7. Use an appropriate substitution and convert the following integral to one in terms of u. Convert the limits of integration as well. DO NOT EVALUATE, just show your selection for u and perform the c
Answers
To convert the integral using an appropriate substitution, we need to identify a suitable substitution that simplifies the integrand and allows us to express the integral in terms of a new variable, u.
Let's consider the integral ∫(4x³ + 1)² dx.
To determine the appropriate substitution, we can look for a function u(x) such that the derivative du/dx appears in the integrand and simplifies the expression.
Let's choose u = 4x³ + 1. To find du/dx, we differentiate u with respect to x:
du/dx = d/dx (4x³ + 1)
= 12x².
Now, we can express dx in terms of du using du/dx:
dx = du / (du/dx)
= du / (12x²).
Substituting this into the original integral, we have:
∫(4x³ + 1)² dx = ∫(4x³ + 1)² (du / (12x²)).
Now, we need to change the limits of integration to correspond to the new variable u. Let's consider the original limits of integration, a and b. We substitute x = a and x = b into our chosen substitution u:
u(a) = 4a³ + 1
u(b) = 4b³ + 1.
The new integral with the updated limits becomes:
∫[u(a), u(b)] (4x³ + 1)² (du / (12x²)).
In this form, the integral is expressed in terms of u, and the limits of integration have been converted accordingly.
It's important to note that we have only performed the substitution and changed the limits of integration. The next step would be to evaluate the integral in terms of u. However, since the instruction states not to evaluate, we stop at this stage.
In summary, to convert the integral using an appropriate substitution, we chose u = 4x³ + 1 and expressed dx in terms of du. We then substituted these expressions into the original integral and adjusted the limits of integration to correspond to the new variable u.
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Related Questions
i dont undersyand jnjnjiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiin
Answers
Answer:
no 36x is not a solution the answer is 36/9=4
Step-by-step explanation:
you plug in 36 for x and then divide by 9
in a _____ sequence, the ratio between consecutive terms is constant.
Answers
Answer:
Geometric.
Step-by-step explanation:
For example
2, 4, 8, 16
where the common ratio is 4/2 = 8/4 = 16/8 = 2.
Suppose that the function f(x,y) defined below is a probability density function: f(x,y) = { cell? if (2,y) € [0, 1] x [0, 1] and y su otherwise Find the value of c. For the probability density function given in the previous problem, find the probability that the pair (x, y) satisfies y < 2x.
Answers
The probability that the pair (x, y) satisfies y < 2x is 1/2.
To help you with your question, let's first restate the problem with the correct terms:
Suppose that the function f(x, y) defined below is a probability density function: f(x, y) = {c if (x, y) ∈ [0, 1] x [0, 1] and y ≤ 2x; 0 otherwise}. Find the value of c. For the probability density function given in the previous problem, find the probability that the pair (x, y) satisfies y < 2x.
To find the value of c, we need to remember that the total probability of a probability density function must be equal to 1. So, we'll integrate f(x, y) over the given region [0, 1] x [0, 1] with the constraint y ≤ 2x:
1. Set up the double integral: ∬[0, 1]x[0, 2x] f(x, y) dy dx.
2. Substitute f(x, y) with the given function: ∬[0, 1]x[0, 2x] c dy dx.
3. Integrate with respect to y: c∫[0, 1] [2x - 0] dx.
4. Simplify c∫[0, 1] 2x dx.
5. Integrate with respect to x: c[x^2] evaluated from 0 to 1.
6. Simplify: c[(1)^2 - (0)^2].
7. Set the integral equal to 1: c = 1.
Now that we have the value of c, we can find the probability that the pair (x, y) satisfies y < 2x. Since f(x, y) is now equal to 1 within the region, we just need to calculate the area of the region where y < 2x, which is a right triangle with legs of length 1:
1. Calculate the area of the triangle: (1/2) * base * height = (1/2) * 1 * 1 = 1/2.
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Inactive Ohio licensees who want to reactivate their licenses after military service must provide ______ in order to be reactivated.
Answers
Inactive Ohio licensees who want to reactivate their licenses after military service must provide evidence of military service in order to be reactivated.
What is an Inactive Ohio Licensee?
The Inactive Ohio licensees are those individuals who currently hold a license or certification and have decided to take a break from practicing or providing services to clients. These inactive Ohio licensees may decide to reactivate their licenses after a period of time. Military Service and License ReactivationThe Ohio Department of Commerce's Division of Real Estate and Professional Licensing provides a dedicated unit to serve active and inactive Ohio licensees who are seeking to reactivate their licenses after military service.
