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
11

A rectangle is constructed with its base on the​ x-axis and two of its vertices on the parabola y equals = 100 100 minus −x squa

red 2. What are the dimensions of the rectangle with the maximum​ area? What is that​ area?
Mathematics
1 answer:
masha68 [24]3 years ago
5 0

Answer:

Step-by-step explanation:

Given that a rectangle is constructed with its base on the x axis and two of its vertices on the parabola

y=100-x^2

This parabola has vertex at (0,100) and symmetrical about y axis.

Any general point above x axis can be written as (a,b) (-a,b) since symmetrical about yaxis.  

Hence coordinates of any rectangle are

(a,0) (-a,0), (a, 100-a^2), (-a, 100-a^2)

Length of rectangle = 2a and width = 100-a^2

Area of rectangle = lw = 2a(100-a^2)=200a-400a^3

To find max area, use derivative test.

A' = 200-800a^2\\A"=-1600a

Hence maxima when first derivative =0

i.e. when a =2

Thus we find dimensions of the rectangle are l =4 and w = 96

Maximum area = 4(96) = 384

You might be interested in
Whats the answer?please tell me!!
zavuch27 [327]
95.72 + 5.228 = 100.948
6 0
3 years ago
Read 2 more answers
A biologist studying the relationship between tilapia and catfish in a pond finds that the ratio of tilapia to catfish is 6:20.
Neko [114]

Answer: 9 tilapia

Step-by-step explanation:

The ratio of 6:20 for tilapia to catfish means that for every six tilapia, there are 20 catfish in the pond.

If there are 30 catfish, use direct proportion to find out the number of tilapia:

6     :      20

x     :       30

Cross multiply:

20x = 180

x = 180 / 20

x = 9 tilapia

5 0
3 years ago
If b is the midpoint of AC, which of the following choices is the value of x?
katrin [286]
If B is the midpoint of AC, that means that the distances from A to B and B to C are the same. The distance from A to B is 8x + 4, and the distance from B to C is 10x - 6, so we can set these two equivalent:

8x + 4 = 10x - 6

Solving for x:

4 = 2x - 6 (subtract 8x from both sides)
10 = 2x (add 6 to both sides)
5 = x (divide both sides by 2)

So, x = 5, which is the second option given.
8 0
3 years ago
Find the surface area of the cylinder and round to the nearest tenth. (It is recommended that you use the π button on your calcu
elena-s [515]

The surface area of the cylinder is 18.84 square feet

<h3>How to determine the surface area?</h3>

The given parameters are

Height, h = 2 ft

Diameter, d = 2 ft

The radius (r) is half of the diameter (d)

This is calculated as:

Radius = Diameter/2

So, we have:

r = d/2

Substitute 2 for d

r = 2/2

Evaluate the quotient i.e. divide 2 by 1

r = 1

The surface area is then calculated using the following formula

A = 2πr² + 2πrh

Substitute the given values in the above equation

So, we have:

A = 2 * 3.14 * 1^2 + 2 * 3.14 * 1 * 2

Evaluate the exponents

A = 2 * 3.14 * 1 + 2 * 3.14 * 1 * 2

Evaluate the products

A = 6.28 + 12.56

Evaluate the sum

A = 18.84

Hence, the surface area of the cylinder with the given height and radius is 18.84 square feet

Read more about surface area at:

brainly.com/question/2835293

#SPJ1

4 0
2 years ago
(PLEASE HELP, DUE IN 30 MINS)
Lera25 [3.4K]

The total amount of her savings 12,058.78

3 0
3 years ago
Read 2 more answers
Other questions:
  • Cameron makes a quilt design using four congruent triangles as shown below. 4 connecting congruent triangles are shown. The bott
    13·2 answers
  • The graph of this system of equations is used to solve 4x^2-3x+6=2x^4-9x^3+2x
    5·2 answers
  • What are the coordinates of the terminal point for 0=330
    13·1 answer
  • Need help asap !!!!!!!!
    7·1 answer
  • Find angle x, giving your answer to 1 decimal place.<br> 38°<br> x<br> 11 cm<br> 8 cm
    13·1 answer
  • Simplify<br><br> -4 (y +1) -2
    14·1 answer
  • One of the angles of a triangle is 110° and the other two angles are equal.What is the measure of each of these equal angles?
    8·2 answers
  • 8x + 12<br> Can someone please factorise this
    12·1 answer
  • Longhorn Corporation provides low-cost food delivery services to senior citizens. At the end of the year on December 31, 2021, t
    15·1 answer
  • Determine the slope and the y-intercept of the line.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!