Trig Ms. T

Problem Statement:

Create 2 formulas, one that will calculate the last number in terms of the first number and a constant increase in rate as well as the total amount of numbers. The second formula will add ass of the resulting numbers from the first formula together after the last number is calculated.

Process:

Kevin’s Decisions:

In order to put the problem into perspective, I first set up my own possible variables for the first platform height, the difference in height between each platform, and the total number of platforms. I came up with the numbers for each variable respectively: 6, 3, and 3. The first platform is 6 feet tall. There are 3 platforms. The distance between each platform is 3 feet. The

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6+9+12=27

I got the answer by just adding the number to check if I get the same if I use my formula. Where m=total length of material.

(x/2) (f+l)=m

(3/2) (6+12)=m

1.518=m

27=27 ✓

Solution:

x=number of platforms d=distance between each platform f=height of the first platform l=height of the last platform m=total length of material

Kevin’s Decisions: (f+(x-1)d)=1

The reason this formula is right is because the formula takes the height of the first platform and adds on the total height difference between the first platform and the last platform. It would not work is the difference in height from platform from platform was not constant.

Camilla’s Dilemma: (x/2)(f=l)=m

This formula for Camilla's Dilemma works because it takes the average of all the platforms. Then it multiplies that average by the total number of platforms there are. The reason this formula works is once again because the rate of increase between each platform is the same. The formula basically takes the average of the first and last platform, and if the rate of increase in height were not the same, the average wouldn't have been able to be calculated the same way. I would have had to add all of the numbers individually and divide by the total amount of numbers to get the average if the rate of increase in height were not