In order to be reactivated, Inactive Ohio licensees who want to reactivate their licenses after military service must provide evidence of military service. The required documents might differ depending on the nature and timing of the service, but in general, proof of military service will be required. The following are the requirements that should be met:You must submit the appropriate application for licensure based on your current standing (active, inactive, or expired) as well as the license type you hold.
The Ohio Department of Commerce's Division of Real Estate and Professional Licensing also mandates that you furnish appropriate evidence of military service (DD-214) and a self-addressed, stamped envelope (for the return of your DD-214).Furthermore, the Ohio Department of Commerce's Division of Real Estate and Professional Licensing should have previously issued the license type you want to reactivate.
If your original license has been replaced, renewed, or altered in any way, you must apply for a new license.In conclusion, Inactive Ohio licensees who want to reactivate their licenses after military service must provide evidence of military service in order to be reactivated.
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430\(\sqrt{x} 34\\\\)
Answers
Answer:
I'm not entirely sure what you are trying to do for this equation, but if you are simplifying, the answer would be 430^x^17
(please help!!!!) The list represents a student's grades on tests in their math class.
59, 65, 70, 80, 98, 71, 45, 79, 77, 85
Find the range for the data set.
45
53
74
98
Answers
Answer:
Range is 53
Step-by-step explanation:
The range is the difference between the maximum and minimum values in a data set.
The minimum value in the data set is 45, and the maximum value is 98.
Therefore, the range is:
98 - 45 = 53
So the answer is 53.
Where would you put the decimal in this product?
3.21 x 4.8 = 1 5 4 0 8
Answers
Answer:
15.408
Step-by-step explanation:
hope this helps :3
if it did pls mark brainliest
what is 13/21 - 1/7 im having a hard time lol
Answers
Answer:
10/21
Step-by-step explanation:
First, you have to find the common denominator! In this equation, 7 is divisible by 21! This means that we could multiply the 7 by 3. If we have to multiply the denominator, we also have to multiply the numerator! This means that it would be 3/21. Final step! 13/21 - 3/21 = 10/21
I hope this helps! :)
Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets $25. The venue has the capacity to hold 400 people. The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise at least $5,000 for her school:
What is the minimum number of at-the-door tickets she needs to sell to make her goal?
A,333
B.334
C.66
D.67
Answers
Hence, the minimum number of at-the-door tickets she needs to sell to make her goal is (B) 334.
Given information: Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets $25. The venue has the capacity to hold 400 people.
The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise at least $5,000 for her school.
The minimum number of at-the-door tickets she needs to sell to make her goal can be calculated as follows;
Let's suppose that x represents the number of pre-sale tickets, and y represents the number of at-the-door tickets Anna needs to sell.
Then the following equation represents the total amount of money Anna will earn after selling the given number of tickets;
10x + 25y ≥ 5,000
If she sells all the tickets, she will have sold a total of x + y tickets. But, we know that the venue has a capacity of 400 people.
So, we also know that;
x + y ≤ 400
Solving the two equations for y gives;
10x + 25y ≥ 5,00025y ≥ 5,000 - 10x y ≥ (5,000 - 10x)/25y ≥ 200 - 0.4xy ≤ 333.3 - 0.4x
Answer: B.334.
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1. Using the right triangle above, fill in the correct ratios for each trigonometric function. (do not simplify) numbers on the triangle: 77, 85, 36 (there is a right angle)
Answers
Answer:
Below in bold.
Step-by-step explanation:
sin S = opposite side / hypotenuse = 77/85
cos S = adjacent side / hypotenuse = 36/85
tan S = opposite side / adjacent side = 77/36.
Answer:
see explanation
Step-by-step explanation:
sin S = \(\frac{opposite}{hypotenuse}\) = \(\frac{TU}{TS}\) = \(\frac{77}{85}\)
cos S = \(\frac{adjacent}{hypotenuse}\) = \(\frac{SU}{TS}\) = \(\frac{36}{85}\)
tan S = \(\frac{opposite}{adjacent}\) = \(\frac{TU}{SU}\) = \(\frac{77}{36}\)
explain what type of a probabilistic result is conveyed by the p-value.
Answers
A p-value conveys the type of probabilistic result known as "statistical significance." Statistical significance refers to the likelihood that a given result occurred by chance.
A p-value is a measure of this likelihood, with a smaller p-value indicating a smaller likelihood that the result occurred by chance. In other words, a smaller p-value indicates a higher level of statistical significance.
For example, if a p-value is 0.01, this means that there is a 1% chance that the result occurred by chance. This is considered to be statistically significant, as it is unlikely that the result occurred by chance. On the other hand, if a p-value is 0.5, this means that there is a 50% chance that the result occurred by chance. This is not considered to be statistically significant, as it is equally likely that the result occurred by chance or not.
