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QUESTION 1Let 9' be a partition of a set Q If 9 contains five distinct blocks, then the power set of Qhas 25 elements at a maximumhas 32 elements at a minimumh...

Question

QUESTION 1Let 9' be a partition of a set Q If 9 contains five distinct blocks, then the power set of Qhas 25 elements at a maximumhas 32 elements at a minimumhas 32 elements at a maximumTne maxima and minima indicated in tne alternative answer choices are incorrect:has 25 elements at a minimum

QUESTION 1 Let 9' be a partition of a set Q If 9 contains five distinct blocks, then the power set of Q has 25 elements at a maximum has 32 elements at a minimum has 32 elements at a maximum Tne maxima and minima indicated in tne alternative answer choices are incorrect: has 25 elements at a minimum



Answers

Use the polynomial function graphs, which include all extrema, for Exercises $1-8$ GRAPH CANT COPY. Give all local extreme points of $Q .$ Tell whether each is a maximum or minimum.

Hello, everyone. Today we're going to solve problem number seven here effects equal toe if I equal toe and said tickle toe. So we ex goto to its zero according to White, Is that a kowtow So that for taking partial derivative off the off x y that a Carter? Okay, two week or two to excel. Two week or two to a whale. One nickel toe. Does that help? Then we can write like one day x could do one. Bye bye. But one guy does that goto X square plus by square plus X square equal to nine through that square, plus two thirds square plus that square equal to nine. I am that square equal toe right is that they called Tau sar minus one. Talk eggs ical toe by equal toe plus or minus two. So effect toe come out to come out. Barney, kowtow now, Nick F off minus two comma minus two minus one physical toe minus nine. So, by evaluating and fourth excellence that at the point two comma toe come out one and minus two comma minus two minus one. They skew the largest and the smallest value well in effect toe tomato comma one you call to nine ridiculous maximum value, then have fit minus two or minus two or minus one, but to minus nine. Ridiculous minimum value. Thank you.

Hello. Children's. And this question we are given that A is a proper subset. It is a proper subset of the. Okay. And we are given number of elements in a. Is equal to five. Okay. And then we have to find out the number of elements in a delta be. Okay. What is delta? Delta? Is the symmetric difference? Okay. So we need to find out the number of elements in a smarter difference will be okay. So first of all, since is the proper subset of B, then we can say that we can see that a intersection be will leave us A. Okay. Because the common between both of them will be a Okay. And a union be will give us be okay. This is the definition of proper subset. No, If we find out the number of elements in A. There to be. That is a cemetery difference of B. It is nothing but a number of uh a number of elements and a union be divided by the number of elements and a intersection be okay because by definition but the definition of symmetric difference, we already know that a delta B is equal to a union. Be divided by a intersection B. Right? So we can we have taken a number of elements both sides. Now, just simplifying this equation, what we get test number of elements in a delta B is equals to a number of elements in a union. Be a union B is nothing but be okay. So it becomes a number of elements and be divided by the number of elements. Now, number of elements in a delta B is equal to the number of elements and be divided by number of elements and is five. Okay, now we need to tell the minimum value of this. Okay, So how can this be minimum when NRB is minimum. Okay. So four and of adult to be to be many moms. Yeah. Number of elements in B should be minimum. Okay. Now we know that is the subset of be. Okay. So since is the subset of B. So which implies that number of elements in a will be less than the number of elements and be okay less than equal to the number of elements and be so minimum possible value, minimum value. Oh and or B is equal to the number of elements in A. Okay, so the minimum value of NFL comes out to be five. Right? So the minimum value of number of elements in air and to be well to be men value of enough area to be comes out to be five divided by five, which is equal to one. Okay, that's it. Thank you.

We're gonna be using linear programming to solve an optimization problem. Our objective function is equals five X plus three Y. And were given the list of four constraints. Our first step is to visualize these constraints by graphing them and finding where those inequalities were. Map. I like to use Dismas. It's free, pretty user friendly graphing calculator. Amy will work if you're using Dismas and you need an or equals to inequality. Type in the less than or greater than sign on your keyboard, then type in the equal sign to get that. Let's look at these constraints. X is greater than equal to zero. So we're working on the right side of the coordinate plain. Working above this line. It's in this purple shaded area so far. Where else? Working about this orange line and above this purple line. So we can see this is unbounded. It's everything on this side above that purple line. Okay. Because it's unbounded, a maximum or minimum may not. We're going to be used

While the graph of a function can't tell for sure what the degree of the function is, we can see from the graph with the minimum possible degree is so what we've look at is how many extreme points there are. So let's I have n extreme points, minimums and maximums that tells me that my minimum possible degree for my function will be n plus one as my minimum degree. For example, if I have zero extreme points, which is a line well, zero plus one is one. This is a first degree function. If I have one extreme point, as in the case of a parabola, one extreme point means that this is a squared function at a minimum. So for this particular function function que if we count our minimums and maximums, we have four extreme points. That means that at a minimum, this is 1/5 degree function


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