find f. (use c for the constant of the first antiderivative and d for the constant of the second antiderivative.) f ''(x) = 32x3 − 18x2 + 10x
Answers
The answer of the function is: \(f(x) = (8/5)x^_5\)\(− (3/2)x^4\)\(+ (5/3)x\³ + cx + d\).
The given function is \(f''(x) = 32x^3 − 18x^2 + 10x\) To find the function f, we need to integrate the given function twice.
The integral of f''(x) with respect to x is given by:
\(∫f''(x) dx = \int (32x^\³ − 18x\² + 10x) dx\)
The antiderivative of 32x³ is \(8x^4\) and the antiderivative of 18x² is \(6x^3\)
, and the antiderivative of 10x is 5x².
Thus,∫f''(x) dx =\(8 x^4 \−6x^3 + 5x\² + c\)
Where c is the constant of integration.The antiderivative of f'(x) is the function f(x).Thus, we integrate the above function again to get the value of f(x).
∫f'(x) dx =\(\int(8x^4\− 6x^3 + 5x\² + c) dx\)
The antiderivative of 8x^4 is (8/5)x^5 and the antiderivative of \(-6x^3\) is \((-3/2)x^4\), the antiderivative of 5x² is (5/3)x³, and the antiderivative of c is cx.
Then,∫f'(x) dx = \((8/5)x^5\− (3/2)x^4 + (5/3)x\³ + cx + d\)
Where d is the constant of integration.Finally, the function f(x) is given by:
f(x) =\((8/5)x^5\− (3/2)x^4 + (5/3)x\³ + cx + d\)
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Related Questions
IBM purchased computer chips from NEC, a Japanese electronics concern, and was billed ¥270 million payable in six months. Currently, the spot USD/JPY rate is 106 and the six-month forward rate is 101. The six-month money market interest rate is 4.0 percent per annum in the U.S. and 1.4 percent per annum in Japan. The management of IBM decided to use the money market hedge to deal with this yen account payable. Calculate today's dollar cost of meeting this yen obligation. (USD, no cents)
Answers
The dollar cost of meeting the yen obligation using a money market hedge is approximately $2,743,197.89.
To calculate the dollar cost of meeting the yen obligation using a money market hedge, we need to consider the forward exchange rate, interest rate differentials, and the time period involved.
First, let's convert the yen obligation into USD using the spot exchange rate:
¥270 million / 106 USD/JPY = $2,547,169.81
Next, let's calculate the interest earned on the USD investment in the U.S. for six months:
Interest earned in the U.S. = $2,547,169.81 * (4.0% / 2)
= $50,943.40
Now, let's calculate the interest paid on the yen borrowed in Japan for six months:
Interest paid in Japan = ¥270 million * (1.4% / 2)
= ¥1,890,000
Next, let's calculate the forward exchange rate adjusted for interest rate differentials:
Adjusted forward rate = Forward rate * (1 + Foreign Interest Rate) / (1 + Domestic Interest Rate)
= 101 * (1 + 0.014) / (1 + 0.04)
= 101 * 1.014 / 1.04
= 98.4904
Finally, let's calculate the dollar cost of meeting the yen obligation using the adjusted forward rate:
Dollar cost = ¥270 million / Adjusted forward rate
= ¥270 million / 98.4904 USD/JPY
= $2,743,197.89
The dollar cost of meeting the yen obligation using a money market hedge is approximately $2,743,197.89.
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la factorizacion de x2 -8x + 15
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The balance of Susu's savings account can be represented by the variable b. The inequality describing her balance is b greater-than 30 dollars. Which could be a solution to the inequality? $15 $20 $30 $35
Answers
Answer:
$35
Step-by-step explanation:
b is greater than 30
35 is the only value greater than 30
Place the variable on the in an inequality statement so that the inequality symbol will the arrow needs to go.
Answers
To determine the direction of the inequality symbol in an inequality statement, we need to consider the value of the variable in relation to another value or expression.
