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
solniwko [45]
3 years ago
9

The diagonals of a convex quadrilateral are mutually perpendicular. The sum of the lengths of the diagonals is 12. We want to fi

nd the maximum possible area of such a quadrilateral. Let us denoted by x and y the lengths of the two diagonals. Then the area of the quadrilateral is the following function of x and y:________.
Mathematics
1 answer:
KIM [24]3 years ago
3 0

Answer:

33

Step-by-step explanation:

Step 1: The Diagonals of the Convex Quadilateral are Mutually Perpendicular this makes the shape a Rhombus Shape

Step 2: The formula for a area of a rhombus is the multiply the two lengths and divide by two.

In this Question we have x×y÷2 or xy/2

Step 3: The sum of the lengths of the diagonals is 12

x+y=12

y=12-x

Therefore, the area, as a function of x alone = x(12-x)/2

Step 4: To find the maximum area, let's find the derivative of the area function in respect to x and then equate to 0.

d/dx(x(12-x)/2)=0

d/dx(12x - x^2) = 0

12-2x=0

12-0=2x

12=2x, divide both sides by 2

x= 6

Step 5: Calculate the Maximum Area

The maximum area will then be 6(12 - 6)/2

= (72-6)/2 = 66/2= 33

So, the maximum area is 33.

You might be interested in
How to write in equation in slope intercept form from graph
IceJOKER [234]

Answer:

mx+b

m=slope

b=y-intercept

Step-by-step explanation:

5 0
3 years ago
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the avera
Veseljchak [2.6K]

Answer:

<h2>Yes, it is likely due to the significant difference in their average scores. </h2>

Step-by-step explanation:

The average number of runs scored by a Little League team in a game is 5.7. If he chooses five games at random in which his team scored 5 , 9, 4, 11, and 8 runs, their average score of the five games is expressed as shown;

Average score of 5 games = (5+9+4+11+8)/5

Average score of 5 games  = 37/5

Average score of 5 games  = 7.4

Comparing the average score in 5 games to the the average number of runs scored nationally, it can be seen that their difference is 7.4 - 5.7 which is 1.7. Since the difference is quite significant, then it is most likely that his team's scores is different from the national distribution.  

7 0
3 years ago
Find the product.<br> (x2+3x+7)(x^7)=<br><br><br> Please help :)
Nesterboy [21]

Answer: x^9+3x^8+7x^7

Step-by-step explanation:

the ^ mean the exponent

4 0
2 years ago
Which conditional statement is represented by the Venn diagram below?
yarga [219]

Answer:

D.  If a shape is an equilateral triangle, then it is an isosceles triangle.

Step-by-step explanation:

3 0
2 years ago
Five less than the product of 3 and a number of 40 . Write in an equation
vagabundo [1.1K]

Answer:

I don't get the "number of 40" part, but here's my best shot!

3(40x)-5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Use substitution. 2x + 3y = 5 4x - y = 17 Use linear combinations: 2x + 3y = 5 4x - y = 17
    5·1 answer
  • "Which triangle can be proven congruent to ABC using the ASA criterion?.
    15·2 answers
  • Write an expression to represent the sum modeled in the following number line.
    6·1 answer
  • Question:
    7·1 answer
  • A drinking glass is shaped like a cylinder with a height of 5 in. and a diameter of 3 in. Maeva adds 25 spherical pieces of ice
    8·1 answer
  • What is 4.75 as a fraction?
    8·2 answers
  • 4n + 3 &lt; 6n + 8 - 2n<br><br> Pls solve in steps
    6·1 answer
  • 3.265 rounded to the nearest tenth
    10·2 answers
  • The length of a rectangle is 5 less than twice its width. The perimeter is 26 meters. Find the dimensions of the rectangle.​
    12·1 answer
  • What is the unit rate of a line that goes through the points (3,1)?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!