In summary, a p-value conveys the type of probabilistic result known as statistical significance, with smaller p-values indicating a higher level of statistical significance.
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Find the mistake in the following : 3 x ( 4 + 2 ) = 12 + 2
Answers
Answer: The mistake is improper use of distribution property.
Step-by-step explanation:
It is given that \(3\times (4+2)=12+2\).
We need to find the mistake.
The given expression is
\(3\times (4+2)\)
Using distribution property, we get
\(3\times (4)+3\times(2)\)
\(12+6\)
So, \(3\times (4+2)=12+6\).
In the given calculation the 3 is not distributed properly because 3 is not multiplied with 2.
Therefore, the mistake is improper use of distribution property.
Figure out 26 and 27 and get 100 points and I will mark as brainliest
Answers
Answer:
Triangle
Area-9 units
Perimeter-9 units
Rectangle
Area- 18
Perimeter- 18
Step-by-step explanation
For the triangle, you first plot the points. Then you find two of the side lengths and multiply them together. After that you divide the result by two. You get the area. You add the sides together for the perimeter. For the rectangle, you have 3 and 6. Multiply to get 18. 3+3+6+6 is also 18.
which value of C would not make the following expression factorable: 6x^2-13x+c
Answers
Answer:
1
Step-by-step explanation:
Reasoning How can you use proportional
easoning to make an estimate about a
population using data from a sample?
Answers
Proportional reasoning can be used to make an estimate about a population using data from a sample by assuming that the sample is representative of the population as a whole.
What is proportional reasoning ?Proportional reasoning involves using the relationship between different parts of a whole to estimate an unknown value.
To apply proportional reasoning to a population estimate, you would first need to gather a random sample of individuals from the population. Then, you could use the data from the sample to estimate the value of a particular characteristic or parameter for the entire population.
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Please answer the questions in order NO LINKS please thanks
Answers
Answer:
Step-by-step explanation:
Sum: 6 * 10^-4 + 1.5*10^-4 = 7.5 * 10^-4
Difference: 6 * 10^-4 - 1.5 * 10^-4 = 4.5 * 10^-4
Product: 6*10^-4 * 1.5 * 10^-4 = 9 * 10^-8
Quotient: 6*10^-4/1.5 * 10^-4 = 4
Notice the answers, because they give you the rules.
When adding exponents and rationales, if the powers are the same then the rationales merely add.
Same rule applies to subtraction. Retain the powers and subtract the rationales.
When multiplying the rationales multiply, but the rationales add. they don't stay the same.
When dividing, the rationales divide and the powers subtract -- numerator minus denominator
How do numbers help us predict the ebbs and flows in our lives? Think about things like circadian rhythms.
Answers
Numbers play a crucial role in helping us predict the ebbs and flows in our lives. They are used to measure and quantify patterns and cycles that occur in our daily lives, such as circadian rhythms.
Circadian rhythms are the physical, mental, and behavioral changes that follow a 24-hour cycle, responding primarily to light and darkness in an organism's environment. Numbers help us measure and track these rhythms, allowing us to predict when we will feel awake or sleepy, hungry or full, and so on.
For example, we know that the average human circadian rhythm is 24.2 hours, and that our bodies produce the hormone melatonin at night to help us sleep. By measuring and tracking these numbers, we can predict when we will feel tired and need to sleep, and when we will feel awake and alert.
Numbers also help us predict other patterns in our lives, such as our menstrual cycles, the best times to exercise, and when we are most likely to get sick. By tracking and measuring these numbers, we can better understand and predict the ebbs and flows in our lives and make more informed decisions about our health and well-being.
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Your aunt has baked 80 cookies, and she gave you 28 to take home with you. What percent of the cookies did she give to you? What percent of the cookies did she keep?
Answers
For an experiment involving 2 Levels of factor A and 3 levels of factor B with a sample of n = 5 in each treatment condition, what is the value for df within treatments?
A 24
B 20
C 29
D 30
Answers
Option A is the correct answer.
For an experiment involving 2 Levels of factor A and 3 levels of factor B with a sample of n = 5 in each treatment condition, we need to calculate the value for df within treatments.
The formula to calculate df within treatments is given by, df within treatments = (A - 1) (B - 1) (n - 1)Where, A = Levels of factor AB = Levels of factor Bn = Sample size= 2 levels of factor A= 3 levels of factor B= 5 in each treatment conditionNow, df within treatments = (A - 1) (B - 1) (n - 1)= (2 - 1) (3 - 1) (5 - 1)= 1 × 2 × 4= 8Hence, the value of df within treatments is 8.
