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3 years ago

Ms. Arango gave his daughter 50 chocolate bars to give to her friends

Mathematics

1 answer:

Maksim231197 [3]3 years ago

4 0

Answer:

Ans: 16

Step-by-step explanation:

50-2=48

48/3=16 friends

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Vertex of parabola (x-7)^2+5

UNO [17]

Answer:

(7,5)

Step-by-step explanation:

You can use the desmos website for math problems like this.

4 0

3 years ago

Read 2 more answers

The average price of gas in 2000 was $1.57 per gallon, and $2.30 in 2005. What is the rate of change for each year between 2000

KATRIN_1 [288]

Answer: $ 0.146 per year.

Step-by-step explanation:

Given: Average price of gas in 2000 = $1.57 per gallon

Average price of gas in 2005 = $2.30 per gallon

The rate of change for each year between 2000 to 2005

= $\dfrac{\text{Change in price}}{\text{Change in time}}$

$=\dfrac{\text{Price in 2005- Price in 2000}}{2005-2000}\\\\=\dfrac{2.30-1.57}{5}\\\\=\dfrac{0.73}{5}=0.146$

Hence, the rate of change for each year between 2000 to 2005 is $ 0.146 per year.

8 0

3 years ago

Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find

inna [77]

Best guess for the function is

$\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}$

By the ratio test, the series converges for

$\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1$

When $x=1$ , $f(x)$ is a convergent $p$ -series.

When $x=-1$ , $f(x)$ is a convergent alternating series.

So, the interval of convergence for $f(x)$ is the closed interval $\boxed{-1 \le x \le 1}$ .

The derivative of $f$ is the series

$\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n$

which also converges for $|x|$ by the ratio test:

$\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1$

When $x=1$ , $f'(x)$ becomes the divergent harmonic series.

When $x=-1$ , $f'(x)$ is a convergent alternating series.

The interval of convergence for $f'(x)$ is then the closed-open interval $\boxed{-1 \le x < 1}$ .

Differentiating $f$ once more gives the series

$\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)$

The first series is geometric and converges for $|x|$ , endpoints not included.

The second series is $f'(x)$ , which we know converges for $-1\le x$ .

Putting these intervals together, we see that $f''(x)$ converges only on the open interval $\boxed{-1 < x < 1}$ .

6 0

2 years ago

Can someone please give me examples of linear, quadratic, Absolute value, square root, cubic, cube root, exponential, logarithmi

Nady [450]

Answer:

Step-by-step explanation:

Consider the cube root parent function.

( graph in photo below )

Complete the statements to make them true.

A cube root function will ( 1 ) ________ have an x-intercept and ( 2 ) ________ have a y-intercept.

For the parent cube root function, ( 3 ) ____________ located at .

Answer:

1. always

2. always

3. both intercepts are

the explination photos below

6 0

3 years ago

Read 2 more answers

When the function f(x) = 5 • 2% is evaluated for x = 3, the output is: O 30. 20 0 10. 0 None of these choices are correct.

MAXImum [283]

5.2 clink the link
Got the Andre

3 0

3 years ago