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The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

To learn more about  Convergent integral :

Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

Answer:

Any number that is greater than 10

Step-by-step explanation:

Tammy is wanting to run more than 28 miles. Having already ran 18, she has to run 10 more to even reach 28 miles in total. She wants to run MORE than 28 so the number of miles she has yet to run in possibility is any number that is GREATER than 10.

ex: 11, 12,13, 14.....

Answer:

7/16 of the shoes were either sandals or clogs.

Step-by-step explanation:

Find a CD, which is 16.

Because we multiplied the denominator, we multiply the numerator as well.

3/8 becomes 6/16.

Now, because both of the denominators are the same, we are free to add both of the fractions together.

6/16 + 1/16 = 7/16.

Because this fraction isn't reducible, the answer will be 7/16.

Answer:

[tex]t=-2.86[/tex]

Step-by-step explanation:

From the question we are told that:

Sample 1 [tex]n_1=8[/tex]

Sample 1 mean blood pressure [tex]\=x_1=89mmHg[/tex]

Sample 1 variance [tex]\sigma_1=81[/tex]

Sample 2 [tex]n_2=8[/tex]

Sample 2 mean blood pressure [tex]\=x_2=105mmHg[/tex]

Sample 2 variance [tex]\sigma_2=169[/tex]

Generally the equation for the test of statistic is mathematically given by

[tex]t=\frac{\=x_1-\=x_2}{\sqrt{\frac{\sigma_2}{n_1}+\frac{\sigma_2}{n_2} } }[/tex]

[tex]t=\frac{89-105}{\sqrt{\frac{81}{8}+\frac{169}{8} } }[/tex]

[tex]t=-2.86[/tex]

therefore the samples test for comparing the two population means

[tex]t=-2.86[/tex]

Answer: Fourth Choice. -2

Step-by-step explanation:

Given

( -9 | 6 + ( -10 ) | ) / 2 · 3²

Expand (-10) parenthesis

= ( -9 | 6 - 10 | ) / 2 · 3²

Expand  (-9|6-10|) parenthesis

= ( -9 | -4 | ) / 2 · 3²

= ( -36 ) / 2 · 3²

Simplify the denominator and get answer

= -36 / 2 · 9

= -36 / 18

= -2

Hope this helps!! :)

Please let me know if you have any questions

A recipe calls for ¾ cups of molasses. If you triple the recipe, 9/4 cups of molasses would be needed

An equation is an expression that shows the relationship between two or more numbers and variables.

A recipe calls for ¾ cups of molasses. If you triple the recipe, the molasses is:

Amount of molasses needed = 3 * (3/4) cup = 9/4 cups

A recipe calls for ¾ cups of molasses. If you triple the recipe, 9/4 cups of molasses would be needed

Find out more on equation at: https://brainly.com/question/2972832

Answer:

8 nights

Step-by-step explanation:

MATH

f(x) = |7m + 4| = 1

First equation by taking positive modules

7m + 4 = 1

7m = -3

m = -3/7 . Ans.

Second equation by taking negative modules

-7m - 4 = 1

-7m = 5

m = -5/7 . Ans.

∴ m = [ -5/7 U -3/7 ] Ans .

The spider needs 15 hours to climb up the top of the wall.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

A spider is trying to climb a wall of height = 15 meters

In each hour, it climbs up 3 meters but falls back 2 meters,

⇒ [tex]+3-2=1[/tex]

Thus spider climbs 1 meter per hour.

For 15 meter wall, the spider needs 15 hours to climb up the wall.

Hence we can conclude that the spider needs 15 hours to climb up the top of the wall.

Learn more about word problems here

brainly.com/question/20594903

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Answer:

-2

Step-by-step explanation:

Answer:

answer is -2

Step-by-step explanation:

5+3=8

8-10= -2

Answer:

21/3 or 7/1

Step-by-step explanation:

Answer:

21/3

Step-by-step explanation:

hope this helps you

Answer:

5/4

Step-by-step explanation:

6 1/4 is equal to 25/4 and if you do 5 times 5/4 you get 25/4 which is 6 1/4

Answer:

5/4

Step-by-step explanation:

Answer:

I'm confused as to what your asking?

Answer:

y= 2x +1

Step-by-step explanation:

slope 9-7/4-3 = 2/1= 2

y-7 = 2(x -3)

y-7 = 2x -6

y = 2x +1

Answer:

5832

Step-by-step explanation:

18 × 18 = 324

324 × 18 = 5832

Answer:

The sum of the first 880 terms in the sequence is 2,273,920.

Step-by-step explanation:

Arithmetic sequence:

The difference between consecutive terms is always the same, called common difference, and the nth term is given by:

[tex]a_{n} = a_0 + (n-1)d[/tex]

In which d is the common difference.

Sum of the first n terms:

The sum of the first n terms of an arithmetic sequence is given by:

[tex]S_{n} = \frac{n(a_1+a_n)}{2}[/tex]

ai = ai-1 + 6

This means that [tex]d = 6[/tex]

In this question:

Sum of the first 800 terms, so [tex]n = 800[/tex]

First term is -53, so [tex]a_1 = -53[/tex]

The 880th term is:

[tex]a_{880} = -53 + (880-1)*6 = 5221[/tex]

Sum

[tex]S_{n} = \frac{880(-53+5221)}{2} = 440(-53+5221) = 2273920[/tex]

The sum of the first 880 terms in the sequence is 2,273,920.

9514 1404 393

Answer:

  144 square meters

Step-by-step explanation:

The formula for surface area of a cuboid is useful.

  A = 2(LW +H(L+W))

  A = 2((6 m)(6 m) +(3 m)(6 m +6 m)) = 2(36 m² +36 m²)

  A = 144 m²

The surface area of the figure is 144 square meters.

Answer:

0.0000000006

Step-by-step explanation:

6* 10^-10= 0.0000000006

basically think of it as moving the decimal back 10 times.

Answer:

The third wine costs $5.70 per litre

Step-by-step explanation:

so we've got 2 parts $4.50 wine, 3 parts $5 wine and 4 parts x wine. The result is $5.20 per part.

2l*$4.50/l + 3l*$5/l + 4l*x = (2l+3l+4l)*$5.20/l

$9 + $15 + 4l*x = $46.80

4l*x = $22.80

x = $5.70/l

Answer:

B

Step-by-step explanation:

Answer: they are complementary but not necessarily congruent

Step-by-step explanation:

Answer:

B. 5(2x+5)

Step-by-step explanation:

Factor 5 out of 10x+25. and you get 5(2x+5)

Answer:

B. 5(2x + 5

Step-by-step explanation:

If you have any questions feel free to ask in the comments

Answer:

$38.75

Step-by-step explanation:

$465/12=$38.75

Answer:

1/2 + 1/4 _ 1/3 = 0.91667

Step-by-step explanation:

Answer:

the answer would be c

Step-by-step explanation:

the answer would be c because its a fraction

Answer:

X and y are supplementary.

Step-by-step explanation:

Choose the first option:

x + y = 180 degrees is the relationship that is always true.

Answer:

touches

crosses

Step-by-step explanation:

[tex]x=a[/tex] is said to be a zero of a function [tex]f(x)[/tex] if [tex]f(a)=0[/tex]

A zero say [tex]x=a[/tex] has a "multiplicity" equal to [tex]n[/tex], if the factor [tex](x-a)^n[/tex] appears in the polynomial.

When a real zero [tex]x=a[/tex] of a polynomial function [tex]f[/tex] is of even multiplicity, the graph of [tex]f[/tex] touches the x-axis at [tex]x=a[/tex], and when it is of odd multiplicity, the

graph of [tex]f[/tex] crosses the x-axis at [tex]x=a[/tex].

Answer:

Given, x = 2 and z = 12

z + 5x³

12 + 5×2³

12 + 5×8

12 + 40

52

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Answer:

249

Step-by-step explanation:

301 - 52 = 249

Answer:

[tex]P(x \le 1)= 0.9093[/tex]

Step-by-step explanation:

Given

[tex]\lambda = 2.4[/tex] -- mean

Required

Determine [tex]P(x \le 1)[/tex]

This is calculated using:

[tex]P(X \le x)= 1 - e^{-\lambda x}[/tex]

So:

[tex]P(x \le 1)= 1 - e^{-2.4 * 1}[/tex]

[tex]P(x \le 1)= 1 - e^{-2.4}[/tex]

[tex]P(x \le 1)= 1 - 0.0907[/tex]

[tex]P(x \le 1)= 0.9093[/tex]