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Si una baraja de cartas tiene 52 cartas divididas en partes iguales en cuatro palos cuál es la probabilidad de sacar un trébol de la baraja
Answers
Probability of drawing a club.
How to calculate card probability?The question asks for the probability of drawing a club from a deck of 52 cards, which are divided equally into four suits. Since one suit is the club, there are 13 club cards in the deck.
The probability of drawing a club is calculated by dividing the number of club cards by the total number of cards in the deck. Therefore, the probability of drawing a club from a standard deck of 52 playing cards is 13/52, which simplifies to 1/4 or 0.25.
This means that there is a 25% chance of drawing a club from a deck of cards.
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What is the quotient of 2 3/4 and 7/8?
Pls help fast
Answers
The quotient of the given expression 2 3/4 and 7/8 is 22/7
Quotient of an expressionQuotient refers to a number resulting from the division of one number by another. 12 ÷ 2 = 6 the quotient is 6
Dividend is number or expression that is to be divided by another. 12 ÷ 2 = 6 the dividend is 12
Divisor is the number or expression that is to be divided by another. 12 ÷ 2 = 6 the divisor is 2
Quotient of 2 3/4 and 7/8?
= 2 3/4 ÷ 7/8
= 11/4 ÷ 7/8
multiply by the reciprocal of 7/8= 11/4 × 8/7
= (11 × 8) / (4 × 7)
= 88/28
= 22/7
Therefore, the quotient of the given expression 2 3/4 and 7/8 is 22/7
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Forrest Lumber purchased a table saw for $810. After 4 years the saw had a depreciated value of $450. What is the amount of yearly depreciation?
Answers
The amount of the annual depreciation has been $90.
The statement provides us with the following data:
The yearly depreciation of the table saw can be calculated by subtracting the depreciated value from the original cost and dividing by the number of years.
Yearly depreciation = (Original cost - Depreciated value) / Number of years
Yearly depreciation = ($810 - $450) / 4
Yearly depreciation = $360 / 4
Yearly depreciation = $90
Therefore, the amount of yearly depreciation for the table saw is $90.
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The two line plots below show the times that Marco and Antonio ran in ten trials of the 40-yard dash.
antonio's:4.5,4.5,4.6,4.6,4.6,4.8,4.8,5.2,5.2,5.3,5.5
Marcos's:4.8,4.8,4.9,4.9,4.9,4.9,5.0,5.0,5.0,5.1
Which of the following can be inferred from the data?
A. Antonio runs the race faster than Marco on average.
B. Marco always runs a better time than Antonio.
C. Marco is more likely than Antonio to improve after a poor race.
D. Antonio's average time is about 5.1 seconds,
Answers
Step-by-step explanation:
The answer is A
Bcz In a race runs faster whoever does it in less time
The line parallel to y=-4x-1 that passes through the point (3,-2)
Answers
Answer:
y=-4x+10
Step-by-step explanation:
-2= -4(3)+b
-2=-12+b
-10=b
Sandra's bird feeder holds 3/5 of a cup of birdseed. Sandra is filling the bird feeder with a scoop that holds 1/10 of a cup. How many scoops of birdseed will Sandra put into the feeder?
Answers
Dante and Erica just returned from a comic bookstore that sells new and used comic books.
Dante spend $10.25 on 2 new and 3 old books, and Erica spend 13.75 on 10 used and 3 new
ones. Which system of equations can be used to find how much the new and old books costs?
Answers
HELP! WILL GIVE BRAINLEST!
Answers
Answer:
A
Step-by-step explanation:
tan theta will equal zero if theta = n × pi where n is an integer
Please help quickly! Both circles have the same center. The circumference of the inner circle is 125.6 inches. What is the area of the shaded region?
Use 3.14 for pi. Write your answer as a whole number or decimal rounded to the nearest hundredth.
Answers
Answer:
The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle. The area of the inner circle is pi multiplied by the square of the radius, or 3.14 * (125.6/2)^2, which equals 19644.8. The area of the outer circle is pi multiplied by the square of the radius, or 3.14 * (125.6)^2, which equals 49766.56. Subtracting the inner circle’s area from the outer circle's area, the area of the shaded region is 30121.76, rounded to the nearest hundredth
Step-by-step explanation:
7. An example for using estimation would be:
O O O O
A) counting back change
B) depositing money in the bank
C) guessing the number of pennies in a jar
D) counting the number of dollar bills in your wallet.
Answers
7d – 8 = 3d + 8 help me
Answers
Answer:
Step-by-step explanation:
7d – 8 = 3d + 8
7d - 3d = 8 + 8
4d = 16
d = 16 /4
d = 4