Which of the following pairs of functions are inverse of each other?
1 answer:
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Volume of a sphere and a cone
We have that the equation of the volume of a sphere is given by:
We have that the radius of a sphere is half the diameter of it:
Then, the radius of this sphere is
r = 6cm/2 = 3cm
<h2>Finding the volume of a sphere</h2>We replace r by 3 in the equation:
Since 3³ = 3 · 3 · 3 = 27
If we use π = 3.14:
Rounding the first factor to the nearest hundredth (two digits after the decimal), we have:
4.18666... ≅ 4.19
Then, we have that:
Then, we have that:
<h2>Finding the volume of a cone</h2>We have that the volume of a cone is given by:
where r is the radius of its base and h is the height:
Then, in this case
r = 3
h = 6
and
π = 3.14
Replacing in the equation for the volume:
Then, we have:
3² = 9
Answer: the volume of the cone that has the same circular base and height is 56.52 cm³
Answer:
<em>The denominator is 12</em>
Step-by-step explanation:
<u>The Number Line</u>
We can represent any real number in a properly segmented line, where the zero-mark is the separation between positive numbers to its right side and negative numbers to the left side.
We are given the number x = 2/3. Since it's positive, its location lies to the right of the zero but before the 1 as shown in the figure below.
We want to locate a second point y at the same distance from 0 as the point x, so we have two options: y is the same as x, or y is negative at the same distance from zero. We chose the last option.
Its numerator must be 8, so we need to multiply it by 4. But we cannot alter the value of x, so we must also multiply the denominator by 4, which gives us the fraction 8/12, but recall it must be negative.
The denominator is 12
