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.
Y=-1/20(x+3)^2
Your could always tell by which way the curve is pointing and if pointing down it’s a negative it’s pointing up it’s a positive
Hope that helped
Answer:
2/1
Step-by-step explanation:
20/10 devided by 10 to both numbers
8:20 is the same as 2:5.
<h3>What is unitary method?</h3>
- The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.
- Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.
- Recognizing the units and values is crucial when using the unitary technique to a problem.
- Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.
acc to our question-
- = 12 + S
- S= (2/5)A
- S= (2/5)(12+S)
- 5S = 24 + 2S
- 3S = 24
- S = 24/3 = 8 = what Sam received
- A= 8+12 = 20 = what Audreyreceived
- 8:20 is the same as 2:5
- divide both 8 and 20 by 4 to get the 2 to 5 ratio.
hence,8:20 is the same as 2:5.
learn more about unitary method click here:
brainly.com/question/24587372
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Answer:
Step-by-step explanation:
First, find the magnitude of the vector:
Then, divide each component of the vector by the magnitude to get the unit vector and rationalise:
