make-the-given-changes-in-the-indicated-examples-of-this-section-and-then-solve-the-given-problem-91

Question

Make the given changes in the indicated examples of this section and then solve the given problems.
In Example $3(\mathrm{a}),$ change $5^{n}$ to $0.5^{n} .$ What other changes occur?

Wendi Zhao · Accepted Answer

Yeah, this infinite series is a converging series And as one equals .5 asked to because 0.75 As three, he calls points 875. And as far because .9375 And as equals a one Over 1- our A one is a first term, which is .5 Or is a common ratio, which is also .5 Enhance the sum equals one.

Lourence Gonhovi · Answer

and on Pete in in my life. But soon it&#x27;s in your hands Candle. Well, C b n uh, and he and in my Okay, so can you even have this? Well, so do is. Well, it&#x27;s fun, but he&#x27;s long Cyril bait. So this is anything actually defined by in my nuts, Victoria. And then this one is in effect, Gloria decided by end my Unless in man Victoria and they signify it&#x27;s infected in my most in because and make it Make it, make it. It&#x27;s, uh, um so is in parts equal. So I looked.

Jason Taylor-Pestell · Answer

I really like how this book talks about you. Substitution. It&#x27;s a really helpful way Toe understands these more complicated questions because one way to approach this is you distribute the square, you distribute the to distribute the square. I mean, you would factor, but this factor times itself and then yeah, distribute. Um, but then you&#x27;re then you&#x27;d have to simplify combining like terms and then factor that. But there&#x27;s actually a much simpler way here. This looks like a try. No meal. If I let you equal five and plus one, then really, what I see here is you squared plus two times you minus three equals zero. And this is an incredibly easy try. No, be able to factor. We have a coefficient of one on the use where term The only things that multiplies. A three or one in three. And we need to get a two from subtractions. So that means that says it&#x27;s positive the three has to be positive that what has to be negative. And then from here we can use the zero product property U plus three house equals zero. Or you might this one house single zero subtract three from both sides on this equation. Add one to both sides on this equation. U is equal to negative three or you is able to What now? This does not solve the problem because all we&#x27;ve sold for as you now we&#x27;re going to substitute five M plus one into the equation and used that to solve for in much of the original variable. That&#x27;s right. It&#x27;s one. All right, so subtract one from both sides. Here&#x27;s have dropped one from both sides here. This is five and equals two. No divide both sides by five. This one is five and equals zero. Divide both sides by five, and we end up with and is equal to 2/5 or zero. Is that the two solutions that should work? If I substitute zero in, then I&#x27;ll have one squared plus two times one minus three, and that equals zero. So that checks out. That&#x27;s also to fits in five times. 2/5 is 10 deaths, which is to +13 squared nine 2/5 times five again is two plus one is three, three times to his six. That doesn&#x27;t look like it&#x27;s going to work. Minus three equals zero That&#x27;s not true. All right, so I&#x27;m gonna post the video to figure out what happens, and I will be right back. All right. Sorry about that. Um, So I made a mistake in this piece right here. I put the three enough thinning to three. So this should actually be negative three minus one So that instead of two, this is negative for hopefully you found my mistake before I did. This is negative. 4/5. Right? So I&#x27;m gonna change my solution here. This is one of the reasons why it&#x27;s so helpful to substitute back in and check your solution. Because it&#x27;s quite possible you might make a mistake like I did. And we want to be able to identify those mistakes. And since one of them worked, that&#x27;s what let me know that the other one definitely like the process was good, but I made a mistake in copying, which is a very common mistake. Um, so now let&#x27;s substitute again. If you substitute negative 4/5 in here, you know, negative 25th which is negative for plus one is negative. Three squared is still nine, but then here is gonna be negative three times to which is negative. Six. And that&#x27;s what I was expecting to get. So this is negative six and the negative threes that does equal zero. So this checks out. We&#x27;ve We&#x27;ve found my mistake and these are the two solutions and is negative 4/5 Brenda zero

Lourence Gonhovi · Answer

blame? No, I see an hour in in my So basically, if you antsy and out and see in Manaus, you get the symbols out. See what you get you. So this is an victor. Oh, in office. And that&#x27;s what this is. It&#x27;s all and it&#x27;s horrible. And my house more most in also here in the house. So is your simplified in my class Victorio in in Mama&#x27;s are I didn&#x27;t see it matches Tim for Tim plateful both these facts he&#x27;s in back.

Kerry Thornton-Genova · Answer

we&#x27;re solving for B. Begin by subtracting three s t to the fourth from both sides. Three s t to the fourth. Minus three is to the 4th 0 We thus have n minus three s t to the fourth equals negative. Five s v Next divide by negative five s. You must do the symbol sides Negative five s to buy by negative five s is one. Unless we have V on its own on this side, we have n minus three s t for the fourth, divided by a negative five s. The Pentagon. How you want to do this? You can also split it up. So here is one way. Or we can have this as and over. Negative five s minus negative. Three s t to the fourth over five s. When we have this, we can have some cancellations. Ask cancels with us, and this becomes a positive. So if you wanted to, you could rewrite this as V equals three t to the fourth over five minus and over five s Did you the same thing? Just manipulated in different ways.

Kerry Thornton-Genova · Answer

we are solving for n. Let&#x27;s begin by subtracting three m from both sides. Three Him minus three m is zero. Thus, we have a minus 3 a.m. on the left equals negative two times Ben on the right, nor to get rid of the negative to we must divide both sides by negative to negative to buy by Negative two is one and one times end is just n Thus we end up with a minus three m divided by a negative two equals and

Problem

Make the given changes in the indicated examples …

Problem 1 Easy Difficulty

Make the given changes in the indicated examples of this section and then solve the given problems.
In Example $3(\mathrm{a}),$ change $5^{n}$ to $0.5^{n} .$ What other changes occur?

Answer

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