Which is the correct form of the partial fraction decomposition for the expression StartFraction 4 x cubed + 3 x squared Over (x + 1) squared (x squared + 7) squared EndFraction?
StartFraction A Over x + 1 EndFraction + StartFraction B Over (x + 1) squared EndFraction + StartFraction C x + D Over x squared + 7 EndFraction + StartFraction E x + F Over (x squared + 7) squared EndFraction
StartFraction A x + b Over x + 1 EndFraction + StartFraction C x + D Over (x + 1) squared EndFraction + StartFraction E x + F Over x squared + 7 EndFraction + StartFraction G x + H Over (x squared + 7) squared EndFraction
StartFraction A squared Over x + 1 EndFraction + StartFraction B squared Over (x + 1) squared EndFraction + StartFraction C x + D Over x squared + 7 EndFraction + StartFraction (E x + F) squared Over (x squared + 7) squared EndFraction
StartFraction A x + b Over x + 1 EndFraction + StartFraction (C x + D) squared Over (x + 1) squared EndFraction + StartFraction E x + F Over x squared + 7 EndFraction + StartFraction (G x + H) squared Over (x squared + 7) squared EndFraction
Answers
The correct form of the partial fraction decomposition for the expression \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\) is:
\(\frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{Cx+D}{x^2+7} + \frac{Ex+F}{(x^2+7)^2}\) (Option 1).
The given expression can be written in the form \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\). To decompose this into partial fractions, we need to find the values of constants A, B, C, D, E, and F such that the expression can be written in the form of the options given.
Using partial fraction decomposition method, we can write the expression as:
\($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2} = \frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{Cx+D}{x^2+7} + \frac{Ex+F}{(x^2+7)^2}$\)
Then we multiply both sides by the denominator of the expression on the left and simplify to get:
\($4x^3+3x^2 = A(x+1)(x^2+7)^2 + B(x^2+7)^2 + (Cx+D)(x+1)^2(x^2+7) + (Ex+F)(x+1)^2$\)
Next, we can solve for the unknown constants by equating the coefficients of the same powers of x on both sides of the equation. We will end up with a system of linear equations, which can be solved using various methods.
After solving, we get the coefficients as:
\(A = -\frac{1}{2}$, $B = \frac{5}{4}$, $C = 0$, $D = -\frac{1}{4}$, $E = 0$, and $F = \frac{3}{28}$.\)
Therefore, the correct form of the partial fraction decomposition for the given expression is:
\($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2} = -\frac{1}{2(x+1)} + \frac{5}{4(x+1)^2} - \frac{1}{4(x^2+7)} + \frac{3}{28(x^2+7)^2}$\)
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Complete Question:
Which is the correct form of the partial fraction decomposition for the expression \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\)?
\($\frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{Cx+D}{x^2+7} + \frac{Ex+F}{(x^2+7)^2}$\)\($\frac{Ax+b}{x+1} + \frac{Cx+D}{(x+1)^2} + \frac{Ex+F}{x^2+7} + \frac{Gx+H}{(x^2+7)^2}$\)\($\frac{A^2}{x+1} + \frac{B^2}{(x+1)^2} + \frac{Cx+D}{x^2+7} + \frac{(Ex+F)^2}{(x^2+7)^2}$\)\($\frac{Ax+b}{x+1} + \frac{(Cx+D)^2}{(x+1)^2} + \frac{Ex+F}{x^2+7} + \frac{(Gx+H)^2}{(x^2+7)^2}$\)Related Questions
What is the most common error when entering a formula is to reference the wrong cell in the formula?
Answers
The most common error when entering a formula is to reference the wrong cell in the formula.
This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.
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Alicia estimates that the surface area of a rectangular prism with a length of 11 meters,a width of 5. 6 meters,and a height of 7. 2 meters is about 334 cubic meters. Is her estimate reasonable?Explain your reasoning
Answers
Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.
To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.
