Find two numbers whose sum 7500 and whose product is the maximum value.
(Round your answer to the nearest whole number.)
Blank = 1
Blank = 2

Answers

Answer 1

The two numbers whose sum is 7500 and whose product  is a maximum value are 3750 and 3750.

Let the two numbers be x and y.

Since their sum equals 7500,

x + y = 7500  (1)

Their product f(x,y) = xy  (2)

We desire to maximize the product.

From (1), x = 7500 - y

Substituting x into (2), we have

f(x,y) = xy

f(x,y) = (7500 - y)y

f(y) = 7500y - y²

To maximize the product, we find the value of y that maximizes f(y), we differentiate f(y) and equate it to zero.

So, df(y)/dy = d(7500y - y²)/dy

f'(y)/dy = d(7500y)/dy - dy²/dy

f'(y)/dy = 7500 - 2y

Equating it to zero, we have

7500 - 2y = 0

7500 = 2y

y = 7500/2

y = 3750

To determine if this gives a maximum for f(y), we differentiate f'(y) with respect to y.

So, f"(y) = d(7500 - 2y)dy

f"(y) = 0 - 2

f"(y) = -2 < 0.

So, y = 3750 gives a maximum for f(y) = f(x, y)

Since x = 7500 - y

Substituing y = 3750 into the equation, we have

x = 7500 - 3750

x = 3750

So, the two numbers whose sum is 7500 and whose product is a maximum product are 3750 and 3750.

Learn more about product of two numbers here:

https://brainly.com/question/15607519


Related Questions

solve for x. 2/x-3=x/12-4x

Answers

Answer:

x=  47 18+2  201  i  ≈0.382978723+0.603295612i x=  47 −2  201  i+18  ≈0.382978723−0.603295612i  Hopefully this makes just the same amount of sense as this question

Acellus. please help me

Answers

by-step explaAnswer:

by-step epla

Step-nation:

a

2 + 2 = 3
prove me wrong

Answers

Answer:

2+2=4................

Answer:

you are wrong because 2+2=4

Interest = $45.58, time = 1 year, rate = 2.25%. Find the principal. Round to the nearest hundredth place

Answers

Answer:

$2,025.78

Step-by-step explanation:

I = Prt ⇒ P = [tex]\frac{I}{rt}[/tex]

2.25% = 0.0225

P = 45.58 ÷ ( 0.0225 × 1 ) ≈ $2,025.78

Dog slept 3 hours . If the dog snored 1/3 of an hour . How many times did he snore

Answers

Answer:

it depends how much the god snores within a certain time period

Which of the following is a correct interpretation of the expression 5−8

Answers

Answer:

start at 5 on the number line and move 8 to the left.

Step-by-step explanation:

The answer is: A - Start at 5 on the number line and move 8 to the left.

Explanation:

5 - 8 = -3

Therefore the final answer should be placed at negative three on the number line.

When you move to the left eight times away from the number five, the answer would be negative three.

x/2 - 3 = 5 Solve the equation algebraically show work to support the answer

Answers

Answer:

x = 16

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

x/2 - 3 = 5

x/2 = 5+3

x/2 = 8

x = 8×2

x = 16

Image attached giving 25 points please help

Answers

Answer:

Rational

Step-by-step explanation:

It isnt whole because its a decimal,

It isnt an Integer because its a decimal

It isnt natural because its a decimal

Meaning it can only be rational

(4 − 3)(−3 + 6) − (2 − )
simplify
show all work

Answers

Answer:

(4 − 3)(−3 + 6) − (2 )

1(3)-2

3-2

1

Hope This Helps!!!

PLS HELP PLEASSSSS IM SERIOUSLY CRYING RN

Answers

i really don’t know 555

[tex]x = 23[/tex]

Step-by-step explanation:

First, we need to write the equations in their standard form, i.e., all the variables and their coefficients are to be placed on the left hand side and the plain numbers on the right hand side. The first equation is already in its standard form:

[tex]2x + 5y = 35\;\;\;\;\;(1)[/tex]

but we need to rewrite the 2nd one. So the standard form of the 2nd equation can be written as

[tex]x + 15y = -10\;\;\;\;\;(2)[/tex]

Now that the equations are in their standard forms, the next step that we need to do is to eliminate one of the variables, namely the y. To do that, we need to multiply either one of the equations so that when we add them together, the y-variable gets eliminated. Note if we multiply Eqn(1) by -3, we'll get -15y on one equation and a +15y on the other equation so that when they are added together, they cancel out. So if we do that, we get

[tex]-6x - 15y = -105\;\;\;\;\;(3)[/tex]

Adding Eqn(3) to Eqn(2), we get

[tex]-5x = -115[/tex]

or

[tex]x = \dfrac{-115}{-5} = 23[/tex]

Mark which expressions represent the distance between 46 and-15

Answers

|-15-46|
...........

Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks

Mrs. McMillan, the PE, teacher, is pairing off students to race against each other. Heather can
run 4 meters per second, and Erin can run 5 meters per second, Mrs. McMillan decides to give Heather a head start of 23 meters since she runs more slowly. Once the students start
running, Erin will quickly catch up to Heather. How far will Erin have to run? How long will
that take?

Please help.

Answers

Answer:

23 seconds later Erin will catch up

Erin will run 115 meters

Step-by-step explanation:

23+4x=5x

x=23

23 seconds later Erin will catch up

Erin will run 115 meters

3
Johnny has been hired to draw a mural on the window of the pet store. The scale drawing he is using is shown below.
4.5 cm
6 cm
If 1 centimeter represents 10 inches on the mural, what is the actual height and width of the hamster that he will be drawing on the
mural?
OA.
66 in by 49.5 in
ОВ.
90 in by 120 in
Od
6 in by 4.5 in
OD. 60 in by 45 in

Answers

Answer:

OD 60 in by 45 in

Step-by-step explanation:

1. Bianca can walk 5/6 of a mile in 1/3 of an hour. What is her walking speed, in miles per hour?
2. How long, in minutes, does it take Bianca to walk 1 mile?

Answers

Answer:

1. 2.5 miles/hour

2. 24 minutes

Step-by-step explanation:

1. 5/6 of mile in 1/3 of an hour. In 1 hour, Bianca can walk 5/6 x 3 = 15/6 miles or 2.5 miles/hour

2. 5/6 of mile in 1/3 of an hour, hour in 1 mile = (1 x 1/3)/(5/6) = 2/5 = 0.4 hour = 24 minutes

You buy 3.18 pounds of ​apples, 1.35 pounds of oranges​, and 2.25 pounds of pears. What is your total​ bill?

Answers

Answer:

6.78

Step-by-step explanation:

Answer:

6.78 pounds

Step-by-step explanation:

Add: 3.18+1.35+2.25=6.78

(If you wanted the cost for the whole thing then you need to include the price for each of the pounds)

What is the standard deviation of 82,93,89 and 88?

Answers

Answer:

4.546, rounded

Step-by-step explanation:

pls mark brainliest!

PLLLZZZ NO ONE WILL HELP ME!!!
Given this equation in slope-intercept form…
y = 2x + 5
Identify or solve for the following:
Slope
y-intercept
x-intercept
Independent variable
Dependent variable
Domain
Range
We would like to represent a line passing through the point (5,0) with a slope of 2. Please write the equation for this line in slope-intercept form and in point-slope form.

What is the rate of change of the function above?

Answers

Answer:

y = m x + b    standard form of straight line

y = 2 x + 5

The slope is m and = 2

the y intercept is 5  because when x = o y = 5

if y = 0 then x = -2/5 and would be the x intercept

x is the independent variable and y is the dependent variable

I am not familiar with your definitions for domain and range but

both x and y can vary from -∝ to = ∝

The verticles of a triangle are the points R(3,c),Q(9,2) and R(3c,11) where c is constant. Given that angle PQR is 90​

Answers

Answer:

Step-by-step explanation:

Find c if ∠PQR = 90°?

I will ASSUME you mean point P is at (3. c)

slope of PQ is (2 - c) / (9 - 3) = (2 - c) / 6

slope of QR is (11 - 2) / (3c - 9) = 9 / (3c - 9)

perpendicular lines have negative reciprocal slopes.

(2 - c) / 6 = -1(3c - 9)/9

9(2 - c) = -6(3c - 9)

18 - 9c = -18c + 54

       9c = 36

         c = 4

Consider the expression 20-(4^2/2). How many terms does the expression have?

Answers

Answer:

huh

Step-by-step explanation:

A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 90 yards, what are its dimensions?

