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
dlinn [17]
3 years ago
5

A rectangle is inscribed under the curve y = 24 – x2 with a portion of the x-axis as its base. What is the area, in square units

, of the largest such rectangle?
Mathematics
1 answer:
8090 [49]3 years ago
3 0
Answer: 90.51 square units

Explanation:

1) The rectangle has one length on the x-axis.

2) Call x, the x-coordinate of the right lower corner of the rectangle.

And the point is (x,0)

3) The x-coordinate of the lef lower corner will be - x.

And the point is (-x,0)

4) The right upper point of the rectangle will be (x,y) where y = 24 - x²

5) The left upper point of the rectangle will be (-x,y) where y = 24 - x² .

6) The area of such rectantle is the length of the base times the length of the height.

The length of the base is 2x

The lenght of the height is y

So, the area is A = 2x(y) = 2x(24 - x²) = 48x - 2x³

7) Now to find the maximum area you have to derivate the function and make it equal to zero:

dA
---- = A' = 48 - 6x² = 0 =>
dx

4x² = 48 => x² = 48/6 = 8 =>

x = (+/-)√8

Then, y = 24 - x² = 24 - (√8)² = 24 - 8 = 16

8) Therefore the area of the rectangle is

A = 2x(y) = 2(√8)(16) = 90.51.

9) You can see if x is a greater or smaller.

For example x = 2 and x = 3

x = 2 => y = 24 - (2)² = 20 => A = 2(2)(20) = 80 which is less than 90.51

x = 3 => y = 24 - (3)² = 15 => A = 2(3)(15) = 90 which is less than 90.51

So, that tells you that your result should be right.
You might be interested in
Find the 10 th term of the following geometric sequence. 1,5, 25, 125, ...​
IceJOKER [234]

Answer:

1953125

Step-by-step explanation:

5: 625

6: 3125

7: 15625

8: 78125

9: 390625

10: 1953125

Sequence

×5

6 0
2 years ago
Round the following to the nearest hundreds. 23457,45289,2458​
djverab [1.8K]

I think it's 23500, 45300, 2500

4 0
2 years ago
Read 2 more answers
Please tell me how can i find x without calculator ?
gtnhenbr [62]
I hope this helps you

3 0
3 years ago
Sean began jogging to live a healthier lifestyle. On his first run, he ran one-half mile. He increased his workouts by adding tw
Slav-nsk [51]
Variable x represents the number of runs Sean takes.
4 0
2 years ago
Read 2 more answers
Can someone tell me what is 8/9+3/5
I am Lyosha [343]
Okay I am going to explain to you and show you how to get the correct answer.

Fist you need to find the Greatest common factor which is 45 because 5×9=45

8/9=40/45

+3/5=27/45
__________
67/45 is reduced to 1 22/45
5 goes into 45 9 times so 3 times 7 equals 27 and 9 goes into 45 5 times so 8 times 5 equals 40 you add both numbers up and get 67. 67 can't go into 45 so you subtract 67 from 45. 45 goes into 67 1 time so that is your whole the number. 22 is left over so that is your numerator. The denominator remains the same.
5 0
3 years ago
Other questions:
  • You are charged 6% sales tax. You purchase a new bicycle and pay $27 in sales tax. What is the purchase price of the bicycle?
    11·1 answer
  • How do you solve this?<br><br>(5+i)(5+2i)
    6·1 answer
  • On a true/false test, the ratio of true questions to false questions is 3 to 7. What is the ratio of true questions to total que
    11·2 answers
  • Would you rather have a pool thats 40ft x 9ft x 4ft or a pool that 7yds x 4yds x 2yds \
    10·1 answer
  • Last night, the temperature fell from 0°F to -13 in 4 § hours. What was the average temperature change per hour? Solve the divis
    9·2 answers
  • Dave buys 18 bunches of bananas for $9 for the after school program. Determine how much Patrick will pay for 8 bunches of banana
    12·1 answer
  • Answer some of the questions, please
    9·2 answers
  • Liam cuts a 48-inch piece of string into two pieces. One piece is 12 inches longer than the other. If s represents the length of
    9·1 answer
  • Which expressions are equivalent to (1/3x + 2x - 5/3x) - (-1/3x + 5)​
    5·2 answers
  • In a certain card​ game, the probability that a player is dealt a particular hand is. Explain what this probability means. If yo
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!