Answer:
see explanation
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
To find k use the condition when r = 4, M = 160, thus
160 = k × 4³ = 64k ( divide both sides by 64 )
2.5 = k
M = 2.5r³ ← equation of variation
(a)
When r = 2, then
M = 2.5 × 2³ = 2.5 × 8 = 20
(b)
When M = 540, then
540 = 2.5r³ ( divide both sides by 2.5 )_
216 = r³ ( take the cube root of both sides )
r = ![\sqrt[3]{216}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B216%7D)
= 6
Answer: See below
Step-by-step explanation:
4 parts of the whole are shaded, and there are a total of 10 parts
So the fraction is: 4/10
Simplifying by dividing both the numerator and denominator by 2 would give <em>2/5</em>
Decimal: 4 divided by 10 is 0.4
Percentage: Decimal * 100 = 0.4 * 100 = 40%
C. 3/2 divided by 3
Alina has 3/2 hours to complete her homework. She should divide her 3/2 hours by the 3 assignments to determine how much time she will spend on each assignment. This turns out to be 1/2 hours, or 30 minutes, on each assignment. 3/2 hours is the same thing as 90 minutes, so this answer makes sense. We want the time to be divided by the number of assignments, not vice versa.