Answers

Answer:

L=30 W=15

Step-by-step explanation:

90 divided by 6 is 15. 15 is the Width. Multiply 15 by 2 and you get 30 which is the Length.

a parking garage charges $4 for the first hour and $1.50 for each additional hour. sydney has 13$ in her purse

Answers

Answer:

7 hours

Step-by-step explanation:

Answer:

she could park there for 7 hours

Step-by-step explanation:

13-4=9 9/1.50=6

Answer them all please ​

Answers

Answer:

see the attachment

i hope it helps u ✌️✌️✌️☠️

a) The highest common factor and the least common multiple are 12 and 48, respectively.

b) The highest common factor and the least common multiple are 12 and 72, respectively.

c) The highest common factor and the least common multiple are 8 and 160, respectively.

d) The highest common factor and the least common multiple are 12 and 48, respectively.

e) The highest common factor and the least common multiple are 14 and 840, respectively.

Procedure - Determination of the Highest Common Factor and the Least Common Multiple of two integers

In this question we must determine the highest common factor and the least common multiple of two integers.

The highest common factor consists in the maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.

Now, we proceed to determine the numbers for each case:

a) 12 and 48

First, we factorize each integer:

[tex]12 = 2^{2}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex]

Then the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{4}\times 3 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]

b) 24 and 36

First, we factorize each integer:

[tex]24 = 2^{3}\times 3[/tex], [tex]36 = 2^{2}\times 3^{2}[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{3}\times 3^{2} = 72[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 72, respectively. [tex]\blacksquare[/tex]

c) 32 and 40

First, we factorize each integer:

[tex]32 = 2^{5}[/tex], [tex]40 = 2^{3}\times 5[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{5}\times 5 = 160[/tex], [tex]HCF = 2^{3} = 8[/tex]

The highest common factor and the least common multiple are 8 and 160, respectively. [tex]\blacksquare[/tex]

d) 24, 48 and 60

First, we factorize each integer:

[tex]24 = 2^{3}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex], [tex]60 = 2^{2}\times 3 \times 5[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{4}\times 3 \times 5 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]

e) 42, 56 and 70

First, we factorize each integer:

[tex]42 = 2\times 3 \times 7[/tex], [tex]56 = 2^{3}\times 7[/tex], [tex]70 = 2\times 5\times 7[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{3} \times 3 \times 5 \times 7 = 840[/tex], [tex]HCF = 2\times 7 = 14[/tex]

The highest common factor and the least common multiple are 14 and 840, respectively. [tex]\blacksquare[/tex]

To learn more on prime numbers, we kindly invite to check this verified question: https://brainly.com/question/4184435

6. The California Tiger Salamander is an endangered species, which decreases at the rate of 4.6% per year in a habitat that currently has 60 of them. Write an exponential function and find how many California Tiger Salamanders will be left after 4 years.

7. Factor and solve the following equation 2x2 + x - 21 = 0.

8. Alvin throws the football to a receiver who jumps up to catch the ball. The height of the ball over time can be represented by the quadratic equation -4.9t2 + 7.5t + 1.8 = 2.1 . This equation is based on the acceleration of gravity -4.9 m/s2, the velocity of his pass is 7.5 m/s and releases the football at a height of 1.8 meters, and the height where the receiver catches the ball of 2.1 meters. Put the equation in standard form and then solve by using the quadratic equation.

9. Examine the graph of f(x) and the table that contains values of g(x). Which function has a greater rate of change over the interval [0,2]? Explain your answer.

Answers

[tex]\rule{2000pt}{1000000pt}[/tex]

some help, I need some answers

Answers

Answer:

Well your Hypotenuse is 10 and your other angle is 8 so it is most likely 6 because you see a change in 2 each time and it is about 2 units smaller because all right triangles follow a pattern

Step-by-step explanation:

if it was too go even higher it would go to 12,14,16 etcetera

Which of the following is the graph of y = |x - 3|

Answers

Answer:

y = | x - 3 | is graphed on the attachment below

Step-by-step explanation:

If you ever need an equation graphed, here's a useful site called Desmos that can do that really well and for free.

(-7,-4) (-11,-2) slope

Answers

Answer:

1/3

Step-by-step explanation:

-2-4 = -6

-7-11 = -18

Help Will give Branliest

Answers

They Y intercept is 1

Tìm nghiệm tổng quát của các phương trình
y"+2y'-3y=0

Answers

Answer:

y € R i guess

Step-by-step explanation:

I hope it correct

Write -37.75 as a mixed number.​

Answers

Answer:

[tex]-37\frac{3}{4}[/tex]

Step-by-step explanation:

0.75 is equivalent to three quarters, or (3/4).

