V = 250 - 10x².
160xz = 250 - 10x²
To solve for x, we need to rearrange the equation:
10x² + 160xz - 250 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 10, b = 160z, and c = -250. Let's substitute these values into the quadratic formula:
x = (-(160z) ± √((160z)² - 4(10)(-250))) / (2(10))
Simplifying further:
x = (-160z ± √(25600z² + 10000)) / 20
Therefore, the equation for the radius of the smaller cylinder is r = (-160z ± √(25600z² + 10000)) / 20.
To find the equation and solution for the radius of the smaller cylinder, we need to set up the given volume equation and solve for the variable, which is the radius (r).
The volume equation given is V = 250 - 10r², where V is the volume inside the larger cylinder but outside the smaller cylinder in cubic centimeters, and r is the radius of the smaller cylinder in centimeters.
From the given information, the volume inside the larger cylinder but outside the smaller cylinder is 160xz cubic centimeters. So we can substitute V = 160xz into the equation: 160xz = 250 - 10r².
To solve for r, we need to rearrange the equation and isolate the variable. Here are the steps:
160xz = 250 - 10r²
160xz - 250 = -10r²
-10r² = 160xz - 250
r² = (250 - 160xz) / 10
r² = (250 - 16xz) / 10
r² = (250 / 10) - (16xz / 10)
r² = 25 - 1.6xz
r² = 25(1 - 0.064xz)
Now we have an equation for r² in terms of x and z. However, in the given answer choices, there are two options for r, which means we can have two possible solutions. To determine the correct solution, we can substitute the given values of x and z into the equation.
Unfortunately, the values of x and z are not provided in the question, so it is not possible to determine the exact value for the radius of the smaller cylinder. Therefore, the correct solution cannot be determined without additional information.