The direction of the inequality symbol depends on the relationship between the variable and another value or expression in the inequality statement.
Inequality statements express a relationship between two values or expressions, indicating whether one is greater than, less than, greater than or equal to, or less than or equal to the other. The direction of the inequality symbol (< or >) indicates the direction of the relationship.
Let's consider an example to illustrate this. Suppose we have the variable x. If we want to express that x is greater than 5, the inequality statement would be written as x > 5. Here, the arrow points to the right because x is greater than 5.
Similarly, if we want to express that x is less than or equal to 3, the inequality statement would be written as x ≤ 3. Here, the arrow points to the left because x is less than or equal to 3.
It's important to note that the direction of the inequality symbol may change depending on the specific values and expressions involved in the inequality statement. The choice of whether to use < or >, ≤ or ≥, depends on the intended relationship between the variable and the other value or expression in the inequality.
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Ferris wheel diameter was 250 feet. Calculate it’s radius. If 40 steel rods were joined at the centre find the total steel required?
Answers
Answer:
785.5ft
Step-by-step explanation:
Given data
Diameter= 250ft
Radius= D/2= 250/2= 125ft
The total steel required can be found from the Circumference
C= 2πr
C= 2*3.142*125
C= 785.5ft
Hence the total steel required is 785.5ft
A gas station has monthly expenses, in dollars, of , where x is the number of gallons of gas sold. It sells the gas at $2.25 per gallon. How many gallons do they need to sell to make a profit of $3000 per month
Answers
If it costs $2.25 for a (1) gallon then you need to divide the profit of $3000 which is 1333.33...... Gallons
Fill in the missing number. % of 98 = 49
Answers
50%
since 98/2 = 49
Thats it
Josh has 27 signed baseballs. He places the baseballs equally on 3 shelves. How many baseballs are on each shelf?
Answers
Answer:
9
Step-by-step explanation:
27 divided by 3 equal 9
what is the x-coordinate of the first car location at 8:30 pm? give your answer to three decimal places.
Answers
Not enough information is provided to determine the x-coordinate.
To determine the x-coordinate of the first car location at 8:30 PM, we need more information about the specific context or scenario. The x-coordinate is typically used to represent the horizontal position of an object on a coordinate plane. Without knowing the initial position or any information about the movement or velocity of the car, it is not possible to determine the exact x-coordinate at a specific time.
If additional details are provided, such as the initial position of the car or any information related to its movement, we can use that information to calculate the x-coordinate at 8:30 PM. However, without any specific context or given data, it is not possible to provide a meaningful answer to this question.
Therefore, without further information, it is not possible to determine the x-coordinate of the first car location at 8:30 PM.
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4. A pizza shop has 12" pizzas with 6 slices and 16" pizzas with slices. Which pizza has bigger slices?
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In April, Francis had math homework 18 out of the 30 days in the month. Which value is equivalent to the fraction of days she had math homework?
Answers
Answer:
Step-by-step explanation:
You didn't give the options but let me try help out.
From the question, we are informed that Francis had math homework 18 out of the 30 days in the month.
For us to get the value that is equivalent to the fraction of days she had math homework, we can reduce the fraction to its lowest term. Therefore,
18/30 = 2/5
2/5 is an equivalent fraction.
If the entries of both A and A^-1 are integers, is it possible that det A=3?
Hint: what is det(A)det(A^-1)?
Answers
it is not possible for det A to equal 3 if the entries of both A and A^-1 are integers.
The determinant of a matrix and its inverse are multiplicative inverses of each other, meaning that det(A)det(A^-1) = 1. If det A = 3, then det(A^-1) = 1/3. However, since the entries of both A and A^-1 are integers, this is a contradiction, as the determinant of a matrix with integer entries must also be an integer. Therefore, it is impossible for det A to equal 3 in this scenario.
it explains the reasoning behind the solution and provides a deeper understanding of the concept of determinants.
