Assume the collisional diameter d of ozone (0) to be 4x10 cm Calculate:
The average root mean square velocity of the gas molecules at 100K and 3000K
Answers
The average root mean square velocity of the gas molecules of ozone (O3) at 100K is approximately 341 m/s, and at 3000K it is approximately 1925 m/s.
The root means square velocity (v rms) of a gas molecule is given by the formula:
v rms = √(3kT/m)
where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of a single molecule. The mass of a single ozone molecule (O3) is approximately 48 g/mol or 4.8x10^-26 kg.
At 100K, the root mean square velocity is calculated as:
v rms = √(3kT/m) = √(3 x 1.38x10^-23 J/K x 100K / 4.8x10^-26 kg) = 341 m/s
At 3000K, the root mean square velocity is calculated as:
v rms = √(3kT/m) = √(3 x 1.38x10^-23 J/K x 3000K / 4.8x10^-26 kg) = 1925 m/s
Therefore, the average root mean square velocity of the gas molecules of ozone (O3) at 100K is approximately 341 m/s, and at 3000K it is approximately 1925 m/s.
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Related Questions
Mark created a flower bed that is semicircular in shape, as shown in the image. The diameter of the flower bed is 5m. What is the perimeter of the flower bed? (Approximate to be 3.14.) Round your answer to two decimal places.
Answers
Answer:
12.85
Step-by-step explanation:
P=1/2(3.14xd)+d
P=1/2x15.7+5
P=12.85
2. If AABC is mapped onto AJED after a translation and AJED is mapped onto ARST after a line reflection, the relationship between AABC and ARST is that they are always
1) congruent and similar
2) congruent but not similar
3) similar but not congruent
4) neither congruent nor similar
Answers
The relationship between AABC and ARST is that they are always is neither congruent nor similar. 4.
The relationship between AABC and ARST, after the described transformations (translation and line reflection), can be determined based on the properties of the transformations.
Congruent and Similar:
Congruent figures have the same shape and size, while similar figures have the same shape but different sizes.
Since the question mentions a translation and a line reflection, these transformations preserve both shape and size.
If AABC and AJED are congruent due to the translation and AJED and ARST are also congruent due to the line reflection, then AABC and ARST would be congruent as well.
However, the question does not specify whether the figures are similar or not, so we cannot conclude that they are similar.
Congruent but Not Similar:
As mentioned earlier, congruent figures have the same shape and size.
If AABC and AJED are congruent due to the translation and AJED and ARST are congruent due to the line reflection, it follows that AABC and ARST would also be congruent.
We cannot determine whether they are similar or not.
Similar but Not Congruent:
Similar figures have the same shape but different sizes.
Since the question does not provide any information about the angles or side ratios of the figures, we cannot conclude that AABC and ARST are similar.
Neither Congruent nor Similar:
Based on the information given, this is the most accurate choice.
Without additional information about the angles or side ratios, we cannot determine whether AABC and ARST are congruent or similar.
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HELP HELP HELP HELP HELP HELP
Answers
Step-by-step explanation:
You can take the numerator as one factor and 1/denominator as another.
Just an example:
a(x + 2) and 1/(a(x - 1)), with a rational value of a ≠ 0.Let a = 1, then the following product will give what we have
(x + 2) × 1/(x - 1) = (x + 2)/(x - 1)the expected value is equal in mathematical computation to the ____________
Answers
The expected value is the long-term average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and summing them up. In simpler terms, it represents the average value we expect to get over many trials.
The expected value is a concept in probability and statistics that represents the long-term average outcome of a random variable. It is also known as the mean or average. To calculate the expected value, we multiply each possible outcome by its probability and sum them up.
