Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent.
Answers
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
Related Questions
In an examination, 40% students passed in Maths only, 30% passed in Science only and 10%
students failed in both the subjects. If 400 students passed in Science, find the total number of
students by drawing a Venn diagram.
help me
Answers
Answer:
The total number of students is 800.
Step-by-step explanation:
Given that in an examination, 40% students passed in Maths only, 30% passed in Science only and 10% students failed in both the subjects, to determine the total number of students if 400 students passed in Science the following calculation must be performed:
100 - 40 - 30 - 10 = 20
20 + 30 = 50
50 = 400
100 = X
100 x 400/50 = X
800 = X
Thus, the total number of students is 800.
PLEASE ANSWER THE QUESTION IN THE PICTURE BELOW
Answers
Answer:
35 cm^3
Step-by-step explanation:
the area is 35 hoped that helped
Find the distance between the points (2, 3) and (2.8).
Answers
Answer:
d = 5
Step-by-step explanation:
For:
(X1, Y1) = (2, 3)
(X2, Y2) = (2, 8)
Distance Equation Solution:
d=(2−2)2+(8−3)2−−−−−−−−−−−−−−−√
d=(0)2+(5)2−−−−−−−−−√
d=0+25−−−−−√
d=2–√5
d=5
The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of catalyst used in the process. The standard deviation of active concentration is known to be 3 grams per liter regardless of the catalyst type. Ten observations on concentration are taken with each catalyst, and the data follow:
Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0
Catalyst 2: 66.4, 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8.
a. Find a 95% confidence interval on the difference in mean active concentrations for the two catalysts. Find the P-value.
b. Is there any evidence to indicate that the mean active concentrations depend on the choice of catalyst? Base your answer on the results of part (a).
c. Suppose that the true mean difference in active concentration is 5 grams per liter. What is the power of the test to detect this difference if α = 0.05?
d. If this difference of 5 grams per liter is really important, do you consider the sample sizes used by the experimenter to be adequate? Does the assumption of normality seem reasonable for both samples?
Answers
Answer:
a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57
b. Yes
c. The power of the test is 0.03836
d. The sample size can be considered adequate
Step-by-step explanation:
a. The given data in the study
Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0
Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8
Using the Average, Standard Deviation function from Microsoft Excel, we have;
The mean for Catalyst 1, [tex]\overline x_1[/tex] = 65.22
The standard deviation for catalyst 1, σ₁ = 3.444416
The mean for Catalyst 2, [tex]\overline x_2[/tex] = 68.42
The standard deviation for catalyst 2, σ₂ = 2.22401
The 95% confidence interval on the difference in mean is given as follows;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]
The critical-z for a 95% confidence interval = 1.96
Therefore, we have;
[tex]\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}[/tex]
Therefore, we have;
The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57
The test statistics is given as follows;
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
Therefore we have;
[tex]z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385[/tex]
The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684
b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst
c. The power of the test
The sample mean difference is given as follows;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]
Therefore, we have;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296[/tex]
The z-value is given as follows;
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
μ₁ - μ₂ = 5
When [tex]\bar{x}_1-\bar{x}_{2} = 2.6296[/tex]
[tex]z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918[/tex]
When [tex]\bar{x}_1-\bar{x}_{2} = -2.6296[/tex]
[tex]z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768[/tex]
The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836
The power of the test = 0.03836
d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean
The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;
(-5.74, -0.66) which also contains -5 which is the difference in the population mean
simplify the sum x-2/x+3 + 10x/x^2-9 please show your work
Answers
Answer:
Step-by-step explanation:
simpify each term
x- 2/x +3+ 10/x -9
combine fractions
x+3 -9 + 8/x
find common denominator then simplify terms [tex]\frac{x*x}{x}+\frac{3x}{x}+\frac{-9x}{x}+\frac{8}{x}[/tex]
[tex]\frac{x^{2}-6x+8 }{x}[/tex]
factor
[tex]\frac{(x-4) (x-2)}{x}[/tex]
Answer:
(x−4)(x−2)x
Step-by-step explanation:
What is the volume of the figure?
Answers
Answer:
12.57
Step-by-step explanation:
same as last time you know
what is 3times9 3/5 as a mixed number
Answers
Please help me with the math question.
Answers
Answer:
MC7. B
MC8. A
Step-by-step explanation:
Given events are mutually exclusive and the probability of either is 0.64, you want possible probabilities for each. Given independent events have a joint probability of 0.16, you want possible probabilities for each.