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Hi pls help me with this problem
Answers
Answer:
Why is base pairing essential to the process of transcription and translation
A park ranger counted the number of squirrels he saw while giving tours in three sections of a national park that have different areas.
Determine the unit rate in terms of the number of squirrels per square mile in the park, and complete the sentences below. Assume the relationship of squirrels to square miles shown in the table can be extended to the entire park.
Fill in the Blank.
The park ranger counted ___ squirrels for every mile in the park.
For every 128 square miles in the park, the park ranger would count ___ squirrels.
For every ___ square miles in the park, the park ranger would count 324 squirrels.
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Area is a measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters or square feet. The area of a shape is found by multiplying the length and width of the shape in most cases, although the formula for finding the area may vary depending on the shape.
In the given question,
To find the unit rate in terms of the number of squirrels per square mile, we need to divide the total number of squirrels by the total area of the park.
Total number of squirrels = 20 + 32 + 128 = 180
Total area of the park = 5 + 8 + 32 = 45
Unit rate of squirrels per square mile = 180/45 = 4 squirrels per square mileFor every 128 square miles in the park, the park ranger would count 512 squirrels. (4 squirrels per square mile x 128 square miles = 512 squirrels)For every 40 square miles in the park, the park ranger would count 324 squirrels. (4 squirrels per square mile x 40 square miles = 160 squirrels)Note: The last blank can be filled with 40, as shown above.
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Answer:
1. 4
2. 512
3. 81
Step-by-step explanation:
Please help me!!! I need this ASAP!!!
Answers
Answer:
number ten: x=5
number two: x=5³/5
Step-by-step explanation:
number ten:
4x + 3x - 9 = 26
4x + 3x = 26+9
7x = 35
x = 5
number two:
3x + 2x - 8 = 20
3x + 2x = 20+8
5x = 28
x = 5³/5
There are 2 blue marbles and 8 yellow marbles in John's pocket. He randomly takes out marbles one by one. What is the probability that there are no blue marbles within the first 4 trials? [2K) 2. What is the probability that there is exactly one blue marble within the first 4? (2K) 2. Given there are at least one blue marble within the first 3 trials, what is the probability the 2 marble is blue? [3] 4. How many trials should John expect to wait before getting a blue marble? (37) 5. Mary and Marylyn are good friends since elementary school. Now they both have two children. Mary has only one son, and Marylyn has at least one son. What are the probabilities of their second children being boys, respectively? [4T]
Answers
The probability of not drawing a blue marble in the first trial is given by the ratio of the number of yellow marbles to the total number of marbles: 8/10. After removing one yellow marble, the probability of not drawing a blue marble in the second trial becomes 7/9. Similarly, for the third trial, the probability is 6/8, and for the fourth trial, it is 5/7. To find the probability of not drawing a blue marble in all four trials, we multiply these individual probabilities together: (8/10) * (7/9) * (6/8) * (5/7) = 0.2.
To calculate the probability of not drawing a blue marble in the first four trials, we use the concept of conditional probability. We assume that each marble is drawn without replacement, meaning that once a marble is selected, it is not put back into the pocket. Since the marbles are drawn randomly, the probability of choosing a specific marble on any given trial depends on the composition of the remaining marbles. In this case, we multiply the probabilities of each trial together because we want to find the probability of multiple independent events occurring consecutively.
2. The probability of having exactly one blue marble within the first four trials can be calculated using a combination of probabilities. There are four possible positions for the blue marble within the four trials: first trial, second trial, third trial, or fourth trial. We can calculate the probability of having the blue marble in each of these positions and sum them up.
The probability of the blue marble being in the first trial is (2/10) * (8/9) * (7/8) * (6/7) = 0.1333.
The probability of the blue marble being in the second trial is (8/10) * (2/9) * (7/8) * (6/7) = 0.1333.
