All categories

14 days ago

Maximum value of x3y3 + 3 x*y when x+y = 8.

Mathematics

2 answers:

Inessa [8.9K]14 days ago

8 0

Response:

The outcome is 4144.

Detailed explanation:

We need to determine the peak value of f(x)= $x^{3}y^{3}+3xy$ when $x+y=8$

We can represent $x+y=8$ as $y=8-x$

Plugging the value of y

$f(x)=x^{3}(8-x)^{3} +3x(8-x)$

= $3x^{2}(8-x)^{2}[-x+8-x]+3[-x+8-x]$

= $3(8-2x)[x^{2}(8-x)^{2}+1]$

To find the maximum, we'll set the equation to 0.

Thus, we find:

$8-2x=0$ => x = 4

And since $y=8-x$

$y =8-4= 4$ > y = 4

Hence, we will substitute these values into the equation to ascertain the maximum value.

= $x^{3}y^{3}+3xy$

= $xy(x^{2}y^{2}+3)$

= $4\times4((16\times16) +3)$

= $16(259)$ = 4144

Svet_ta [9.4K]14 days ago

6 0

The highest value of x³y³ + 3 x.y, given x + y = 8, is 4144. For clarity, let's revisit foundational concepts related to derivatives:

Let's get started on solving this!

First, we have the equation: with x + y set to 8, which gives us y = 8 - x. Now, we can proceed to analyze the equation further.

You might be interested in

What is the following product? RootIndex 3 StartRoot 16 x Superscript 7 Baseline EndRoot times RootIndex 3 StartRoot 12 x Supers

PIT_PIT [9117]

Response:

I'm uncertain about the problem, but I believe it relates to: $4x^5\sqrt[3]{3x}$

$\sqrt[3]{16x^7} \times \sqrt[3]{12x^9} =$

$= \sqrt[3]{16 \times 12 \times x^{16}}$

$= \sqrt[3]{192 \times x^{15} \times x}$

$= \sqrt[3]{64 \times 3 \times (x^5)^3 \times x}$

$= \sqrt[3]{4^3 \times 3 \times (x^5)^3 \times x}$

$= 4x^5\sqrt[3]{3x}$

8 0

13 days ago

A toy train moves along its track at a rate of 132 feet per minute. What is this rate in miles per hour?

tester [8820]

Answer:

1.5 miles per hour

Step-by-step explanation:

Multiply 132 feet by 60 seconds to get 7920. Subtract 5280, the number of feet in a mile, leaving you with 1 mile and an additional 2640 feet, which amounts to half a mile.

8 0

5 days ago

Una persona observa un pájaro que esta en la copa de un árbol de 2 m de altura y un gato que esta en el pie del mismo árbol a la

Leona [9267]

a) Approximately 40° for depression and 5° for elevation; b) it relates to the height of the observer; c) none. Step-by-step explanation: (a) Angles of depression and elevation: The angle of depression is roughly 40°, while the angle of elevation is around 5°. (b) The angles depend on the observer's height. A taller individual will have a smaller angle of elevation paired with a larger angle of depression. (c) None of the angles can reach or exceed 99°, since they are components of a right triangle. If one angle is a right angle, both of the others must be lesser than 90°.

7 0

8 days ago

Math 1314 lab module 2

Svet_ta [9496]

Is there a question or not?

8 0

18 days ago

1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms? Round your answer t

AnnZ [9099]

The weight of an orangutan is 64.5 kilograms

Solution:

It is stated that the orangutan's weight is 142 pounds