Answer:
16,242. 7 cm^3.
Step-by-step explanation:
We need to cut off a square piece at the 4 corners of the cardboard.
Let the length of their edges be x cm.
The volume of the box will be:
V = height * width * length
V = x(100-2x)(40-2x)
V = x(4000 - 200x - 80x + 4x^2)
V = x(4x^2 - 280x + 4000)
V = 4x^3 + - 280x^2 + 4000x
Finding the derivative:
dV / dx = 12x^2 - 560x + 4000 = 0 ( when V is a maxm or minm.)
4(3x^2 - 140x + 1000) = 0
x = 37.86, 8.80.
Looks like x = 8.80 is the right value but we can check this out be looking at the sign of the second derivative:
V" = 24x - 560, when x = 8.8 V" is negative so this is a Maximum for V.
So the maximum volume of the box is when x = 8.8 so we have
V = 8.8(100-2(8.8)(40 - 2(8.8)
= 16,242. 7 cm^3.
Answer:
The answer is 148.27
Step-by-step explanation:
I dont know what rounded 2 DP means but rounded to the nearest tenth is 148.3 and rounded to the nearest whole number is 148
First, figure out the slope of the line by solving for the slope between the two given coordinates.
Slope = y2 - y1 / x2 - x1
Substitute the coordinates.
Slope = 2 - (-4) / 2 - (-1)
Slope = 2 + 4 / 2 + 1
Slope = 6 / 3
Slope = 2
So, the slope of the equation here is 2.
Next, look for the y-intercept. You can find the y-intercept by looking on the graph. At what coordinate does the line intersect or cross the y-axis? By looking at the graph, you can see that the line intersects the y-axis at the coordinate point (0, -2). So, your y-interceot is -2.
Now, choose the equation that has a slope of 2 and a y-intercept of -2.
Remember that the standard form of any given linear equation should be in slope-intercept form.
y = mx + b
Substitute the slope and y-intercept
y = 2x - 2
By doing this, you can eliminate choices 1 and 4 because the equation should have 2x to represent the slope of 2.
The best choice is 2x - y = 2.
You have a slope of 2x and if the equation is put in standard form you would have a y-intercept of -2.
Solution: 2x - y = 2
I think the answer is (a) love:(
Step-by-step explanation:
the answer is 2/9
2/9 is .2222222 continuing
2/10 is 0.2
22/1000 is 0.022
2/8 is 0.25