The probability of the blue marble being in the third trial is (8/10) * (7/9) * (2/8) * (6/7) = 0.1333.
The probability of the blue marble being in the fourth trial is (8/10) * (7/9) * (6/8) * (2/7) = 0.1333.
Adding these probabilities together gives a total probability of 0.1333 + 0.1333 + 0.1333 + 0.1333 = 0.5333.
We use the concept of conditional probability and calculate the individual probabilities for each position where the blue marble can be found. In each calculation, we multiply the probability of selecting a blue marble in the given position with the probabilities of selecting yellow marbles in the other positions. Then, we add up these individual probabilities to find the overall probability of having exactly one blue marble within the first four trials.
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Theorem 7.4. For any two n×n matrices, A and B,det(AB)=det(A)det(B). Proof Suppose one of A and B is not invertible. Without loss of generality, say A is not invertible. Then the columns of A are linearly dependent, and the columns of AB are also linearly dependent. So, by Theorem 7.3,det(A)=0 and det(AB)=0; so det(AB)=det(A)det(B) follows. Having taken care of that special case, assume A and B are both invertible. By Theorem 6.5,A is a product of elementary matrices. The proof then follows upon showing that, for an elementary matrix E,det(EB)=det(E)det(B). We leave this as an exercise. Exercise 47. Show that if E is an elementary matrix, then det(EB)=det(E)det(B).
Answers
The det(EB) = det(E) det(B).Therefore, the proof is complete, and we conclude that if E is an elementary matrix, then det(EB) = det(E) det(B).
Theorem 7.4 states that for any two n x n matrices A and B, det(AB) = det(A) det(B).
Proof: Suppose one of A and B is not invertible.
Without loss of generality, let A be non-invertible.
It implies that the columns of A are linearly dependent.
Because AB is a product of A and B, the columns of AB are also linearly dependent,
which follows from Theorem 7.3. Therefore, det(A) = 0 and det(AB) = 0.
Hence det(AB) = det(A) det(B) holds.
Having taken care of that special case, suppose A and B are invertible.
A is a product of elementary matrices according to Theorem 6.5. The proof is then completed if we can demonstrate that det(EB) = det(E) det(B) for an elementary matrix E.
It is left as an exercise for the reader.Exercise 47. If E is an elementary matrix, demonstrate that det(EB) = det(E) det(B).
Solution:An elementary matrix E has only one row that contains nonzero elements (because only one row operation is done), so we only need to consider the following two types of elementary matrices:
Type 1, in which one elementary row operation of type 1 is done. In this case, let E be obtained from I by adding a multiple of one row to another. We have:
E = I + cekj
for some scalar c, where k != j. If B is any matrix, then
det(EB) = det(I + cekj B)
= det(I) + c det(ekj B)
= det(I) + c 0
= det(I)
= 1,
where we have used the fact that adding a multiple of one row to another does not alter the determinant (Corollary 7.2) and that det(ekj B) = 0 because two of the rows of ekj B are equal (Theorem 7.3).
Therefore, det(EB) = det(E) det(B).
Type 3, in which one elementary row operation of type 3 is done.
In this case, let E be obtained from I by multiplying one row by a nonzero scalar c.
Let B be any matrix. If c = 0, then E = 0 and det(E) = 0, which implies that det(EB) = det(E) det(B) = 0.
If c != 0, then E and B have the same row swaps (as the matrix is invertible), so they have the same determinant (Corollary 7.2).
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3×2=6
4×2=8+6=14
5×2=10+14=24
6×2?
