A retirement community has a sign at its main entrance that says "Residents over the age of 55 welcome." Which of the following
2 answers:
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Answer:
x = 0.53 cm
Maximum volume = 1.75 cm³
Step-by-step explanation:
Refer to the attached diagram:
The volume of the box is given by
Let x denote the length of the sides of the square as shown in the diagram.
The width of the shaded region is given by
The length of the shaded region is given by
So, the volume of the box becomes,
In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.
We are left with a quadratic equation.
We may solve the quadratic equation using quadratic formula.
The quadratic formula is given by
Where
Volume of the box at x= 1.59:
Volume of the box at x= 0.53:
The volume of the box is maximized when x = 0.53 cm
Therefore,
x = 0.53 cm
Maximum volume = 1.75 cm³
Answer:
Hello!
After reviewing the problem you have provided I have come up with the correct solution:
x= 9
Step-by-step explanation:
To come up with this solution you have to first realize that the smaller triangle is a proportionally scaled down version of the entire larger triangle! (I will show what I mean in a linked picture)
So after we have realized that the smaller triangle is a scaled down version of the larger one, we can then create a formula or ratio to calculate the value of the missing side of the larger triangle (being x+6=??).
To create the formula/ratio I divided 10inches by 4inches. Thus the larger triangle is 2.5 times larger than the smaller one.
I then use this ratio to figure out the missing length of the larger triangle by doing:
6inches x 2.5 = 15inches.
I then inputed the 15inches into the formula of the missing side:
x+6=15
Subtracted 6 from both sides to simplify, and came up with the solution!
x=9
Let me know if this helps!
