A.) Let the length of the sides of the bottom of the box be y and z, and let the length of the sides of the square cut-outs be x, then
V = xyz . . . (1)
2x + y = 24 => y = 24 - 2x . . . (2)
2x + z = 24 => z = 24 - 2x . . . (3)
Putting (2) and (3) into (1), gives:
V = x(24 - 2x)(24 - 2x) = x(24 - 2x)^2 = x(576 - 96x + 4x^2)
V = 4x^3 - 96x^2 + 576x
b.) For maximum volume, dV/dx = 0
dV/dx = 12x^2 - 192x + 576 = 0
x^2 - 16x + 48 = 0
(x - 4)(x - 12) = 0
x = 4 or x = 12
but x = 12 is unrearistice
Therefore, x = 4.
y = z = 24 - 2(4) = 24 - 8 = 16
Therefore, the dimensions of the box that enclose the largest possible volume is 16 inches by 16 inches by 4 inches.
c.) Maximum volume = 16 x 16 x 4 = 1024 cubic inches.
Answer:
As x increases , y decreases then increases
Step-by-step explanation:
There are two situation
1> when x < 0
2> when x>= 0
let see
when x < 0
we see that as value of x moves from -ve value towards zero (i.e x is increasing) then value of y is decreasing( value of x has moved from positive side of y( above x-axis) towards negative side of (below x-axis)\
Thus, we can say that
for x < 0
As x increases , y decreases
________________________________________
when x>= 0
we see that as value of x moves from 0 towards +ve value(i.e x is increasing) then value of y is increasing( value of x has moved from negative side of y( below x-axis) towards positive side of (above x-axis)\
Thus, we can say that
for x >= 0
As x increases , y increases
_________________________________________
combining both observation it can be said that
As x increases , y decreases then increases which is equal to fouth option
Answer:
31.4 cm
Step-by-step explanation:
Hence, length of arc = 31.4 cm.
Answer:
x=12
Step-by-step explanation:
11x - 17 + 65 = 180
11x + 48 = 180
<u> -48 -48 </u>
<u>11x </u>= <u>132</u>
11 11
x = 12
I'm sorry, I didn't fully understand your question, but if it is What is the percent of liberal in State B the answer is 60%
x% * 35 = 21
x/100 * 35 = 21
35x/100 = 21
35x = 2100
x = 2100/35
x = 60
or 60 %
