An engineer needs a metal box to shield sensitive electronic devices from external electric fields. One side of the box should b
e open so that it can be placed over the components. The box can be made from a 6 ft by 4 ft sheet of metal by cutting squares from the corners and folding up the sides.
a. What is the maximum volume of the box?
b. What dimensions of the box result in the maximum volume?
a. What is the maximum volume of the box?
b. What dimensions of the box result in the maximum volume?
1 answer:
Answer:
a. 8.4 ft³
b. 4.44 ft × 2.44 ft × 0.78 ft
Step-by-step explanation:
a. <em>Maximum volume </em>
We are creating a box with dimensions
l = 6 – 2x
w = 4 – 2x
h = x
V = lwh = x(6 – 2x)(4 – 2x)
We must determine the value of x that makes V a maximum.
One way is to plot the function V = x(6 – 2x)(4 – 2x).
The maximum appears to be at about (0.78, 8.4).
Thus, the maximum volume is 8.4 ft³.
b.<em> Dimensions </em>
l = 6 – 2 × 0.78 = 6 – 1.56 = 4.44 ft
w = 4 – 2 × 0.78 = 4 – 1.56 = 2.44 ft
h = 0.78 ft
The box with maximum volume has dimensions 4.44 ft × 2.44 ft × 0.78 ft.
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Answer:
The required amount of mice is 11.82 gram.
Step-by-step explanation:
Given : Assuming that it is known from previous studies that σ = 4.5 grams. If we wish to be 95% confident that the mean weight of the sample will be within 3 grams of the population mean for all mice subjected to this protein diet.
To find : How many mice should be included in our sample?
Solution :
The formula used in the situation is
Where, z value at 95% confidence interval is z=1.96
gram is the mean of the population
gram is the standard deviation of the sample
Substituting the value, to find x sample mean
Therefore, The required amount of mice is 11.82 gram.