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
Vinil7 [7]
3 years ago
15

A rectangle is constructed with its base on theâ x-axis and two of its vertices on the parabola yequals=2525minusâxsquared2. wha

t are the dimensions of the rectangle with the maximumâ area? what is theâ area?
Mathematics
1 answer:
Nina [5.8K]3 years ago
6 0
You should have drawn1 - x-axis and y-axis in light pencil.2 - graphed a down-facing parabola with the top of the frown on the y-axis at y = 2.  It should be crossing the x-axis at ±√2.  This should be in dark pencil or another color.3 - In dark pencil or a completely new color, draw a rectangle with one of the horizontal sides sitting on top of the x-axis and the other horizontal side touching the parabola at each of the top corners of the rectangle. The rectangle will have half of its base in the positive x-axis and the other half on the negative x-axis.  It should be split right down the middle by the y-axis.  So each half of the base we will say is "x" units long.  So the whole base is 2x units long (the x units to the right of the y-axis, and the x units to the left of the y-axis)  I so wish I could draw you this picture...   In the vertical direction, both vertical edges are the same length and we will call that y.   The area that we want to maximize has a width 2x long, and a height of y tall. So A = 2xy     This is the equation we want to maximize (take derivative and set it = 0), we call it the "primary equation", but we need it in one variable. This is where the "secondary equation" comes in.  We need to find a way to change the area formula to all x's or all y's. Since it is constrained to having its height limited by the parabola, we could use the fact that y=2 - x2 to make the area formula in only x's.   Substitute in place of the "y", "2 - x2" into the area formula. A = 2xy = 2x(2 - x2)   then simplify A = 4x - 2x3     NOW you are ready to take the deriv and set it = 0 dA/dx = 4 - 6x2       0 = 4 - 6x2   6x2 = 4    x2 = 4/6 or 2/3 So x = ±√(2/3) Width remember was 2x.   So the width is 2[√(2/3)]Height is y which is 2 - x2 = 2 - 2/3  =4/3
You might be interested in
50 POINTS!!
Charra [1.4K]

Answer:

FH=73

Step-by-step explanation:

We are given that a segment FH and G is the midpoint of FH.

FH=14x-4

FG=5x+9

We have to find the measure of FH.

When G is the midpoint of segment FH

Then , FG=GH

FH=FG+GH

Segment addition property

14x-4=FG+FG

Substitution property

14x-4=2FG

14x-4=2(5x+9)

14x-4=10x+18

14x-10x=18+4

4x=22

x=\frac{22}{4}=5.5

Substitute the values then we get

FG=5(5.5)+9=36.5

FG=GH=36.5

FH=14(5.5)-4=73

8 0
3 years ago
ginny has two vegetable gardens. in the first garden ginny grows tomatoes every 2 years. in the second garden ginny grows tomato
Margarita [4]
Ginny will take 5 years to replant
5 0
3 years ago
Use the cubes shown at the right to estimate the volume of the rectangular prism
MariettaO [177]
Where are the cubes???????.
7 0
3 years ago
Divide the fractions: 2/3 divided by 3/11
Alina [70]
2/3 ÷ 3/11
flip the second one and multiply:
2/3 × 11/3
22/9
2 4/9

Hope this helps :)
6 0
3 years ago
Describe and compare protraction and retraction
disa [49]

Answer:

Protraction and retraction are the movements of the mandibule. <em>Protraction is when the lower mandibule is pushed forward and retraction is when the lower jaw is pulled backward. </em>You can see in the image I added the example of these movements.

I hope you find this information useful and interesting! Good luck!

4 0
2 years ago
Other questions:
  • HELP 15 POINT AND WILL MARK BRIANLYEST. Emma said that when you multiply three negative decimals, the product will be positive.
    5·2 answers
  • In the figure below, lines that appear to be tangent are tangent. Point O is the center of the circle. Which of the following is
    6·2 answers
  • (7•7•7•7•7)•6•6•6•6•6•6. Write your answer using a exponent.
    9·2 answers
  • Help so hard!!! i need help
    5·2 answers
  • Please help !!!! The leg of a right triangle is 2 units and the hypotenuse is 5 units. What is the length, in units, of the othe
    12·1 answer
  • U will see and plz help worth 34 points
    5·1 answer
  • Find 7/8 (-2 • 2/5) Write your answer in simplest form.
    13·1 answer
  • In terms of pie, what is the area of the circle?
    9·1 answer
  • Emily Bought the Following items for Christmas gifts for her Friends: 5 Hannah Montana calendars, 3 DVDs, 2 books, 1 Monopoly ga
    9·1 answer
  • Please help! thanks in advance!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!