The formula for calculating the volume of a rectangular prism is:
Volume = length x width x height
Substituting the given values in the formula, we get:
Volume = 11 meters x 5.6 meters x 7.2 meters
Volume = 449.28 cubic meters
As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.
It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.
In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.
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Please help asap:) thanks in advance !
Answers
Answer:
The photo is not showing up
due last weeeekk help!!!!
Answers
A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:
Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).
In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;
(x, y) → (y, -x)
Ordered pair B' (-2, 1) → E (1, 2)
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show that there are infinitely many primes of the form 4k 3, where k is a nonnegative integer
Answers
According to the question we have our assumption must be false and there are indeed infinitely many primes of the form 4k+3.
To prove that there are infinitely many primes of the form 4k+3, where k is a nonnegative integer, we can use a proof by contradiction. Assume that there are only finitely many primes of this form, say p1, p2, p3, ..., pn.
Consider the number N = 4(p1p2p3...pn) - 1. This number is of the form 4k+3, since the product of primes is also of this form.
Now, any prime factor of N must also be of the form 4k+3, since any prime factor of N cannot be 2 (since N is odd) and it cannot be of the form 4k+1 (since N leaves a remainder of 3 when divided by 4).
However, this contradicts our assumption that p1, p2, p3, ..., pn are the only primes of the form 4k+3, since N is a prime greater than pn and is also of this form.
Therefore, our assumption must be false and there are indeed infinitely many primes of the form 4k+3.
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Find the area of the circle. Round to the nearest tenth. Use 3.14 or 22/7 for π.
Answers
The area of a circle is 158.3 sq. m.
Consider we need to find the area of the given circle.
The radius of a circle is 7.1 m.
The area of a circle is the place occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the circumference of a circle is called the area of the circle.
The area of the circle is:
\(A = \pi r^{2}\) , where r is the circle's radius.
Putting r = 7.1 , π = 3.14, we get
\(A = 3.14 *(7.1)^{2}\)
A = 158.2874
A ≈ 158.3
So, the area of a circle is 158.3 sq. m.
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A study on students drinking habits wants to determine the true average number of alcoholic drinks all UF "greek" students have in a one week! period. We know from preliminary studies that the standard deviation is around 6.3. How many students should be sampled to be within 0.5 drink! of population mean with 95% probability? 609 *305 304 610
Answers
Number of students should be sampled to be within 0.5 drink of population mean with 95% probability is 617 students.
To determine the sample size required to estimate the population mean with a given level of precision, we can use the formula for the margin of error
Margin of error = Z × (standard deviation / sqrt(sample size))
where Z is the critical value of the standard normal distribution corresponding to the desired level of confidence. For a 95% confidence level, Z is 1.96.
We want the margin of error to be no more than 0.5 drinks, so we can set up the equation
0.5 = 1.96 × (6.3 / sqrt(sample size))
Solving for the sample size, we get
sqrt(sample size) = 1.96 × 6.3 / 0.5
sqrt(sample size) = 24.82
sample size = (24.82)^2
sample size = 617
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PLS HELP OF AREA ON TRIANGLE!!!
Answers
Answer:
Area for Triangle is: 1/2bh or bh/2
Area for Trapezoid (As shown in picture):
1/2h(b1+b2)
You’d have to do 1/2 x 18(15+37) for the quesyion in the picture
Hope this helped!
Answer:
\( area = (\frac{1}{2} (a + b) \times h) \\ \frac{1}{2} \times (15 + 37) \times 18ft \\ \frac{1}{2} \times 52ft \times 18ft \\ divide \: 52 \: by \: 2 \\ 26ft \times 18ft = 468 {ft}^{2} \\ answer = 468 {ft}^{2}\)
help please fast i beg
Answers
Answer:
2,3
Step-by-step explanation:
X=2
Y=3
Which of the equations below represents the second step of the solution process?
Step 1: 15x + 21 = 39 -15x
Step 2:
Step 3: 30x = 18
Step 4: x=1.6
A 5(6x + 1) + 4 = 39 C 30x + 4 + 1 = 39
B 5(6x + 5) = 39 D 30x + 21 = 39
Answers
if there are 20 apples and 40 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made.