MC7. Mutually exclusiveMutually exclusive events cannot occur simultaneously (by definition). This means the probability of occurrence of either is the sum of the probabilities of occurrence of each:
P(A∪B) = P(A) + P(B) . . . . . . . only if P(A∩B) = 0
The answer to this question will be two probabilities that have a sum of 0.64. This requirement is met by ...
b.) P(A) = 0.42, P(B) = 0.22
MC8. IndependentEvents are independent when their conditional probability is the same as the unconditioned probability:
P(A|B) = P(A∩B)/P(B) . . . . . definition of conditional probability
When this is the same as P(A), you have ...
P(A) = P(A∩B)/P(B)
P(A)·P(B) = P(A∩B)
The answer to this question will be two probabilities that have a product of 0.16. This requirement is met by ...
a.) P(A) = 0.4, P(B) = 0.4
__
Additional comment
So, the two formulas used here are the one for "or" (union) and the one for conditional probability:
P(A∪B) = P(A) +P(B) -P(A∩B) . . . . . . "mutually exclusive" means P(A∩B)=0
P(A|B) = P(A∩B)/P(B) . . . . . . . "independent" means P(A|B) = P(A)
The plus sign (+) is often used in probability and in logic to mean "or". That is, P(A∪B) can also be written P(A+B). That is NOT the same as P(A)+P(B), where this "+" means addition.
The multiplication symbol (·, or no symbol) is often used in probability and in logic to mean "and", or "intersection." That is, P(A∩B) can also be written P(A·B) or P(AB). That is NOT the same as P(A)·P(B), where the symbol means multiplication in this context.
<95141404393>
The possible probabilities are given as follows:
7 b) P(A) = 0.42, P(B) = 0.22.
8 a) P(A) = 0.4, P(B) = 0.4.
How to calculate a probability?The two parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.
For mutually exclusive events, we have that:
P(A U B) = P(A) + P(B).
Hence:
0.42 + 0.22 = 0.64.
For independent events, we have that:
P(A and B) = P(A) x P(B)
Hence:
0.8 x 0.8 = 0.64.
Learn more about the concept of probability at https://brainly.com/question/24756209
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Which triangles are similar to triangle ABC ?
Answers
Answer:
The answer is A
Step-by-step explanation:
Triangle DEF was rotated and dilated so that's why is looks different than triangle ABC, but it maintained the same shape that is presented in ABC and that is why A is the answer.
Help plz find x and y
Answers
Answer:
y = 18
x = 15.588
Answer:
The value of X should be 0
The value of Y should be 30
However your teacher gave next to no context, so these might be wrong
Step-by-step explanation: protractor
Find the value of x.
6
14
3x-12
A
o
21
x = [?]
Enter
Answers
Answer:
Bueno esto es lo que yo calculo
3×‐12
3(×‐4)
3 14x12
A calcule
A 12×3 =14
es lo que me calcula
Answer:
7Step-by-step explanation:
14/6 = 21 / 3x - 12
first, cross multiply
14 (3x - 12) = 6*21
Remove the brackets
42x - 168 = 126
Add 168 to both sides
42x = 168 + 126
Combine
42x = 294
Divide by 42
x = 294/42
x = 7
Please help me out here.............
Answers
Does the equation below represent a relation, a function, both a relation and a function or neither
y = x2 – 9x
Answers
Select all possible cross sections of a sphere.
А
circle
B
square
C
triangle
D
point
Answers
1) Determine if the side lengths given form a triangle
Answers
Using the triangle inequality theorem, we can figure this out.
2- Yes
3- No
4- No
5- Yes
6- Yes
Can someone give me the answer to question 4
Answers
Answer:
105+54=Z [being sum if interior angle of triangle equal to opposite exterior angle]159=Ztherefore,Z=159Review the simple interest rate based on FICO scores to answer the question:
FICO Score Simple Interest Rate
800–850 5.295%
740–799 6.597%
670–739 9.132%
580–669 10.358%
300–579 14.313%
Kamryn plans to borrow $13,250.00 with a simple interest rate loan. Determine the amount of interest Kamryn will save if she is able to raise her credit score from 665 to 680.
Answers
Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.
According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.
Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.
Interest = Principal * Rate
= $13,250.00 * 0.10358
≈ $1,370.56
Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.
Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.
Calculating the interest with a credit score of 680:
Interest = Principal * Rate
= $13,250.00 * 0.09132
≈ $1,210.57
Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.
Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
For more question on interest visit:
https://brainly.com/question/25720319
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PLEASE ANSWER EXTRA POINTS AND NAMED BRAINLIEST

Answers
Answer:
5,8 8,3
Step-by-step explanation:
hoped this helped <33
http://www.gilbertmath.com/uploads/1/4/2/7/14279231/3c_u4_assignment1.pdf
i need DESPERATE HELP!!!
my teacher didn't even teach us this and expects us to do it
heres the link for it if needed theres the other work sheet thing to fill out the answers and i have no idea how to do it please im begging you!!
