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
Pepsi [2]
3 years ago
6

A rectangle is constructed with its base on the​ x-axis and two of its vertices on the parabola yequals=4949minus−xsquared2. Wha

t are the dimensions of the rectangle with the maximum​ area? What is the​ area?
Mathematics
1 answer:
xxMikexx [17]3 years ago
8 0

Answer:

Dimensions of rectangle : Width = 2x , Length = 49 - x^2

Area of Rectangle = 98x - 2x^3

Step-by-step explanation:

A rectangle constructed with its base on the​ x-axis and two of its vertices on the parabola

Supposing coordinates of upper right vertex of rectangle are P = (x,y)

Due to parabola symmetry, width of rectangle is twice the horizontal (X) axis distance between Y axis & point P.

Width of rectangle :  2x

Length of rectangle :  y = 49 - x^2

Area of Rectangle = Length x Width

(2x) (49 - x^2)

= 98x - 2x^3

You might be interested in
How do you calculate surface area of trapezium with an angle<br>​
Kay [80]

Answer:  There are eight steps and two methods. I will be showing you one of them. If you're wondering, I am in 7th grade. I go to K12 online school.

Step-by-step Explanation: 1. Add together the lengths of the bases. The bases are the 2 sides of the trapezoid that are parallel with one another. If you aren’t given the values for the base lengths, then use a ruler to measure each one. Add the 2 lengths together so you have 1 value.[1]

For example, if you find that the top base (b1) is 8 cm and the bottom base (b2) is 13 cm, the total length of the bases is 21 (8 cm + 13 cm = 21 cm, which reflects the "b = b1 + b2" part of the equation).
2. Measure the height of the trapezoid. The height of the trapezoid is the distance between the parallel bases. Draw a line between the bases, and use a ruler or other measuring device to find the distance. Write the height down so you don’t forget it later in your calculation.[2]

The length of the angled sides, or the legs of the trapezoid, is not the same as the height. The leg length is only the same as the height of the leg is perpendicular to the bases.

3. Multiply the total base length and height together. Take the sum of the base lengths you found (b) and the height (h) and multiply them together. Write the product in the appropriate square units for your problem.[3]

In this example, 21 cm x 7 cm = 147 cm2 which reflects the "(b)h" part of the equation.

4. Multiply the product by ½ to find the area of the trapezoid. You can either multiply the product by ½ or divide the product by 2 to get the final area of the trapezoid since the result will be the same. Make sure you label your final answer in square units.[4]

For this example, 147 cm2 / 2 = 73.5 cm2, which is the area (A).

7 0
2 years ago
camela is trying to find the equation of a line that passes through the points (-1, 16) and (5, 88). does the equation y= 12
lutik1710 [3]
I'm assuming you meant does y=12x pass through those coordinates, and if that's the case, then the answer is no. 

Hope that helps :)
6 0
3 years ago
The measurement of one angle of a right triangle is 34°.
Svetllana [295]
The third angle is 56 degrees because it is a right <u>triangle</u>, so the three angles will add up to 180 degrees.  Since it is a right triangle, you know one angle is 90 degrees.  All you have to do is add 90 and 34, and then subtract that from 180 to get your third angle.
4 0
3 years ago
According to the rules of Major League Baseball, the infield must be 30 feet by 30 feet in a diamond shape with perpendicular (9
nlexa [21]

Answer:

No Major League ballparks are exactly alike, but certain aspects of the field of play must be uniform across baseball.

The infield must be a square that is 90 feet on each side, and the outfield is the area between the two foul lines formed by extending two sides of said square (though the dirt portion of the field that runs well past the 90-foot basepaths in all Major League parks is also commonly referred to as the infield). The field must be constructed so that the bases are the same level as home plate.

The rulebook states that parks constructed by professional teams after June 1, 1958, must have a minimum distance of 325 feet between home plate and the nearest fence, stand or other obstruction on the right- and left-field foul lines, and 400 feet between home plate and the nearest fence, stand or other obstruction in center field. However, some clubs have been permitted to construct parks after that date with dimensions shorter than those specified.

The pitcher's plate must be a 24-inch by 6-inch slab of whitened rubber that is 10 inches above the level of home plate and 60 feet, 6 inches away from the back point of home plate. It is placed 18 inches behind the center of the mound -- which is erected within an 18-foot diameter circle -- and surrounded by a level area that is 5 feet by 34 inches. The slope of the pitcher's mound begins 6 inches in front of the pitcher's plate and must gradually decrease by 1 inch every foot for 6 feet in the direction of home plate.

Home plate is a 17-inch square of whitened rubber with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 8 1/2 inches each and the remaining two sides are 12 inches each and set at an angle to make a point. The 17-inch side faces the pitcher's plate, and the two 12-inch edges coincide with the first- and third-base lines. The back tip of home plate must be 127 feet, 3 and 3/8 inches away from second base.

The other bases must be 15-inch squares that are between 3 and 5 inches thick, covered by white canvas or rubber and filled with soft material.

Step-by-step explanation:

4 0
3 years ago
If Jenny’s salary is $350 per week and she works 40 hours, what does she earn per hour?
diamong [38]

Answer:

$8.75  an hour

Step-by-step explanation:

Just do 350 / 40 and you get 8.75

7 0
3 years ago
Read 2 more answers
Other questions:
  • nan cut a submarine sandwich into 4 equal parts and parts and ate one part what fraction represented the part of the sandwich he
    6·1 answer
  • Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. 2, 9, 16, 23
    14·2 answers
  • A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria
    11·1 answer
  • The vice-president of a bank earns $1635 per week. This is $55 more than two times the weekly wage of a bank manager. Write an e
    10·1 answer
  • Solve for x: −3|x 7| = −12 x = 5 over 3, x = −19 over 3 x = −3, x = −11 x = −3, x = 11 no solution
    14·1 answer
  • I need help please this isath i need my grade thx alot
    8·2 answers
  • Complete the expanded form of this number.
    14·1 answer
  • Butter kruse made 522 glaze donuts and 323 chocolate covered donuts. They put the donuts in boxes. Each box holds 12 donuts. How
    12·1 answer
  • What is the area of the circle?​
    11·2 answers
  • Question is down below:
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!