SOMBODY PLZ HELP!!!! I WILL GIVE BRAINLIST
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Answer:
a) h = 123/x^2
b) S = x^2 +492/x
c) x ≈ 6.27
d) S'' = 6; area is a minimum (Y)
e) Amin ≈ 117.78 m²
Step-by-step explanation:
a) The volume is given by ...
V = Bh
where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:
123 = x^2·h
h = 123/x^2
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b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.
__
c) The derivative of the area with respect to x is ...
When this is zero, area is at an extreme.
__
d) The second derivative is ...
This is positive, so the value of x found represents a minimum of the area function.
__
e) The minimum area is ...
The minimum area of metal used is about 117.78 m².
Answer:
The solution set can be given as:
Step-by-step explanation:
Given function:
To find the domain of the function in set notation.
Solution:
For the function to exist the denominator must be ≠ 0
We have the denominator which cannot be = 0.
Thus, we can find the domain of the function using the above relation.
The function will not exist when:
Solving for
Subtracting both sides by 6.
Dividing both sides by 2.
∴
Thus, the function will not exist at . This means it has all real number solutions except -3.
The solution set can be given as:
Math is about number sense and matching patterns. You get number sense by playing with numbers: counting, arranging. Most people do not find it difficult to match patterns, as our brains are wired to see them--sometimes even when they aren't there.
The picture below is pretty much all you need to know to answer these questions. It is a short course on arithmetic and geometric sequences. (We have left out some simplifications that can be made to the formulas for Nth term, and we have not shown formulas for the sum of a sequence.)
1. Geometric sequence with first term 5, common ratio 2. It will have the formula
.. f(n) = 5*2^(n-1) . . . . . . I can't read your picture to tell whether that is B or D
2. Arithmetic sequence with first term 1 and common difference 3. It will have the formula
.. f(n) = 1 +3(n -1) . . . . . . matches A
3. Geometric sequence with first term 2 and common ratio 3/2 = 1.5. It will have the formula
.. f(n) = 2*1.5^(n -1) . . . . . matches C
4. Geometric sequence with first term 600 and common ratio 60/600 = 0.1. It will have the formula
.. f(n) = 600*0.1^(n-1)
This can be simplified using the rules of exponents to
.. f(n) = 600*(0.1^-1)*(0.1^n)
.. f(n) = 6000*0.1^n . . . . . . matches A
5. The sequence is 12, 11, 10, 9, .... It is an arithmetic sequence with first term 12 and common difference -1. It will have the formula
.. f(n) = 12 +(-1)*(n -1)
.. f(n) = 12 -(n -1) . . . . . . matches B
6. This is an arithmetic sequence with first term 8 and common difference -0.5. It will have the formula
.. f(n) = 8 -0.5(n -1)
.. f(n) = 8.5 -0.5n . . . . . . matches C
The picture below is pretty much all you need to know to answer these questions. It is a short course on arithmetic and geometric sequences. (We have left out some simplifications that can be made to the formulas for Nth term, and we have not shown formulas for the sum of a sequence.)
1. Geometric sequence with first term 5, common ratio 2. It will have the formula
.. f(n) = 5*2^(n-1) . . . . . . I can't read your picture to tell whether that is B or D
2. Arithmetic sequence with first term 1 and common difference 3. It will have the formula
.. f(n) = 1 +3(n -1) . . . . . . matches A
3. Geometric sequence with first term 2 and common ratio 3/2 = 1.5. It will have the formula
.. f(n) = 2*1.5^(n -1) . . . . . matches C
4. Geometric sequence with first term 600 and common ratio 60/600 = 0.1. It will have the formula
.. f(n) = 600*0.1^(n-1)
This can be simplified using the rules of exponents to
.. f(n) = 600*(0.1^-1)*(0.1^n)
.. f(n) = 6000*0.1^n . . . . . . matches A
5. The sequence is 12, 11, 10, 9, .... It is an arithmetic sequence with first term 12 and common difference -1. It will have the formula
.. f(n) = 12 +(-1)*(n -1)
.. f(n) = 12 -(n -1) . . . . . . matches B
6. This is an arithmetic sequence with first term 8 and common difference -0.5. It will have the formula
.. f(n) = 8 -0.5(n -1)
.. f(n) = 8.5 -0.5n . . . . . . matches C