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Oliga [24]
3 years ago
8

Sketch the Cartesian product on the x-y plane R^2: Zx Z.

Mathematics
1 answer:
Minchanka [31]3 years ago
7 0

Answer:

\mathbb{Z}\times \mathbb{Z}=\{(a,b)\lvert a, b\in \mathbb{Z}\}

Step-by-step explanation:

In general, the Cartesian product of two sets A,B is a new set defined by

A\times B=\{(a,b)\lvert a\in A,b\in B\}

The pair (a,b) is ordered pair because the order is important, that is to say, in general (a,b)\neq (b,a).

One of the most important Cartesian products in mathematics is \mathbb{R}\times \mathbb{R}=\{(x,y) \lvert x,y \in \mathbb{R}\} which is precisely the Cartesian Plane xy. The set \mathbb{Z}\times \mathbb{Z} is a subset of \mathbb{R}\times \mathbb{R} which is the set of all the points in the Cartesian plane whose coordinates are integers numbers. So, sketching the set \mathbb{Z}\times \mathbb{Z} we have a picture as the shown below.

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Anne, Bridget, and Sasha shared a sum of money. Anne took 1/3 of the total amount, and Bridget took 1/4 of the remaining money.
lesya692 [45]

Answer:

180

Step-by-step explanation:

160= 1/3 * total
160*3 = total
480 = total

bridget = 1/4(total)
bridget = 1/4(480)
bridget took  120

Sasha took 1/2 of 360
Sasha took $180.

7 0
2 years ago
Determine whether the equation x^3 - 3x + 8 = 0 has any real root in the interval [0, 1]. Justify your answer.
nikdorinn [45]

Answer:

The equation does not have a real root in the interval \rm [0,1]

Step-by-step explanation:

We can make use of the intermediate value theorem.

The theorem states that if f is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:

  1. If a continuous function has values of opposite sign inside an interval, then it has a root in that interval. This is also known as Bolzano's theorem.
  2. The image of a continuous function over an interval is itself an interval.

Of course, in our case, we will make use of the first one.

First, we need to proof that our function is continues in \rm [0,1], which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval \rm [0,1], which means to evaluate the equation in 0 and 1:

f(x)=x^3-3x+8\\f(0)=8\\f(1)=6

Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval \rm [0,1]. I attached a plot of the equation in the interval \rm [-2,2] where you can clearly observe how the graph does not cross the x-axis in the interval.  

6 0
3 years ago
Help please asap ??!!?
vampirchik [111]

Answer:

Religious Officials

This could be wrong, but I hope it helps!

4 0
2 years ago
What does the line of -4 x + 3y = 6 look like
Llana [10]

Answer:

The line slopes upwards from left to right wit a positive gradient and cuts the y-axis at y=2 and the x-axis at x=-3/2

Step-by-step explanation:

We first rearrange the equation to the order y=mx+c where m is the gradient and c the y intercept.

3y=4x+6

y=(4/3)x+2

The gradient is therefore 4/3 and the y intercept is 2.

At the c intercept, y=0

0=(4/3)x +2

(4/3)x=-2

x=-2×3/4

=3/2

The line slopes upwards from left to right with a positive gradient and cuts the y-axis at y=2 and the x-axis at x=-3/2

8 0
3 years ago
Read 2 more answers
Help with this one please 20 points brain lest and a thanks on your page honestly just giving points away
Kitty [74]
The answer is C.

It has a negative slope (-40) and a y-intercept at 200.
3 0
3 years ago
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