Answers
Answer:
Step-by-step explanation:
If $120.00 is borrowed for 3 years at 5% how much interest will be generated by the end of the loan? please answer will mark brainelist
Answers
Answer:
I = prt / 100
120x3x5 / 100
= 18
Sketch the graph of a function that satisfies all of the given conditions. f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if x <0 or 2 < x < 4, f'(x) < 0 if 0 < x < 2 or x > 4, f"(x) > 0 if 1 < x < 3, f"(x) < 0 if x < 1 or x > 3 y y 2 6 6 6 X 2 4 6 M N MW -2 2 2 2 X X 6 -2 2 4 2 2 4 6 2 2 4 6 -6 -2F -2F -21 O
Answers
The correct option is `(B)` for the graph based on the given function.
We have been given several conditions for the function `f(x)` that we need to sketch.
We know that `f'(0) = f'(2) = f'(4) = 0` which indicates that `f(x)` has critical points at `x = 0, 2, 4`. Moreover, we have been given that `f'(x) > 0` if `x < 0` or `2 < x < 4`, and `f'(x) < 0` if `0 < x < 2` or `x > 4`. Thus, `f(x)` is increasing on `(-∞, 0)`, `(2, 4)`, and decreasing on `(0, 2)`, `(4, ∞)`. We also know that `f"(x) > 0` if `1 < x < 3` and `f"(x) < 0` if `x < 1` or `x > 3`.Let's first draw the critical points of `f(x)` at `x = 0, 2, 4`.
Let's also draw the horizontal line `y = 6`.
From the given conditions, we see that `f'(x) > 0` on `(-∞, 0)`, `(2, 4)` and `f'(x) < 0` on `(0, 2)`, `(4, ∞)`. This indicates that `f(x)` is increasing on `(-∞, 0)`, `(2, 4)` and decreasing on `(0, 2)`, `(4, ∞)`.
Let's sketch a rough graph of `f(x)` that satisfies these conditions.
Now, let's focus on the part of the graph of `f(x)` that has `f"(x) > 0` if `1 < x < 3` and `f"(x) < 0` if `x < 1` or `x > 3`. Since `f"(x) > 0` on `(1, 3)`, this indicates that `f(x)` is concave up on this interval.
Let's draw a rough graph of `f(x)` that satisfies this condition:
Thus, the graph of a function that satisfies all of the given conditions is shown in the attached figure. The function has critical points at `x = 0, 2, 4` and `f'(x) > 0` on `(-∞, 0)`, `(2, 4)` and `f'(x) < 0` on `(0, 2)`, `(4, ∞)`.
Furthermore, `f"(x) > 0` if `1 < x < 3` and `f"(x) < 0` if `x < 1` or `x > 3`.
The graph of the function is shown below:
Therefore, the correct option is `(B)`.
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Given n(a) = 61, n(b) = 47 and n(a u b) = 82, use the union rule for sets to find n(aub
Answers
The union rule for sets to find n(aub), which was found to be n(a U b) = n(a) + n(b) - n(a ∩ b) = 61 + 47 - 26 = 82.
To find n(a U b), which represents the number of elements in the union of sets a and b, you can use the union rule for sets.
The union rule states that
n(a U b) = n(a) + n(b) - n(a ∩ b),
where n(a) represents the number of elements in set a, n(b) represents the number of elements in set b, and n(a ∩ b) represents the number of elements common to both sets a and b.
In this case, you have been given n(a) = 61, n(b) = 47, and n(a U b) = 82.
Using the union rule, we can rearrange the equation to solve for n(a U b):
n(a U b) = n(a) + n(b) - n(a ∩ b)
Substituting the given values:
82 = 61 + 47 - n(a ∩ b)
Now, rearranging the equation to solve for n(a ∩ b):
n(a ∩ b) = 61 + 47 - 82
Simplifying the equation:
n(a ∩ b) = 108 - 82
n(a ∩ b) = 26
Therefore, n(a U b) = n(a) + n(b) - n(a ∩ b) = 61 + 47 - 26 = 82.
