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Solve for the following word problems
1 answer:
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A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or
ancestors.
In the third generation we have 8 ancestors ot
ancestors.
We can see that each succesive generation has two times more members. The sum is:
To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
</span>
<span>Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements
For this question:
a1 = 2
r = 2
n = 40
</span>
<span>
b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years
c.
Total number of people who have ever lived = </span>
Number of ancestors in 40 generations =
The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or
In the third generation we have 8 ancestors ot
We can see that each succesive generation has two times more members. The sum is:
To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
</span>
<span>Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements
For this question:
a1 = 2
r = 2
n = 40
</span>
<span>
b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years
c.
Total number of people who have ever lived = </span>
Number of ancestors in 40 generations =
The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.
Answer:
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.
Step-by-step explanation:
Given that, the volume of cylindrical can with out top is 25 cm³.
Consider the height of the can be h and radius be r.
The volume of the can is V=
According to the problem,
The surface area of the base of the can is =
The metal for the bottom will cost $2.00 per cm²
The metal cost for the base is =$(2.00× )
The lateral surface area of the can is =
The metal for the side will cost $1.25 per cm²
The metal cost for the base is =$(1.25× )
Total cost of metal is C= 2.00 +
Putting
Differentiating with respect to r
Again differentiating with respect to r
To find the minimize cost, we set C'=0
⇒r=1.71
Now,
When r=1.71 cm, the metal cost will be minimum.
Therefore,
⇒h=2.72 cm
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.