Answer:
97.7 cm
Step-by-step explanation:
The volume of a cylinder is given by the equation
where:
r is the radius of the cylinder
h is the height of the cylinder
V is the volume
In this problem, we know that the volume of the cylinder is
Here we are not given the height; here, let's assume it is
h = 20 cm
Therefore, we can re-arrange the equation to find the missing dimension, which is the radius of the cylinder:
The hanger diagram ideally should be in balance with all the shapes hung on it.
On the left side, it shows that the circles are 9 grams and the squares are 12 grams. The triangles are 2t grams. Therefore, on the left side we have,
9 + 12 + 2t
On the right side, it shows the circles are 6 grams and the squares are 6 grams, while the triangles are 5t grams. Therefore on the right side we have
6 + 6 + 5t.
For the hanger to be in balance, we should have
Answer:
Step-by-step explanation:
To find the inverse function, solve for y:
f(x) is an even function, so f(-x) = f(x). Then the inverse relation is double-valued: for any given y, there can be either of two x-values that will give that result.
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A function is single-valued. That means any given domain value maps to exactly one range value. The test of this is the "vertical line test." If a vertical line intersects the graph in more than one point, then that x-value maps to more than one y-value.
The horizontal line test is similar. It is used to determine whether a function has an inverse function. If a horizontal line intersects the graph in more than one place, the inverse relation is not a function.
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Since the inverse relation for the given f(x) maps every x to two y-values, it is not a function. You can also tell this by the fact that f(x) is an even function, so does not pass the horizontal line test. When f(x) doesn't pass the horizontal line test, f^-1(x) cannot pass the vertical line test.
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The attached graph shows the inverse relation (called f₁(x)). It also shows a vertical line intersecting that graph in more than one place.