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Find the area of a circle with a radius of 5 feet. Please help
Answers
Answer:
see below
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi (5)^2
A = 25 pi
Using 3.14 for pi
A = 78.5 ft^2
Using the pi button
A =78.53981634 ft^2
write the exponential equation that passes through the points (-2,1) and (2,16)
Answers
The equation that represents the exponential function passing through the points (-2, 1) and (2, 16) is: y = 4(2)^x
To write the exponential equation that passes through the points (-2, 1) and (2, 16), we can use the general form of an exponential function:
y = ab^x
Where y is the dependent variable, x is the independent variable, a is the initial value or y-intercept, and b is the base of the exponential function.
Step 1: Determine the value of a.
To find the value of a, substitute the coordinates of one of the given points into the equation. Let's use (-2, 1):
1 = ab^(-2)
Step 2: Determine the value of b.
To find the value of b, substitute the coordinates of the other given point into the equation. Let's use (2, 16):
16 = ab^2
Step 3: Solve the system of equations.
We now have a system of two equations with two unknowns (a and b):
1 = ab^(-2)
16 = ab^2
We can solve this system of equations to find the values of a and b. To do this, divide the second equation by the first equation:
16 / 1 = (ab^2) / (ab^(-2))
16 = b^4
Taking the fourth root of both sides, we get:
b = ±2
Step 4: Substitute the value of b back into one of the original equations to solve for a.
Let's substitute b = 2 into the first equation:
1 = a(2)^(-2)
1 = a / 4
a = 4
Alternatively, if we had chosen b = -2, we would have obtained a = -4, and the equation would be:
y = -4(-2)^x
Both equations represent exponential functions that pass through the given points.
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allowing 16% discount on the MP of a television and leying 13% Vat buyer has pay RS 18984 to buy it . Find MP of that television
Answers
The marked price of the television is Rs. 20,000.
What is Marked Price?The market price is the current price at which a good or service can be purchased or sold.
Here, let the marked price of the television be Rs. x
Discount = 16% on MP
VAT = 13% additional on MP
Total paid amount = Rs. 18984
Now, according to question;
MP X (1 - Discount) X (1 + VAT) = 18984
x (1 - 0.16)(1+0.13) = 18984
x = 18984/(0.84 X 1.13)
x = 18984 / 0.9492
x = 20,000
Thus, the marked price of the television is Rs. 20,000.
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If it took 0.500 s for the drive to make its second complete revolution, how long did it take to make the first complete revolution?
Answers
We know that it took 0.500 s divided by 2, or 0.250 s, to make the first complete revolution.
If it took 0.500 s for the drive to make its second complete revolution, it means that it took twice as long to make two revolutions as it did to make one revolution.
Therefore, it took 0.500 s divided by 2, or 0.250 s, to make the first complete revolution.
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Saw a board 8 ft 4 in. long into nine equal pieces. If the loss per cut is in., how long will each piece be?
Answers
When the board is cut into 9 pieces, each piece will be 100 inches / 9 pieces = 11 1/4 inches long.
So, first we need to convert the length of the board into inches, which is 8 feet x 12 inches/foot + 4 inches = 100 inches.
Next, we divide the length of the board by 9 pieces, which is 100 inches / 9 pieces = 11.1111... inches/piece.
Finally, we subtract the loss per cut (1 inch) from each piece, which means each piece will be 11.1111... inches - 1 inch = 10.1111... inches.
So, each piece will be 10 inches and a fraction of an inch long.
HELP!!!! GEOMETRY PLS HELP
Answers
Answer:
180 is whole mark me as brainliest
Step-by-step explanation:
Another one y'all ready know it's algebra!
Answers
Answer:
-3x²-12x is your answer
Answer:
Step-by-step explanation:
How do I solve this?
