The two sales people for a local advertising firm are Trinity and Jason. Trinity sold $2,330 in ads and Jason sold $1,740. What
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We have that every quarter, he will get an 0.8% interest rate. We also have that there will be 14*4=56 periods of repayment. We have that by the formula, if there are n periods and x% is the interest rate, the capital is multiplied by (100+x%)^n.
Suppose Micah invests x money. Then, we have that after 14 years, the capital available will be C=
. We have that C=18500$ and hence that 18500=x*1.562. Thus, solving for x we have that x=11841$.
Micah will need to invest only 11841$ in order to pay for his boat; this shows the importance of saving since he earns a lot of money, around 7k $.
Suppose Micah invests x money. Then, we have that after 14 years, the capital available will be C=
Micah will need to invest only 11841$ in order to pay for his boat; this shows the importance of saving since he earns a lot of money, around 7k $.
Answer:
- trapezoidal rule: 14.559027
- midpoint rule: 14.587831
- Simpson's rule: 14.577542
Step-by-step explanation:
We assume you want the integral ...
The width of each interval is 1/6 of the difference between the limits, so is ...
interval width = (14 -4)/6 = 10/6 = 5/3
Then the point p[n] at the left end of each interval is ...
p[n] = 4 +(5/3)n
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<u>Trapezoidal Rule</u>
The area of a trapezoid is the product of its average base length multiplied by the width of the trapezoid. Here, the "bases" are the function values at each end of the interval. The integral according to the trapezoidal rule can be figured as ...
integral ≈ 14.559027
If you're doing this on a spreadsheet, you can avoid evaluating the function twice at the same point by using a weighted sum. Weights are 1, 2, 2, ..., 2, 1.
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<u>Midpoint Rule</u>
This rule uses the area of the rectangle whose height is the function value at the midpoint of the interval.
integral ≈ 14.587831
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<u>Simpson's Rule</u>
This rule gives the result of approximating the function over each double-interval by a parabola. It is like the trapezoidal rule in that the sum is a weighted sum of function values. However, the weights are different. Again, multiple evaluations of the function can be avoided by using a weighted sum in a spreadsheet. Weights for 6 intervals are 1, 4, 2, 4, 2, 4, 1. The sum of areas is ...
integral ≈ 14.577542
