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2 years ago

Which relation is a function?

Mathematics

1 answer:

Aliun [14]2 years ago

8 0

{(-1, -2), (1, 3), (1, 5), (3, 5)}.

[that's it]:)

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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:

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.

Additional note

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