Answers
Answer:
using SOHCAHTOA
USE SOH
sin45= x/9
cross multiply ❌ and the find sin45 using ur calculator and multiply by 9 and then your x will be found
A turtle dives towards deeper water at a rate of 8 inches per second. It continues for a total of 16 seconds. Which expression represents this situation?
Answers
Could someone help me please
Answers
Answer:
Cannot
Can
Cannot
Cannot
Step-by-step explanation:
10+3 < 18
16+8>23
6.5+3.4 < 10.8
7+7< 23
Answer:
what's the question men let me no
please help with full explanation!! thank you!! :))
Answers
The value of angle x is 70⁰.
What is the value of angle x?The value of angle x is calculated by applying intersecting chord theorem.
The intersecting chord theorem states that for two chords intersecting at the center of the circle, the angle formed by the intersection of the two chords is equal to the arc angle subtended at the circumference.
The value of the angle adjacent to angle x is calculated as follows;
∠QON = arc angle QN
∠QON = 110⁰
The value of angle x is calculated as;
x + ∠QON = 180
x = 180 - ∠QON
x = 180 - 110⁰
x = 70⁰
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What is the value of the expression All of 2.6 multiplied by 10 to the power 9 over all of 1.3 multiplied by 10 to the power 2?
1.3 × 107
2.0 × 107
1.3 × 1011
2.0 × 1011
Answers
Answer:
I think the answer is D
Step-by-step explanation:
Answer:
The answer is A
I think
Step-by-step explanation:
total-revenue function r(x)=900 and a total-cost function c(x)=1400, both in thousands of dollars, find the rate at which total profit is changing when x items have been produced and sold.
Answers
The rate at which profit change when x items produced and sold for the given revenue function and cost function is equal to P'(x) = 450(2x - 0.1 )/ √(x² - 0.1x) - 2800/3 (x) / ( x² + 2)2/3 and for x = 0 P'(x) is undefined.
Total revenue function r(x) = 900√x² - 0.1x
Total cost function c(x) = 1400( x² + 2)1/3 + 800
Profit of the function = Revenue function - Cost function
⇒ P(x) = r(x) - c(x)
Rate at which profit is changing for 'x' items produced and sold
⇒P'(x) = r'(x) - c'(x)
Differentiate r(x) and c(x) we get,
r(x) = 900√x² - 0.1x
⇒ r'(x) = 900 ( (1/2)(2x - 0.1 )/ √(x² - 0.1x)
⇒ r'(x) = 450(2x - 0.1 )/ √(x² - 0.1x)
c'(x) = 1400/3 (2x) / ( x² + 2)2/3
Substitute the value we get,
P'(x) = 450(2x - 0.1 )/ √(x² - 0.1x) - 2800/3 (x) / ( x² + 2)2/3
For x = 0
P'(x) is undefined.
Therefore, rate at which total profit is changing for the given revenue function and cost function is equal to P'(x) = 450(2x - 0.1 )/ √(x² - 0.1x) - 2800/3 (x) / ( x² + 2)2/3 and for x = 0 P'(x) is undefined.
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The above question is incomplete , the complete question is :
total-revenue function r(x)=900√x² - 0.1x and a total-cost function c(x)=1400( x² + 2)1/3 + 800 , both in thousands of dollars, find the rate at which total profit is changing when x items have been produced and sold.
use the venn diagram to compare and contrast the definitions of the linnaean class answers
Answers
The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.
By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.
The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.
First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.
Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.
Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.
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try
(x
-2y = 16)
(- 6x +5y =-26)
x
-2y = 16
-6x +5y = -26
=
0 |xo|y=
Answers
Answer: I belive the answer is 0lxoly+39.56
Step-by-step explanation:
SIKE
A wheelchair access ramp has an angle of elevation of 23 degrees. If the ramp reaches the top of a 23 inch high porch, how long is the ramp?
Answers
Answer:
5 ft(60 in) long
Answer:
The ramp is 54.18 inches long.
Step-by-step explanation: