Which statement is FALSE about the triangles shown on the graph?

Determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.

Arada [10]

The sequence $a_n=\frac{n^2}{n^3+5n}$ diverges.

For given question,

We have been given a sequence $a_n=\frac{n^2}{n^3+5n}$

We need to determine whether the sequence converges or diverges.

From given sequence we have, $a_{n+1}=\frac{(n+1)^2}{(n+1)^3+5(n+1)}$

We use Ratio Test.

According to Ratio Test, $r=\frac{a_{n+1}}{a_n}$ , where sequence converges if and only if |r| < 1.

Consider,

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty$

Since $\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |$ is not defined, the sequence $a_n=\frac{n^2}{n^3+5n}$ diverges.

Therefore, the sequence $a_n=\frac{n^2}{n^3+5n}$ diverges.

Learn more about the sequence here:

brainly.com/question/17175513

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4 0

2 years ago

A gardener plants two types of trees in a park:

slega [8]

Answer:

8 years

Step-by-step explanation:

Lets write an equation for Type A

The initial value is 5 ft and the slope 12 inches

We need to have the same units, so lets change 5 ft to inches

5 ft * 12 inches / ft = 60 inches

y = mx+b

y = 12 x + 60

Lets write an equation for Type B

The initial value is 3 ft and the slope 15 inches

We need to have the same units, so lets change 3 ft to inches

3 ft * 12 inches / ft = 36 inches

y = mx+b

y = 15 x + 36

We want to know when y is the same value. We can set the equations equal.

12x + 60 = 15x+36

Subtract 12 x from each side

12x-12x+60 = 15x-12x +36

60 =3x+36

Subtract 36 from each side

60-36 = 3x+36-36

24 = 3x

Divide each side by 3

24/3 = 3x/3

8 =x

It will take 8 years for the trees to be the same height

7 0

3 years ago

In Exercises 1–4, let S be the collection of vectors cxyd in R2that satisfy the given property. In each case, either prove thatS

Artyom0805 [142]

Answer:

S is not the subspace of $R^2$

Step-by-step explanation:

Let us suppose two vectors u and v belong to the S such that the property of xy≥0 is verified than

$u=\left[\begin{array}{c}-1 \\0\end{array}\right]$

$v=\left[\begin{array}{c}0 \\1\end{array}\right]$

Both the vectors satisfy the given condition as follows and belong to the S

$x_u y_u=-1\times 0=0 \geq 0\\x_v y_v=1\times 0=0 \geq 0\\$

Now S will be termed as subspace of R2 if

u+v also satisfy the condition
ku also satisfy the condition

Taking u+v

$u+v=\left[\begin{array}{c}-1 \\0\end{array}\right]+\left[\begin{array}{c}0 \\1\end{array}\right]\\u+v=\left[\begin{array}{c}-1+0 \\0+1\end{array}\right]\\u+v=\left[\begin{array}{c}-1 \\1\end{array}\right]$

Now the condition is tested as

$\\x_{u+v} y_{u+v}=-1\times 1=-1$

This indicates that the condition is not satisfied so S is not the subspace of $R^2$

3 0

3 years ago

Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends o

Rus_ich [418]

<h2><u>Answer with explanation:</u></h2>

Let $\mu$ be the population mean strain in a way that conveys information about precision and reliability.

The sample mean is the best point estimate of the true population mean .

As per given , we have

Sample size : n= 12

degree of freedom : $df=12-1=11$

Sample mean : $\overline{x}=25.0$

The true average strain in a way that conveys information about precision and reliability= 25.0

sample standard deviation : s= 3.3

Significance level : $\alpha= 0.05$

Since sample population standard deviation is unknown , so we use t-test.

Critical t-value for t : $t_{\alpha/2, df}=t_{0.025, 11}=2.201$

95% Confidence interval for true average strain in a way that conveys information about precision and reliability:

$\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}$

$25.0\pm (2.201)\dfrac{3.3}{\sqrt{12}}\\\\=\approx 25.0\pm2.10\\\\=(25.0-2.10, 25.0+2.10)=(22.9,\ 27.1)$

The 95% Confidence interval for true average strain in a way that conveys information about precision and reliability: $(22.9,\ 27.1)$

We 95% confident that the true population average strain in a way that conveys information about precision and reliability lies between 22.9 and 27.1 .

4 0

4 years ago

Plzz I need help asap 45 points Find The missing side

Studentka2010 [4]

Answer:

4x^2

Step-by-step explanation:

Call the unknown side y

The area of the figure is

8x^3 *y = 32 x^5

Divide each side by 8 x^3

8x^3 *y / 8x^3 = 32 x^5 / 8x^3

y = 4 x^2

The unknown side is 4 x^2

7 0

3 years ago

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