Answer:
Length = 13 cm
Step-by-step explanation:
Length (L) = 2 x Width (W) + 5
2 x (L + W) = 34
2 x (2W + 5 + W) = 34
6W + 10 = 34
6W = 34-10 = 24
W=4
L = 13
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.
Answer:
B
Step-by-step explanation:
Pints and Quarts are measures of volume. The relationship between them is rather simple.
We know 2 pints = 1 Quart
The problem gives us the number of pints and we need to find the number of quarts. From the relationship, we see that "pints divided by 2 will give us quarts"
Given >> 10 pints
Hence, number of quarts would be 10/2 = 5
Hence 10 pints = 5 quarts
Answer choice B is right.
Answer:
B
Step-by-step explanation:
lets say the cost for a pound is 2$
if the watermelon weighs 3 pounds it would cost $6.
2(3)
The weight is the variable in the parenthesis because that is what is constantly changing.
Answer:
-12
Step-by-step explanation:-3y+12=48
48-12= 36
36/ (-3) = -12
