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2 years ago

Determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5. Justify your answer.

Mathematics

1 answer:

Rudik [331]2 years ago

7 0

Step-by-step explanation:

Given

The function is $f(x)=x+4$

for $x_2>x_1$ , we will check the values of $f(x_1)$ and $f(x_2)$

Take 3 and 4

$f(4)=4+4\\f(4)=8$

Similarly,

$f(3)=3+4\\f(3)=7$

Thus, $f(4)>f(3)$

Also, $f'(x)$ is 1 i.e. a constant value. So, the function is increasing linearly for the given interval.

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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If $\sum a_n$ is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

$\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho$

If $\rho$ < 1, the series converges absolutely

If $\rho > 1$ , the series diverges

If $\rho = 1$ , the test fails.

Given the series $\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}$

To test for convergence or divergence using ratio test, we will use the condition above.

$a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}$

$\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\$

$\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\$

aₙ₊₁/aₙ =

$\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\$

note that any constant dividing infinity is equal to zero

$|\frac{1+2/\infty+1/\infty^2}{5}|\\\\$

$\frac{1+0+0}{5}\\ = 1/5$

$\rho = 1/5$

Since The limit of the sequence given is less than 1, hence the series converges.

5 0

2 years ago

If y is directly proportional to x square and y equal 1/8 when x = 1/2 what is the positive value of x when y it was 9/2?

mojhsa [17]

Answer:

Step-by-step explanation:

Given y is directly proportional to x² then the equation relating them is

y = kx² ← k is the constant of proportion

To find k use the condition y = $\frac{1}{8}$ when x = $\frac{1}{2}$ , then

$\frac{1}{8}$ = k( $\frac{1}{2}$ )² = $\frac{1}{4}$ k ( multiply both sides by 8 )

1 = 2k ( divide both sides by 2 )

k = $\frac{1}{2}$

y = $\frac{1}{2}$ x² ← equation of proportion

When y = $\frac{9}{2}$ , then

$\frac{9}{2}$ = $\frac{1}{2}$ x² ( multiply both sides by 2 )

9 = x² ( take the square root of both sides )

x = ± $\sqrt{9}$ = ± 3

with positive value x = 3 → d

8 0

3 years ago

Divide 3 1/3 by 2/3 bbbbbbbb

iris [78.8K]

Answer:

jgjhi

Step-by-step explanation:

vbnhjkui

5 0

3 years ago

If all the dimensions of the rectangular pyramid are multiplied by 1/5, what is the effect on the volume

Pachacha [2.7K]

Answer:

If all the dimensions of the rectangular pyramid are multiplied by 1/5, the volume will be 125 times smaller.

Step-by-step explanation:

A rectangular pyramid has the following dimensions:

length(l), height(h) and width(w)

The volume is:

$V = \frac{l*h*w}{3}$

If all the dimensions of the rectangular pyramid are multiplied by 1/5

Then we have that:

$l = \frac{l}{5}, w = \frac{w}{5}, h = \frac{h}{5}$

The modified volume will be:

$V_{M} = \frac{\frac{l}{5}*\frac{w}{5}*\frac{h}{5}}{3} = \frac{\frac{l*w*h}{125}}{3} = \frac{l*h*w}{125*3} = \frac{1}{125}(\frac{l*h*w}{3}) = \frac{V}{125}$

If all the dimensions of the rectangular pyramid are multiplied by 1/5, the volume will be 1/125 of the original, that is, 125 times smaller.

4 0

2 years ago

Example on worksheet (subtracting by adding up)

Lisa [10]

Answer:

(49 - 29) + 1 =(50 - 29)

Step-by-step explanation:

The 20 comes from the subtraction of 29 in both sides of the previous step equality. In the following, I transcript the complete procedure and I add the step that you need to understand why 20 appears (in bold numbers):

29+20=49

49+1=50

(49 - 29) + 1 =(50 - 29)

20+1=21

50-29=21

hence, it was only nesseraty to subtract 29

3 0

3 years ago