A ibc with no lid is made by cutting four squares if side length x from each corner of a 10 cm by 20 cm rectangle sheet of metal.
Sketch the graph of the function and state restriction
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-5. 5. 10. 15
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Please proofread.
What is a ibc?
Where should periods and capital letters go?
Oh -- and what is your school subject?
To sketch the graph of the function, we first need to determine the equation that represents the height of the box as a function of the width.
Given that a rectangle measuring 10 cm by 20 cm is used, and squares of side length x are cut from each corner to create the box, we can see that the base of the box will have dimensions (10 - 2x) by (20 - 2x).
The height of the box will be x because the squares that are cut from the corners determine the height of the box.
Therefore, the volume of the box can be expressed as V(x) = x(10 - 2x)(20 - 2x).
To sketch the graph, we can create a table of values by substituting different values of x into the equation.
Let's choose some values for x and calculate the corresponding values of V(x):
For x = 0:
V(0) = 0(10 - 2(0))(20 - 2(0)) = 0
For x = 1:
V(1) = 1(10 - 2(1))(20 - 2(1)) = 16
For x = 2:
V(2) = 2(10 - 2(2))(20 - 2(2)) = 48
For x = 3:
V(3) = 3(10 - 2(3))(20 - 2(3)) = 72
For x = 4:
V(4) = 4(10 - 2(4))(20 - 2(4)) = 64
For x = 5:
V(5) = 5(10 - 2(5))(20 - 2(5)) = 0
Using these values, we can plot the points (x, V(x)) on a graph.
Next, let's determine the restrictions on x. Since we are cutting squares from the corners of the rectangle, the values of x should be restricted such that the resulting dimensions of the base are positive.
To determine this condition, we set the width (10 - 2x) and the length (20 - 2x) greater than zero:
10 - 2x > 0
20 - 2x > 0
Simplifying these inequalities, we have:
-2x < -10
-2x < -20
Dividing both sides by -2 (and reversing the inequality sign because we are dividing by a negative number):
x > 5
x > 10
Therefore, the restriction on x is x > 10.
Now, we can plot the points on a graph and draw a smooth curve connecting them. The x-axis represents the values of x, and the y-axis represents the values of V(x). Make sure to label the axes appropriately.
The graph should have a line of symmetry at x = 5 and symmetric shapes on each side.
Based on the given table of values, the graph might resemble a downward-opening parabola, starting with a point at (0,0) on the y-axis, reaching a maximum point, and then descending back towards the x-axis.