SOLUTION:
A box has a square base of side x and height y where x,y > 0.
Its volume is V = x^2y and its surface area is
S = 2x^2 + 4xy.
(a) If V = x^2y = 12, then y = 12=x^2 and S(x) = 2x^2 C 4x (12=x2) = 2x2 + 48x^-1. Solve S'(x) = 4x - 48x-2 = 0 to
obtain x = 12^1/3. Since S(x/) ---> infinite as x ---> 0+ and as x --->infinite, the minimum surface area is S(12^1/3) = 6 (12)^2/3 = 31.45,
when x = 12^1/3 and y = 12^1/3.
(b) If S = 2x2 + 4xy = 20, then y = 5^x-1 - 1/2 x and V (x) = x^2y = 5x - 1/2x^3. Note that x must lie on the closed interval [0, square root of 10]. Solve V' (x) = 5 - 3/2 x^2 for x>0 to obtain x = square root of 30 over 3 . Since V(0) = V (square root 10) = 0 and V(square root 30 over 3) = 10 square root 30 over 9 , the
maximum volume is V (square root 30 over 3) = 10/9 square root 30 = 6.086, when x = square root 30 over 3 and y = square root 30 over 3 .
Answer:
Circumference = PI * diameter
Circumference = 3.14159 * 14
Circumference = 43.98226 inches
Area = PI * radius^2
Area = PI * 7^2
Area = PI * 49
Area = 153.9380400259 square inches
Step-by-step explanation:
Answer:
It has three solutions.
Step-by-step explanation:
- Elimination method
- Substitution method
- Graphical method
Here are the ones which i know.
3 minutes
750 x 4 = 3000
there are 1000 mL in each liter.
Answer: a. Population = Fortune companies
b. Parameter = proportion of companies did not find that such surveys intruded significantly on their workday.
c. Sampling frame= List of all Fortune companies.
d. sample size = 500.
Step-by-step explanation:
Population is the largest group of individuals of objects that are point of interest for a researcher.
Here, Population = Fortune companies
Parameter is the measure of characteristic of a population.
Here, Parameter = proportion of companies did not find that such surveys intruded significantly on their workday.
Sampling frame = List of all individuals in population.
Here , Sampling frame= List of all Fortune companies.
Sample is a subset of population , here sample size = 500.