Answers
what is pleaseee help
2+-2 (4+)
Answers
2 + (-2)(+4)
2 + (-8)
-6
2+-8=
2-8=
-6
A team of researchers working on COVID-19 believes that, on average, an infected child in school infects more people than an infected working adult does. Assume it is known that an infected working adult, on average, infects 1.32 other people (sidenote: this is in the ballpark of current estimates for the highest state-level R, in the US). The researchers collect a sample of n=50 infected children, and find that the average number of people each child infected was 1.55. The sample standard deviation was 0.8. They want to test at significance level a = 0.05 Use the dropdowns to select the correct answers: The null hypothesis is: [Select] The alternative hypothesis is: [Select) The test statistic is: [Select) The critical value is: (Select) 1. the null hypothesis is: null is not equal to 1.32 null is less than 1.32 null is greater than 1.32 null is 1.32 2. the alternative hypothesis is: null is not equal to 1.32 null is less than 1.32 null is greater than 1.32 null is 1.32 3. the test statistic is: a. 4.065 b. (1.55-1.32) = 2.0329 c. 2.0125 d. (1.32-1.55) = 2.0329 4. the critical value is: a. qt(p=0.975, df=49) = 2.009 b. qt(p=0.975, df=50) = 1.6759 c. qt(p=0.05, df=49) = 1.67655 d. qt(p=0.95, df=49) = 1.67655
Answers
The null hypothesis is: null is 1.32
The alternative hypothesis is: null is greater than 1.32
The test statistic is: a. 4.065
The critical value is: a. qt(p=0.975, df=49) = 2.009
In this scenario, the null hypothesis (H0) is that the average number of people an infected child infects is equal to the average number of people an infected adult infects, which is 1.32. The alternative hypothesis (H1) is that an infected child infects more people than an infected adult, so the average is greater than 1.32.
To calculate the test statistic, we use the t-test formula: (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). In this case, it would be (1.55 - 1.32) / (0.8 / sqrt(50)), resulting in a test statistic of 4.065.
To find the critical value, we use the t-distribution table with a significance level of 0.05 and degrees of freedom equal to the sample size minus 1 (50 - 1 = 49). The critical value is found by looking up the value of qt(p=0.975, df=49), which is 2.009.
Since the test statistic (4.065) is greater than the critical value (2.009), we reject the null hypothesis in favor of the alternative hypothesis. This means that there is significant evidence to suggest that, on average, an infected child in school infects more people than an infected working adult does.
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Which expression is equivalent to (18x + 9k) + (2x + 6k)?
O 16x+3%
O 20x+ 15%
O 20X+ 16k
O 36x+54K
Answers
\((18x + 9k) + (2x + 6k)\)
\(18x + 2x = 20x\)
\(9k + 6k = 15k\)
\(20x + 15k\)
What is a discrete probability distribution? What are the two conditions that determine a probability distribution? What is a discrete probability distribution? Choose the correct answer below. A. A discrete probability distribution exclusively lists probabilities. B. A discrete probability distribution lists each possible value a random variable can assume, together with its probability. C. A discrete probability distribution lists each possible value a random variable can assume. D. None of the above
Answers
Answer:
The answers to the question above are given below:
Step-by-step explanation:
Question: What is a discrete probability distribution?
Answer
A discrete distribution is very important in data research as it shows in tabular form the probabilities that can be found in a list of distribution values and their individual probabilities in counted data. Usually, from the pool of distribution of numbers, the discrete distribution shows the probability of having countable numbers out of the pool.
Question: Choose the correct answer below. A. A discrete probability distribution exclusively lists probabilities. B. A discrete probability distribution lists each possible value a random variable can assume, together with its probability. C. A discrete probability distribution lists each possible value a random variable can assume. D. None of the above
The correct answer is: option B "discrete probability distribution lists each possible value a random variable can assume, together with its probability."
Question: What are the two conditions that determine a probability distribution?
The correct answer is:
1. Since each value may not be zero, each probability must include between 0 and 1.
2. When probabilities are totaled, it must give 1.
A planet has a circular orbit around a star it is distance of 67,000,000 km from the center of the star it orbits at an average speed of 35,000 km/h how many earth days does it take the planet to orbit the star give your answer to 2sf
Answers
The number of earth days that it will take the planet to orbit the star is 500 earth days.
