Answer:
Base Side Length =1.59m
Height = 3.16 m
Step-by-step explanation:
Volume of the box =
Let the base dimensions = x and y
Let the height of the box =h
<em>However, for any optimal configuration, Width = Length as varying the length and width to be other than equal reduces the volume for the same total(w+l)</em>
Volume, V=xyh=8
Since x=y
Surface Area of the box
The material for the top and bottom costs twice as much as the material for the sides.
Let the cost of the sides =$1 per square meter
Cost of the material for the sides = 4xh
Cost of the material for the top and bottom =
Therefore:
Total Cost,
Substitution of into C
To minimize C(x), we find its derivative and solve for the critical points.
To verify if it is a minimum, we use the second derivative test
Since C''(x) is greater than zero, it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the cost are:
Base Side Lengths of 1.59m; and
Height of 3.16 m
Answer:
1/2, 3
Step-by-step explanation:
This is a pretty involved problem, so I'm going to start by laying out two facts that our going to help us get there.
- The Fundamental Theorem of Algebra tells us that any polynomial has <em>as many zeroes as its degree</em>. Our function f(x) has a degree of 4, so we'll have 4 zeroes. Also,
- Complex zeroes come in pairs. Specifically, they come in <em>conjugate pairs</em>. If -2i is a zero, 2i must be a zero, too. The "why" is beyond the scope of this response, but this result is called the "complex conjugate root theorem".
In 2., I mentioned that both -2i and 2i must be zeroes of f(x). This means that both and are factors of f(x), and furthermore, their product, , is <em>also</em> a factor. To see what's left after we factor out that product, we can use polynomial long division to find that
I'll go through to steps to factor that second expression below:
Solving both of the expressions when f(x) = 0 gets us our final two zeroes:
So, the remaining zeroes are 1/2 and 3.
Answer:
assets to be overstated
Step-by-step explanation:
Given that a credit to an asset account was posted to an expense account.
We know that debit all comes in and credit all goes out for asset account
When asset account has to be credited there is a sale of asset and hence asset has to be reduced in value.
If wrongly posted to expenses account, then expenses would be credited by that amount. This will give assets a higher value and expenses a lower value.
When expenses are lower, profits high and hence capital would be ovestated.
So correct option is
assets to be overstated
Answer:
whats the problem?
Step-by-step explanation:
Answer:
x - y = 5
x + y = 23
x = 14, y = 9
Step-by-step explanation:
Make x subject:
x = 5 + y
Substitute c by (5 + y) :
( 5 + y) + y = 23
2y = 18
y = 9
Substitute y (9):
x = 5 + 9
x = 14