1)Use the provided information to identify each of Mr. Nicholson’s earning opportunities as arithmetic or geometric. For each op
portunity, include the common difference or ratio. In your final answer, use complete sentences to explain how you identified each opportunity as arithmetic or geometric. 2)Model each of Mr. Nicholson’s salary options with a recursive sequence that includes his potential earnings for the first three years of employment.
According to the first three terms of each sequence, can you conclude that there is a significant difference in Mr. Nicholson’s potential earnings with each increase option? Use complete sentences to explain your conclusion.
The missing provided information is that Mr. Nicholson accepts a job that pays an annual salary of
$60,000. And he is given the option of choosing between two annual raises:
a) an annual raise of $3,500 or b) an annual raise of 5% of his current salary.
Then, with that information you have to answer the given questions.Which I am going to do step by step.
<span>
1) identify each of Mr. Nicholson’s earning opportunities as arithmetic or
geometric. For each opportunity, include the common difference or
ratio. In your final answer, use complete sentences to explain how you
identified each opportunity as arithmetic or geometric.
- An annual raise of fix $3500 means that every year the salary increase in a constant amount driving to this sequence:
In this case, the increase is geometrical because you have that two adjacent terms differentiate by a constant factor, e.g.: 69,457.50 / 66,150 = 1.50.
2)Model each of Mr. Nicholson’s salary options with a recursive sequence
that includes his potential earnings for the first three years of
employment.
According to the first three terms of each sequence, can you conclude
that there is a significant difference in Mr. Nicholson’s potential
earnings with each increase option? Use complete sentences to explain
your conclusion.
Models
- Atrihmetic progression option
Annual salary the year n= Sn Initial Salary = S1 = 60,000 difference, d = 3500 number of year: n
Model: S = S1 + (n-1)*d
S = 60,000 + (n-1)*3500
Potential earnings for first three years:
You can use the fomula for the sum of n terms in an arithmetic progression: [S1 + S3]*(n) / (2)
Sum = [60,000 + 67000] * 3 / 2 = 190,500
This is the same that [60,000 + 63,500 + 67,000] = 190,500.
- Geometric progression:
S1 = 60,000 r = 1.05
Sn = S1 * r^(n-1) = 60,000 - (1.05)^(n-1)
Potential earnings the first three years:
60,000 + 63,000 + 66,150 = 189,150 </span> Now you got that there is a substantial difference in potential earnings with each option: the constant increase of $3500 (arithmetic progression) during three years results in a bigger earning for that time, because 5% of difference the second year is only 3000, and the third year 3150; both below $3500. This results in that the arithmetic progression is better for Mr. Nicholson during the first three years.
Answer: Area of square PQRS is 81cm^2 and of ABCD is 25cm^2
You know its a square. Which means all the sides are equal and same length. If you dont know what's a square then here is the definition:
Square is a plane figure with four equal sides and four right (90°) angles.
So now we know both of are squares, in case of the first square, PQRS, one side length is already given which is PQ=9cm. Now one side is 9cm which means all the sides are 9cm's (PQ=9cm, QR=9cm, RS=9cm,SP=9cm). So to find area just multiply them:
9cm * 9cm = 81cm^2
Now you found the area of the first square. So for the second square, ABCD, one side length is 5 cm so all the rest three sides are also 5 cm. Again, multiply them in order to find the area:
5cm * 5cm = 25cm^2
So square PQRS is 81cm^2 to that of square ABCD is 25cm^2