Speed of an object.The rate of distance moved in a specific direction to the time taken can be referred to as the speed.
i.e speed = distance/ time taken
In the given question, the total distance covered is the length of the orbit.
So that,
length of the orbit = 2πR
where R is the radius i.e the distance of the star to the planet.
length of the orbit = 2 * 3.142 * 67000000
= 421028000 km
speed = distance/ time taken
⇒ time taken = distance/ speed
= 421028000 km/ 35,000 km/h
= 12029.37 h
But,
1 earth day = 24 hours
x = 12029.37 h
x = 12029.37 h * 1 earth day/ 24 h
= 501.2238 earth days
The number of earth days it will take the planet to orbit the star is 500 earth days.
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While solving an equation, if the variable term becomes zero, and the equation makes a true statement, then the solution is
Answers
The equation's remaining constant is the answer if the variable term eventually equals zero and the equation can be said to be true.
By isolating the variable on one side of the equation, we can arrive at a numerical value that satisfies the equation. However, in rare circumstances, the variable term may become zero while the equation is being simplified.
When a common factor is eliminated or an expression containing the variable is simplified, this can take place. The equation has a solution, and that solution is the constant value left over if, after removing the variable element, we arrive at a true assertion.
This is due to the equation's ability to be simplified to a declaration of equality between two constants if the variable term is zero. The constant value is the answer to the equation if the aforementioned assertion is accurate.
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Please help me this question
Answers
Answer:
∠ BNM = 150°
Step-by-step explanation:
Project MN to meet AB at point P, then
Δ ANP is a right triangle with sum of angles = 180°, thus
x = 180° - (90 + 30)° = 180° - 120° = 60°
∠ BNM = x + 90 = 60 + 90 = 150°
Using the segment addition postulate, which is true?
Answers
Answer:
I don't know your question sorry
Work out the value of 5 to the power of a if it equal 1/125
Answers
Answer:
a = -3
Step-by-step explanation:
Step 1: Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:
5^a = 1/125
Step 2: Take the log of both sides
log(5^a) = log(1/125)
Step 3: According to the power rule of logs, we can bring a down and multiply it by log(5):
a * log(5) = log (1/125)
Step 4: Divide both sides by log(5) to solve for a:
(a * log(5) = log(1/125)) / log(5)
a = -3
Optional 5: We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:
5^-3 = 1/125
1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator
1/125 = 1/125
Convert to radian measure: 240°
Answers
The radian measure of 240 degrees is 4π/3.
To convert an angle from degrees to radians, we can use the fact that π radians is equivalent to 180 degrees. We can set up a proportion to find the radian measure.
We know that 180 degrees is equal to π radians. Therefore, we can set up the following proportion:
180 degrees / π radians = 240 degrees / x radians
To solve for x, we can cross-multiply and divide:
180x = 240π
x = (240π) / 180
x = 4π/3
In terms of explanation, when converting from degrees to radians, we use the fact that one complete revolution around a circle is equal to 2π radians or 360 degrees. Therefore, to convert a given angle from degrees to radians, we divide the angle by 360 and multiply by 2π. In this case, since 240 degrees is two-thirds of a full revolution, it corresponds to 4/3 times the value of π, which gives us 4π/3 as the radian measure.
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Plz help!!! I’ll give 10 points to the first person to give me a correct answer...I need to get my grade up before the end of the semester
Answers
Answer:
A= 30
B= 60
C= 90
Step-by-step explanation:
A is already shown.
B has a right angle making it 90 degrees.
A triangle is 180 degrees 30+90= 120
180-120=60
Is 25 a prime number?
Answers
No, 25 is not a prime number. It can be divided by 5 without a remainder, so it has factors other than 1 and itself.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and by itself. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.
The factors of 25 are 1, 5 and 25. Prime numbers are numbers that are divisible by only 1 and themselves. So 25 is not a prime number.
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