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
lina2011 [118]
3 years ago
13

Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed in the region enclosed

by the graphs of f(x)=18-x^2 and
Mathematics
1 answer:
garik1379 [7]3 years ago
4 0
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards. 
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards. 
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x. 
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
 => Area, A 
= 2x (y1 - y2) 
= 2x (18 - x^2 - 2x^2 + 9) 
= 2x (27 - 3x^2) 
= 54x - 6x^3 
For area to be maximum, dA/dx = 0 and d²A/dx² < 0 
=> 54 - 18x^2 = 0 
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants) 

d²A/dx² = - 36x < 0 for x = √3 
=> maximum area 
= 54(√3) - 6(√3)^3 
= 54√3 - 18√3 
= 36√3. 
You might be interested in
Pls help pls I’ll mark you brain
Sergeeva-Olga [200]

Answer:

option b is the correct one l

4 0
3 years ago
Please please helppp answer correctly !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!
marusya05 [52]

Answer:

holy.... that's a lot of variables.

4t+2s+w+u+x+v

4 0
3 years ago
HELP! BRAINLIEST AND 15 POINTS!
Rus_ich [418]

Step-by-step explanation:

first solve for h

fh(4)=f(\frac{4+3}{3} )=f(\frac{7}{3} )

f(\frac{7}{3} )=-3(\frac{7}{3} )-1=-7-1=-8

so fh(4)=-8

6 0
2 years ago
Solve for x. x-17=-57<br> i need help
seraphim [82]
X - 17 = -57
-17. -17
x = -74

hope this helps xo
7 0
3 years ago
Class be boring but anyways what is ( 2 x 2 − 1 )?
mina [271]

Answer:

3

Step-by-step explanation:

In order to do this equation, your first step is to use the Order of Operations, or PEMDAS, which means that you multiply (M) two times two first before subtracting the equation (S). 2 times 2 is 4.  4 - 1 = 3. Hope I helped! :)

5 0
3 years ago
Other questions:
  • the equation of a circle is x - y + 1 = 0 . if one end of the diameter is ( 3, p) and other end is ( a, 2 ) , find the equation
    8·1 answer
  • Subtract (–x – 3) – (5x + 2).<br> help pls Thx!!!!
    13·2 answers
  • Can so one help ?? picture shown
    14·2 answers
  • Marsha’s scores on seven tests were: 82, 78, 77, 93, 85, 91, and 86. What does she need to score on her next test to have an 86
    11·1 answer
  • Jeff uses 3 fifty-size strips to model 3/5. He wants to use tenth-size strips to model an equivalent fraction. How many tenth-si
    6·2 answers
  • In Beijing in 2008, the Women's 3,000-meter Steeplechase became an Olympic event. What is this distance in kilometers? Quick ple
    7·1 answer
  • Check your solution to 2(a - 2) = 2a - 4
    13·2 answers
  • Write the equation of the line whose slope and the point through which it passes are given. Express the equation in point-slope
    15·1 answer
  • If two angle of a right angle triangle are in the ratio 1:2,find them​
    6·2 answers
  • What is the slope of a line that is parallel to the line y= 3/4 x + 2?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!