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We’re on problem 17. The sum of three consecutive odd integers is 111 that’s what it tells the top. If n represents the least of the three integers which of the following equations represents the statement above. So n is the least of the three integer’s right. So let’s say that’s n. So the least of three consecutive odd integers, so what’s the next odd integer going to be? It's not going to be n + 1 because n + 1 is going to be even integer right if this was three then the next odd integers going to be 5 which is going to be n + 2. And in the next one above that is going to be n + 4 and you could try it out. Let’s say that n was 3 and this is 5 and this is 7 right that’s 3 consecutive odd integers and they’re telling us that the sum is a 111. So the sum is 111. What’s the sum of these three terms? Well you add 3n n + n + n = 3n and then 2 + 4, 3n + 6 and that’s going to be equal to 111 and that is choice D. And if this confuse how I wrote this, all I did is I said that’s the same thing as n + n + 2 +n + 4 = 3n + 6.
Problem 8 and they drew this arch something like that. Actually looks better than what I just drew but hit the point. Okay so this is like a distance of 2 and then there’s a distance of b it looks like—so it's 2 then b then 2 then b then 2 the b again. The figure above shows part of a circle whose circumference is 45. So circumference of a circle is 45. If arches of length 2 and length b continue to alternate around the entire circle so this is just part of the circle. They just keep going around the circle. Just keep going around the circle so that they’re 18 arches of each length. What is the degree measure of each of the arches of length b?
So they’re saying that there’s—so when they say there’s 18 arches of each length. You see that there are 18 of these arches of length too right and there are 18 of these b segments. Because they’re saying this is—what they drew is just part of the whole circle right. So that means if this entire circumference is 45 but in terms of two’s and b’s we know that there’s 18 two’s so it's 18 x 2 and then we also know that there are 18 b’s plus 18 b. Right this is another way of writing the circumference of the circle because they say that the circumference is made of 18 of these arches and 18 of this b arches here. So this is also equal to circumference of a circle which they told us is 45. Let’s see this 36 right 18 x 2 + 18b = 45 subtract 36 from both sides you get 18b = 9b = 9/18 which is equal to 1/2.
Now what do they asking? What is the degree measure of each of the arches of length b. So we know that each b is 1/2 and actually we know it we could have gone to this step. We could have said that the length of each b is a length of 1/2 right. So what fraction is that of the entire circumferences? This length right here is 1/2 that’s what we just saw right. You’re saying there’s going to be 18b’s and 18 set of arches of length too and they all add up to 45. We solve for b is 1/2. So we want to figure out what’s the degree measure? So they figure out the degree measure, we figure out we say well 1/2 is two of the circumference of the entire circle which is 45, is equal to the degree measure over the total degrees in the entire circle right because the fraction in each of these circumference is the same thing as going to be in terms of degrees of the fraction of 360 degrees. Why because they’re 360 degrees in the circle. So let’s cross multiply this, 1/2 x 360 degrees so you get 180 degrees as 1/2 times 360 is equal to 45x. So x = 180 divided by 45 and what’s 180 divided 45? Let’s see 40 goes into 160 it's 4 times right x = 4, 4 x 45 right, so x is equal to 4 degrees and that’s choice A and then it also make sense intuitively right. 4 degrees is a very small amount of degrees right so that make sense if you’re going for the center. I know it is true I just probably confuse you. Hopefully you get the idea. igure out how long the b’s are and then what fraction that is of the entire circumference and then that’s what fraction it is of 360 degrees.
Problem 19, the cost of maintenance on an automobile increases each year by 10% and Andrew paid $ 300.00 this year for maintenance on his automobile fine. If the cost see from maintenance on Andrew’s automobile and years from now is given by the function so C(n) = 300, x^n what is the value of x. So they say every year the cost increases by 10% so what does it mean to increase by 10% if let me say the cost in year one, let’s say the cost in year one is going to be—what’s the cost in year two? It's going to be the cost of year one increased by 10% so plus .1 times the cost in year one which is equal 1.1 times the cost in year one.
The cost in year three is equal to 1.1 times the cost in year two which is the same thing as one. 1.1 times—write the cost of year two which is this. 1.1 times 1.1 costs of year one which is the same thing as 1.1². So every year that you go out, you essentially just taking 1.1 to that power of how many years you’re going out. Actually, I should probably make this cost of you zero, makes this cost of year one zero. Zero is probably confusing you but cost of year two so then the exponents at least match up. One and zero, then the exponents match up right. The cost of year two is 1.1² times of year is zero. So you can see all were doing when we were doing this you know this is kind of an exponential gross problem but they’re saying what is this base or when you increase something by 10% you’re essentially multiplying it by 1.1. So that’s all they’re asking, so that’s choice C.
Problem 20, okay they drew this parallelogram sorry I have not drawn well and gets the point. A B C D if the 5 line segments in the figure above were all congruent, okay so the five line—these are all congruent, so they are all equal to each other all those sides. What is the ratio of the length of AC not drawn so they want to know AC so that’s this length? They want to know AC is a length BD. All right, so all of those lines are congruent so you know let’s just pick a number, that’s what I find to be easiest when you know they tell us at all. So let’s say that this is one, this is one, and this is one. This whole thing is going to be one, so how long is this and this?
This will bisect to this line right and I think we know that about parallelograms that the two lines bisect to each other, the two diagonals. So this is going to be 1/2 and this is going to be 1/2. And there is also something else we know. We know that this is 60 degrees that this whole angle is 60 degrees and then how do we know that? Before we draw the green line we knew that both of those triangles are equal with all triangles right. So if this whole angle was 60 degrees, then this angle right here is going to be 30 degrees and I think you see where I’m going with this. This is a 30 60 90 triangle or this is one that’s the hypotenuse, this is 1/2 and then what is the side opposite the 60 degrees side which is this, √3 times this side right here. The √3 over 2 and so with this one was also be √3 over 2 and I know maybe it's a little bit confusing actually I’m about to run out of time so I will continue this in the next video.
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