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
Sever21 [200]
3 years ago
5

Find the dimensions of the shaded region so that its area is maximized. x= y=

Mathematics
1 answer:
musickatia [10]3 years ago
3 0
1.  Find the equation of the line AB.  For reference, the answer is y=(-2/3)x+2.
2.  Derive a formula for the area of the shaded rectange.  It is A=xy (where x is the length and y is the height).
3.  Replace "y" in A=xy with the formula for y:  y= (-2/3)x+2:
       
                 A=x[(-2/3)x+2]    This is a formula for Area A in terms of x only.
4.  Since we want to maximize the shaded area, we take the derivative with respect to x of    A=x[(-2/3)x+2] , or, equivalently, A=(-2/3)x^2 + 2x.
This results in   (dA/dx) = (-4/3)x + 2.
5.  Set this result = to 0 and solve for the critical value:  

(dA/dx) = (-4/3)x + 2=0, or (4/3)x=2   This results in x=(3/4)(2)=3/2

6.  Verify that this critical value x=3/2 does indeed maximize the area function.
7.  Determine the area of the shaded rectangle for x=3/2, using the previously-derived formula          A=(-2/3)x^2 + 2x.

The result is the max. area of the shaded rectangle.
You might be interested in
If 2580 people watched one show and 2920 people watched another show. How many people need to watch the third show for there to
Leokris [45]

Answer:

340

Step-by-step explanation:

2920 - 2580 = 340

There need to be 340 people to watch the third show.

8 0
3 years ago
Read 2 more answers
Anybody know this answer need answer asap
Darya [45]
If P = b + a + c, and we are to solve for b, subtract a and subtract c from both sides:

P - a - c = b (answer)
8 0
3 years ago
Which decimal is between 1.5 and 1.7?
anyanavicka [17]
B is definitely between those decimals
8 0
3 years ago
Read 2 more answers
Graph the line with the equation y = -x - 6
AlladinOne [14]

here you go . i hope this helps

6 0
3 years ago
An equilateral triangle and a square both have perimeters of 48 inches. what is the ratio of the length of the side of the trian
labwork [276]
A square with a perimeter of 48 inches would have 12 in sides, while a triangle of the same perimeter would have 16 in sides. The ratio would be 16/12 which simplified to 4/3.
8 0
3 years ago
Other questions:
  • Rodrigo is sitting on the branch of an apple tree. He tosses an apple to a friend who is sitting on the ground.
    9·1 answer
  • Select the pair of functions representing f(x) and g(x) if f(g(x))=8x+1
    14·1 answer
  • on a suspension bridge the roadway is hung from cables hanging between support towers. the cable of one bridge segment of the pa
    8·1 answer
  • What is (are) the solution(s) to the equation <br>2<br>(x−4)<br>2<br>=50
    5·1 answer
  • Shila read the
    12·1 answer
  • Find the greatest common factor of 24, 36, and 48. help
    11·2 answers
  • NO LINKS NO FILES. Write the next two integers: -48, -24, -12, _, _
    5·1 answer
  • Tiny's Tattoo Parlor sold 389 tattoos this month. 43 of those tattoos were arm tattoos.
    15·1 answer
  • Does anyone know how many feet this is if i do it is 1,474 x 829 just make it into a small number
    15·1 answer
  • A minor league hockey team had the following scores for the start of the season for the start of the season 3,6,2,1,2,3,0,4,5,1,
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!