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Contact [7]
2 years ago
7

Which relation is a function?

Mathematics
1 answer:
Aliun [14]2 years ago
8 0

<em><u>{(-1, -2), (1, 3), (1, 5), (3, 5)}</u></em><em><u>.</u></em>

<em>[</em><em>that's</em><em> </em><em>it]</em><em>:</em><em>)</em>

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Jill has two hamsters Each hamster drinks 3 ounces of water each day.
sveta [45]

Answer:

4 oz

Step-by-step explanation:

2 hamsters 3 ounces each per day

6 ounces per day  is drank

Monday 6 oz Tuesday 6 oz

16-12=4

8 0
2 years ago
Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 9 3x + 2 , c = 6
san4es73 [151]

Answer:

\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........

The interval of convergence is:(-\frac{2}{3},\frac{16}{3})

Step-by-step explanation:

Given

f(x)= \frac{9}{3x+ 2}

c = 6

The geometric series centered at c is of the form:

\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.

Where:

a \to first term

r - c \to common ratio

We have to write

f(x)= \frac{9}{3x+ 2}

In the following form:

\frac{a}{1 - r}

So, we have:

f(x)= \frac{9}{3x+ 2}

Rewrite as:

f(x) = \frac{9}{3x - 18 + 18 +2}

f(x) = \frac{9}{3x - 18 + 20}

Factorize

f(x) = \frac{1}{\frac{1}{9}(3x + 2)}

Open bracket

f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}

Rewrite as:

f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}

Collect like terms

f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}

Take LCM

f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}

f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}

So, we have:

f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}

By comparison with: \frac{a}{1 - r}

a = 1

r = -\frac{1}{3}x + \frac{7}{9}

r = -\frac{1}{3}(x - \frac{7}{3})

At c = 6, we have:

r = -\frac{1}{3}(x - \frac{7}{3}+6-6)

Take LCM

r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

\frac{9}{3x + 2} =  \sum\limits^{\infty}_{n=0}ar^n

Substitute 1 for a

\frac{9}{3x + 2} =  \sum\limits^{\infty}_{n=0}1*r^n

\frac{9}{3x + 2} =  \sum\limits^{\infty}_{n=0}r^n

Substitute the expression for r

\frac{9}{3x + 2} =  \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n

Expand

\frac{9}{3x + 2} =  \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n]

Further expand:

\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................

The power series converges when:

\frac{1}{3}|x - \frac{7}{3}| < 1

Multiply both sides by 3

|x - \frac{7}{3}|

Expand the absolute inequality

-3 < x - \frac{7}{3}

Solve for x

\frac{7}{3}  -3 < x

Take LCM

\frac{7-9}{3} < x

-\frac{2}{3} < x

The interval of convergence is:(-\frac{2}{3},\frac{16}{3})

6 0
2 years ago
Which of the following describes the polynomial function ??? HELP
JulsSmile [24]

Answer:

B. The function has an even degree.

Step-by-step explanation:

We have been given an image of a polynomial function. We are asked to choose the correct options about our given polynomial.

A. The function has a negative leading coefficient.

Upon looking at our given graph, we can see that it is an upward opening parabola, so leading coefficient can't be negative, therefore, option A is not true.

B. The function has an even degree.

Upon at our given graph, we can see that it is symmetric to y-axis, therefore it has an even degree polynomial and option B is the correct choice..

C. The function has zero turning points.

Upon looking at our given graph, we can see that as function approaches towards 0 from negative infinity it is decreasing. As function increases positive infinity from 0, it is increasing, therefore, our function has a turning point at x=0, therefore, option C is incorrect.

D. The function has one x-intercept.

Since our function never intersects x-axis, therefore, function has no x-intercept and option D is incorrect as well.

6 0
3 years ago
Using side lengths only, could the triangles be similar? Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Si
ruslelena [56]

Answer:

  no

Step-by-step explanation:

In ∆XYZ, we can write the ratios of the sides from shortest to longest as ...

  y : z : x = 1 : 1.5 : 2 = 2 : 3 : 4

In ∆QSR, we can write the ratios of the side lengths from shortest to longest as ...

  r : s : q = 0.5 : 1 : 1.5 = 1 : 2 : 3

Based on side lengths only, the triangles cannot be similar.

__

<em>Additional note</em>

Even if shortest-to-longest side ratios were the same, the triangle naming is incorrect for them to be similar.

5 0
3 years ago
Alloy, c, weighing 500 ounces and having 35% aluminum, is obtained from melting together x ounces of alloy, a, containing 25% al
boyakko [2]
From the given scenario in this item, we can say that the sum of x and y is 500. By the aluminum balance, the equation that we can formulate from this,
                            0.25x + 0.40y = (500)(0.35)
The system of linear equations that can best express the given is,
                                   x + y = 500
                                0.25x + 0.40y = 175
3 0
3 years ago
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