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
If Mallory makes $42.50 per hour and she works 20 hours a week, we multiple those two and we get:
42.5 * 20 = 850
So she earns $850 per week.
Mallory saves half of that amount she would have $425 per week.
In 4 weeks she would have:
425 * 4 = 1700
Mallory will save $1,700 in four weeks.
Answer:
Step-by-step explanation:
Expression for the rectangular area and perimeter are, respectively:
After some algebraic manipulation, area expression can be reduce to an one-variable form:
The first derivative of the previous equation is:
Let the expression be equalized to zero:
The second derivative is:
According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:
The maximum area is:
The answer is 48--- 64% of 75=48