Answers
Answer:
1=94 max 2=96 max
Step-by-step explanation:
WITH STEPS PLEASE CAN YOU HELP
Answers
Because u multiply 2 by 4 =8 and 8 is less than ten the sign represents less than or equal to so 8
Determine the missing factor in × 4.3 = 12.9
Answers
Answer: 3
Step-by-step explanation:
12.9/4.3 will give you the number it was multiplied by.
What number is equal to its opposite? Please enter your answer as a number.
Answers
Answer:
there is no opposite number but no means opposite
Step-by-step explanation:
Can someone help me ASAP!!!
Answers
9514 1404 393
Answer:
f(x) = {-x for x < 2; 2x-3 for x ≥ 2}
Step-by-step explanation:
The blue line extending to the left has a slope of -1 and a y-intercept of 0. Its equation is y = -x. That part of the definition of f(x) is applicable for values of x less than 2. (The open dot at (2, -2) tells you that point is not included.)
The red line extending to the right has a slope = rise/run = 2/1 = 2. The y-intercept can be found by extending the line to the y-axis, or from the computation ...
b = y -mx
b = 1 -2(2) = -3 . . . . . for the point (x, y) = (2, 1)
Then the slope-intercept equation for the red line is ...
y = 2x -3
That part of the definition of f(x) is applicable for values of x ≥ 2. The solid dot tells you the point (2, 1) is included.
Putting these parts together, we get ...
[tex]f(x)=\left\{\begin{array}{cc}-x&\text{if $x<2$}\\2x-3&\text{if $x\ge2$}\end{array}\right.[/tex]
Can anyone help me out with this answer?
Answers
9514 1404 393
Answer:
7×10⁻¹ +6×10⁻² +5×10⁻³
Step-by-step explanation:
Place value in any place-value number system increases by a factor of the base for each place to the left of the "decimal" point. It is reduced by a factor of the base for each place to the right of the "decimal" point.
For base-10 numbers, the powers of 10 are -1, -2, -3, ... as you go to the right of the decimal point. Hence the number 0.765 decomposes as ...
7×10⁻¹ +6×10⁻² +5×10⁻³
Select all numbers that have an absolute value of 6.3.
Answers
Answer:
-6.3
Step-by-step explanation:
Its the only thing I can think of. |-6.3| |6.3|
please help !
Find the value of x. Round to the
nearest tenth.
26°
12
X
x = [?]
Answers
Answer:
x = 5.85
Step-by-step explanation:
Given that,
One angle = 26°
Middle angle = 90°
Third angle = 180-(90+26) = 64°
Height, H = 12
We need to find the value of x. Using trigonometry to find it such that,
[tex]\tan64=\dfrac{12}{x}\\\\x=\dfrac{12}{\tan(64)}\\\\x=5.85[/tex]
So, the value of x is equal to 5.85.
Answer:
5.9
Step-by-step explanation:
im doing this rn
a2 + b ÷ 3= helpppppppp mmmmmeeeeeeeee! pls
Answers
Answer: 2a/3 + b/3
Since it has two different variables, there is no final answer. To find the answer, you must first expand the equation and then apply the fraction rule.
The radius of the cylindrical construction pipe is 2.5ft, if the pipe is 25ft long, what is the volume? Use the value 3.14 for pi, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer. Please helpp.
Answers
Answer:
Step-by-step explanation:
radius of the cylindrical construction pipe = 2.5 ft
height of cylinder = 25 ft
volume of cylinder = [tex]\pi r^{2} h[/tex]
= 3.14 x 2.5 x 2.5 x 25
= 490.625
= 490 [tex]ft^{3}[/tex]
Hope this helps
please mark as brainliest!!!
Answer:
490 ft³
Step-by-step explanation:
The radius of the cylindrical construction pipe is 2.5ft, if the pipe is 25ft long, what is the volume? 490 ft³
NO LINKS!! URGENT HELP PLEASE!!!
Solve each continuous exponential growth problem.
24. A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1727.00, what will the balance be 6 years from now?
Answers
Answer:
$2,067.59
Step-by-step explanation:
To calculate the balance of the savings account, we can use the continuous compounding interest formula:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given values:
P = $1,727.00r = 3% = 0.03t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\begin{aligned}A&=1727 \cdot e^{0.03 \cdot 6}\\&=1727 \cdot e^{0.18}\\&=1727 \cdot 1.19721736...\\&=2067.59438...\\&=2067.59\end{aligned}[/tex]
Therefore, the balance of the savings account 6 years from now is $2,067.59.
Only two more questions
Answers
Answer:
60
Step-by-step explanation:
if it has a square in the center of the angle it means it is 90 degrees
so a straight line adds up to 180b
90 +30+x=180
x=60