Question

Find two non-negative numbers whose sum is 30 that make the maximum product of the square of one and the cube of the other.

58

likes
291 views

Answer to a math question Find two non-negative numbers whose sum is 30 that make the maximum product of the square of one and the cube of the other.

Expert avatar
Cristian
4.7
117 Answers
Let's denote the two numbers as x and y . We need to find the maximum product of x^2 \times y^3 subject to the constraint that x + y = 30 . We can rewrite the constraint as y = 30 - x .

Now, we can express the product x^2 \times y^3 in terms of one variable:
P = x^2 \times (30 - x)^3

To find the maximum product, we can differentiate P with respect to x and set the derivative equal to 0:
\frac{dP}{dx} = 2x \times (30 - x)^3 - 3x^2 \times 3 \times (30 - x)^2 = 0
Simplify:
2x \times (30 - x)^3 - 9x^2 \times (30 - x)^2 = 0

Solving the above equation will give us the value of x , and then we can find the corresponding value of y using y = 30 - x .

Finally, we can calculate the maximum product:
\text{Product} = x^2 \times y^3

\textbf{Answer:} The two non-negative numbers that make the maximum product are x = 10 and y = 20 . The maximum product is 10^2 \times 20^3 = 8,000,000 .

Frequently asked questions (FAQs)
Question: Find the derivative of f(x) = √(3x^2 + 4x - 2), where x β‰  -2/3, 1/3.
+
What is the value of √(34) + √(50) - √(12)?
+
Math question: What is the smallest positive integer solution for x in the equation x^n + y^n = z^n, satisfying Fermat’s Theorem with n>2? (
+
New questions in Mathematics
Find an arc length parameterization of the curve that has the same orientation as the given curve and for which the reference point corresponds to t=0. Use an arc length s as a parameter. r(t) = 3(e^t) cos (t)i + 3(e^t)sin(t)j; 0<=t<=(3.14/2)
a ferry travels 1/6 of the distance between two ports in 3/7 hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour.
String x = 5 Int y=2 System.out.println(x+y)
I) Find the directional derivative of 𝑓(π‘₯, 𝑦) = π‘₯ sin 𝑦 at (1,0) in the direction of the unit vector that make an angle of πœ‹/4 with positive π‘₯-axis.
Derivative of x squared
What is the r.p.m. required to drill a 13/16" hole in mild steel if the cutting speed is 100 feet per minute?
-3x 2y = -6; -5x 10y = 30
Identify a pattern in the list of numbers.Then use this pattern to find the next number. 37,31,25,19,13
is the x element (180,270), if tanx-3cotx=2, sinx ?
4x + 8y = 5 2x + 4y = 10
20% of 3500
Task 1 angel has 3 quarters 3/8 of a tank of gasoline and Miguel 7/8, who has more gasoline? number line on number line
Calculate the minimum size of a simple random sample assuming a sampling error of 5% assuming that the population size is 100 elements
cube root of 56
A natural gas company has a fixed rate of 1,320 pesos plus 1,590 pesos per cubic meter of gas consumed monthly per customer. Indicate the cost function to determine the value in pesos of the cubic meters of gas consumed in a month per customer. How much did a customer who consumed 18 cubic meters of gas pay? If a customer paid 34,710 pesos, how many cubic meters of gas did he consume?
Find the vertex F(x)=x^2-10x
Log0
A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.
4m - 3t + 7 = 16
Let A denote the set of all people who were alive in 2010. Let B denote the set of all real numbers. Let f assign, to each person in A, their weight during the year 2010. Is f a function? Explain in complete sentences.