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
A jewelry store sells charm bracelets and charms. A bracelet with two charms costs $36.00. A bracelet with four charms costs $50
Slav-nsk [51]

Answer:

36+50

Step-by-step explanation:

4 0
3 years ago
Help me please thanks before
sdas [7]
-17 + 28 = 11

hope this helps, give brainliest 
8 0
3 years ago
Read 2 more answers
Does anyone know this???
Grace [21]

Answer:

see explanation

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent.

Thus ∠D = ∠A and substituting values

2x = x + 31 ( subtract x from both sides )

x = 31

Hence

∠A = x + 31 = 31 + 31 = 62

∠D = 2x = 2 × 31 = 62

8 0
3 years ago
At the car show Inez saw a truck wheel shaped like a circle with a radius of 3 ft. She wants to know the area of the truck wheel
Nadusha1986 [10]

Answer:

28.27ft^2

Step-by-step explanation:

To solve this problem, we can use the area of a circle formula:

A=\pi r^2

<em>A = area</em>

<em>r = radius</em>

Lets plug the values into the equation:

A=\pi (3^2)     Calculate 3^2

A=\pi (9)       Multiply \pi and 9 together

A=28.27

The area of the truck wheel is 28.27ft^2

3 0
2 years ago
PLZ HELP ILL MARK AS BRAINLIEST
Rainbow [258]

Answer:

1092 cm^2

Step-by-step explanation:

Formula = 2 * Height (Length + Width)

2 * 26 (15 + 6) = 1092

6 0
2 years ago
Other questions:
  • Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 71°, a
    15·2 answers
  • I solved the equation but I can’t seem to answer the ordered pair correctly... (21, )
    9·1 answer
  • What fraction of an hour is 5 minutes in its lowest terms ?
    15·2 answers
  • How many times does 12 go into 144
    13·2 answers
  • Given the expotential function f(x) = 4(3)^x find f(0) and f(1)
    14·1 answer
  • Why is 315 the lcm of 21 and 45?
    11·1 answer
  • The area of one fabric is 4.85 square what is the area of a quilt made with 10.2 fabric squares​
    8·1 answer
  • Darrien is making a solid figure out of folded paper. His solid figure has six congruent faces that are all squares. What sold f
    8·1 answer
  • Translate it and Simplify if needed :Four more than three times a number decreased by six
    10·1 answer
  • The reason why I don’t like helping people is because sometimes when I help them they never do the same to me :(... pls just thi
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!