3/4 would be the fraction. -37 would be the whole number.

[tex]-37.75 = \boxed{-37\frac{3}{4}}[/tex]

Hope this helps.

Answer:

- 37 3/4

Step-by-step explanation:

Need help please ……………………………..

Answers

Answer:

[tex]-2^{-2} = \frac{1}{-2^{2} } = \frac{1}{4} = 0.25[/tex]

[tex]-2^{-1} = \frac{1}{-2 } = -0.5[/tex]

[tex]-2^{0} = 1[/tex]

[tex]-2^{1} = -2[/tex]

[tex]-2^{2} = 4[/tex]

Step-by-step explanation:

Other Questions
8 less than the sum of u and 2 please help.with the steps.just b, please 5 grams of sodium bicarbonate, a white powdery solid, is placed in an empty red balloon. 100 grams of acetic acid, a clear aqueous solution, is placed in the plastic bottle. The balloon is carefully attached to the bottle so that no air can get in or out and the powder does not fall into the bottle. Once attached, the apparatus is placed on a balance and the contents are mixed. Bubbles form, the balloon inflated, and the white powder is no longer visible. Which of the these statements would match your observations? A) A chemical reaction has occurred and the mass will increase. B) A chemical reaction has occurred and the mass will decrease. C) A physical reaction has occurred and the mass will decrease. D) A chemical reaction has occurred and the mass will remain the same. A car travels 80 km at an avarage speed of 40 km/h. It travels the remaining distance in 3h. What is its dis placement if the average speed of the car is 30 km/h.? And explainA) 100 kmB)120 kmC)150kmD)180km Any ideas. I need to select a company that has been around since world war 2. I have to create a presentation showing the generations. Baby boomers, gen x. Gen y, Gen Z. I must have one advertisement for each generation in the figure given alongside if X=3y find the sizes of angles represented by a and b Question 1 of 15What did people who opposed westward expansion often argue?A. Expanding farther west would allow slavery to spread outside theSouthB. Expanding into the West would weaken the U.S. federalgovernment too much.C. Settlers living in western territories had no right to join the UnitedStates.D. The environment in western territories was too dangerous forsettlements. What is the purpose of a persuasive letter? When a stone is dropped from a height, the time taken to fall, t, is proportional to the square root of the distance fallen, d. Write down a formula, using k, connecting the time taken to fall and the distance traveled. in a dilation, what is preserved and what is altered? HELPPPP MEEE PLEASE I AM BEGGING. Between the American Revolution and the French Revolution, which one do you think was the most successful and why? 10. What is a major difference between socialism and communism? (1 point) Socialism seeks to distribute wealth more evenly in society, while communism does not, Socialism is democratic, while communism is not, Socialism does not criticize capitalism, while communism does. Socialism is not widely present in society today, while communism is. Which statement would the author of the passage mostlikely agree with?Passage:3. The Patriot Act updated the law to reflect new technologies and new threats. The Act brought the law up to date with current technology, so we no longer have to fight a digital-age battle with antique weapons-legal authorities leftover from the era of rotary telephones. When investigating the murder of Wall Street Journal reporter Daniel Pearl, for example, law enforcement used one of the Act's newauthorities to use high-tech means to identify and locatesome of the killers.-"The USA PATRIOT Act:Preserving Life and Liberty,"Department of Justice The Patriot Act is essential to the United States'efforts to combat terrorism.O The Patriot Act is essential to the United States'efforts to combat war.O The Patriot Act is needed to help the United Statesprotect privacy rights.O The Patriot Act is needed to help the United Statesprotect suspects' rights.A is the correct answer! :) Use the Fundamental Theorem of Calculus to find y. pls help Which of these questions should you ask while surveying to help you betterunderstand what you're about to read?O A. What do I already know about this topic?O B. What is the source of conflict?O c. What kind of highlighters will I need?O D. What words do I not understand?SUBMIT an example of contractionary fiscal policy would be: Fill in the blanks below with the correct word to complete the sentence.Water is warmed by the sun and It is then cooled andFinally, it is brought back to Earth in the form of A person of 600 newtonsgets on an elevator whichlifts him 6 meters in10 seconds. How muchpower was used? Find the sale price and then add tax.Pete wants to buy a new PlayStation 5 controller that is on sale. The controller cost $70 and is on sale for 40% off. If the sales tax is 10.1% how much will he pay for the controller? Solve 2x^2 - x 15. Show your work