1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
N76 [4]
3 years ago
5

Two numbers whose sum is 44 and whose product is a maximum

Mathematics
1 answer:
Mashcka [7]3 years ago
4 0

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x)                    Remove the brackets

Max = 44x - x^2                   Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x )               Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done  is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

The maximum occurs when x = 22. That's because - (x - 22) becomes 0.

If it is not zero it will be minus and that will subtract from 484

x + y = 44

xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.


You might be interested in
What is 24/16 in simplest form?
-Dominant- [34]
Well you can divide by 8 and it gives you 3/2or  you can divide by 4 and get 6/4 then divide by 2 and get 3/2 either way there both correct
6 0
3 years ago
Can some plz help me plz!!!!!
LiRa [457]
The choices are in the slope-intecept form: y = mx + b, where m is the slope and b is the y-intercept. Looking at the graph, the y-intercept is the point at which it intersects the y-axis. That would be -1. So, the answer is either  the 1st or 2nd choice. Next, we find the slope. Take 2 points that lie along the line. For example, points (1,2) and (2,5). Calculate for the slope.

m = (y2-y1)/(x2-x1)
m = (5-2)/(2-1)
m = 3

Hence, the graph is y = 3x - 1
8 0
4 years ago
Please help me!<br><br> ty :)
dalvyx [7]

Answer:

x intercept= (-3,0)  y intercept= (0,3)

Step-by-step explanation:

for x intercepts, y should equal zero

for y intercepts, x should equal zero

x intercept: -x+0=3

-x=3

x=-3  (x,y)--> (-3,0)

y intercept: 0+y=3

y=3 (x,y)--> (0,3)

4 0
2 years ago
Read 2 more answers
"Scenario: You have to pay your share of the rent today. The total rent for your apartment is $1762.50. You have two roommates t
topjm [15]

Answer:

You would be required to pay $587.50

Step-by-step explanation:

Divide $1762.50 by three:

You get $587.50

To find how much you have left:

Subtract 587.50 from 668.72:

You'd be left with

$81.22

3 0
3 years ago
Read 2 more answers
Need help ASAP.<br> 50×50+60-105=?
Mandarinka [93]

Answer:

2,455

Step-by-step explanation:

Use PEMDAS to solve

First multiply 50x50, which is 2,500

50 x 50 + 60 - 105   becomes

2,500 + 60 - 105

Now to the addition or subtraction from left to right

2,560 - 105

  2,455

4 0
3 years ago
Read 2 more answers
Other questions:
  • AB and PQ are lines of length 6 cm a) AX: AB 1:3 Mark where point X would be on the line, with a cross. A B b) PX: XQ 1 :3 Mark
    6·2 answers
  • Suppose you want to solve the following problem. 8 sandwich rolls cost $2.48, how much will 15 rolls cost? Wich os te following
    7·1 answer
  • Nicks poster has an Area of 2 1/2 feet. If the width is 1 1/4 feet what is the length?
    11·1 answer
  • Krissy ran three miles one morning she ran the first mile in 11. 74 minutes the second mile in 11. 26 minutes in the third mile
    14·1 answer
  • Can someone help me with my homework
    12·1 answer
  • Factor tree for 30 and 54
    5·2 answers
  • The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?
    12·1 answer
  • A submarine changes its position by −7 meters every second.
    7·2 answers
  • PLEASE HELP!!!!!!!!!!!!!!!!ASAP!!!!!!!!!!NOW!!!!!!!!!!RIGHT AWAY!!!!!!!!
    11·1 answer
  • Please help me for 20 points
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!