Help me with this please
1 answer:
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The volume of a cuboid is given by length × width × height
We have:
Volume = 7.6 ft³
Height = 3x - 1
Length = x + 5
Width = x
Substituting these into the formula, we have:
7.6 = (3x - 1) (x + 5) (x)
7.6 = [3x² + 15x - x - 5] (x)
7.6 = [3x² + 14x - 5](x)
7.6 = 3x³ + 14x² - 5x
0 = 3x³ + 14x² - 5x - 7.6
Drawing the graph is one way of finding the solution (refer to the graph below):
We have three solutions (where the curve crosses the x-axis):
x = -4.9
x = -0.6
x = 0.8
Putting these solutions back into the context, since we are looking for the value of x which is part of measurement of length, we cannot have negative value, so we will take the value of x = 0.8 ft
Converting 0.8 ft into inches = 0.8 × 12 inches = 9.6 inches
Answer: x = 9.6 inches
We have:
Volume = 7.6 ft³
Height = 3x - 1
Length = x + 5
Width = x
Substituting these into the formula, we have:
7.6 = (3x - 1) (x + 5) (x)
7.6 = [3x² + 15x - x - 5] (x)
7.6 = [3x² + 14x - 5](x)
7.6 = 3x³ + 14x² - 5x
0 = 3x³ + 14x² - 5x - 7.6
Drawing the graph is one way of finding the solution (refer to the graph below):
We have three solutions (where the curve crosses the x-axis):
x = -4.9
x = -0.6
x = 0.8
Putting these solutions back into the context, since we are looking for the value of x which is part of measurement of length, we cannot have negative value, so we will take the value of x = 0.8 ft
Converting 0.8 ft into inches = 0.8 × 12 inches = 9.6 inches
Answer: x = 9.6 inches
<em>It's nice of you to offer, but no thanks.</em>
To correctly graph this, you need to set up a simple equation and table of values. Luckily, this equation is dead-simple; I'll define <em>y</em> as the total cost and <em>x</em> as the number of water bottles sold.
Since 1.50$ is the cost for one bottle, multiplying that with your variable that defined the amount of bottles, <em>x</em>, gets you the total, <em>y</em>. Now that we have a basic equation, we can begin plugging in values.
Recall that a function is basically just something that takes in a value and returns another one; in our case, it takes the <em>amount of bottles</em> and returns the <em>total cost. </em>Now, plug in the x-values present on the graph (specifically only whole numbers, since you can't have a half bottle). I can't make a proper table but I'll make do.
x y
--------
0 0
1 1.5
2 3
3 4.5
4 6
5 7.5
-----------
Great, now that you have a table of values all you have to do is plug them into the graph, which I've attached. It's pretty crude since I drew it in mspaint but I'm sure you get the point at this point.