For example, let's say we have a fair six-sided die. The possible outcomes are numbers 1 to 6, each with a probability of 1/6. To find the expected value, we multiply each outcome by its probability:
1 * 1/6 = 1/62 * 1/6 = 2/63 * 1/6 = 3/64 * 1/6 = 4/65 * 1/6 = 5/66 * 1/6 = 6/6Summing up these values gives us:
1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 21/6 = 3.5
Therefore, the expected value of rolling a fair six-sided die is 3.5. This means that if we roll the die many times, the average outcome will be close to 3.5.
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Find the mean, median, interquartile range and mean absolute deviation of the set of numbers. Round to the nearest tenth, if necessary. 1, 1, 4, 8, 9, 3, 8 please help
Answers
Answer:
mean- 4.9
median- 4
interquartile range- 7
Step-by-step explanation:
Hope this helps! :)
Sixteen increased by twice a number is 20
Answers
Answer:
n = 2
Step-by-step explanation:
16 + 2n = 20
2n = 4
n = 2
The number of cups of strawberries in a shortcake recipe is proportional to the number of cups of sugar in the recipe. The recipe uses 5 cups of strawberries per 1/4 cup of sugar.
PART A - What is the constant of proportionality for the relationship between cups of strawberries and cups of sugar
Answers
The constant of proportionality is 20.
What is constant of proportionality?
The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.
Given,
the recipe uses 5 cups of strawberries per 1/4 cup of sugar.
And let constant of proportionality is k.
that is
5 α 1/4
5 = k1/4
k = 5(4)
k = 20
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assume that a fair die is rolled. the sample space is (1,2,3,4,5,6) and all of the outcomes is equally likely. find p(greater than 0)
Answers
The probability of rolling a number that is greater than 0 when rolling a fair die is 1, or 100%.
The probability of an event is a measure of the likelihood that the event will occur. In this case, we are interested in finding the probability of rolling a number that is greater than 0 when rolling a fair die with the sample space of (1, 2, 3, 4, 5, 6) and all the outcomes equally likely.
Since the die is fair, each number in the sample space has an equal chance of being rolled. Therefore, the probability of rolling any one of the six numbers is 1/6.
Since all of the numbers in the sample space are greater than 0, we can find the probability of rolling a number that is greater than 0 by adding up the probabilities of all the outcomes. This gives:
P(greater than 0) = P(1) + P(2) + P(3) + P(4) + P(5) + P(6)
= 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6
= 6/6
= 1
Therefore, the probability of rolling a number that is greater than 0 when rolling a fair die is 1, or 100%.
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a. What is the nth fraction in the following sequence? 2
1
, 4
1
, 8
1
, 16
1
, 32
1
,… b. What is the sum of the first n of those fractions? To what number is the sum getting closer and closer? Two forces, A=80 N and B=44 N, act in opposite directions on a box, as shown in the diagram. What is the mass of the box (in kg ) if its acceleration is 4 m/s 2
?
Answers
A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.
a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`
Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`
b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)
`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)
`Simplifying:`S_n = 2*(2^n - 1)
`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.
Thus, the sum is getting closer and closer to infinity.
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What is the unknown number that makes the equation true?
44 x 32 =
+ 120 + 80 + 8 (3 points)
1,200
1.100
800
700
Marked !
Answers
Explanation: 44 x 32= 1,408
120+80+8=208
1,408-208=1,200.
Data was collected from 32 random students on the number of hours spent studying for the final and their corresponding exam score in a statistics class. If a 99% confidence interval for resulted in (3.59, 6.96), what is the most you would expect the exam score to increase by if the student studied an extra 3 hours
Answers
The maximum expected increase in exam score if a student studies an extra 3 hours is 4.11 points.
Since we have a 99% confidence interval, we can assume a t-distribution with 31 degrees of freedom (n-1). Using this distribution, we can find the margin of error (E) for the mean difference in exam score (µD) between students who study for an extra 3 hours and those who do not.
E = t* (s/√n), where s is the sample standard deviation and n is the sample size.
We don't have the standard deviation, but we can estimate it using the range rule of thumb, which states that the standard deviation is approximately equal to the range of the data divided by 4.
s ≈ (6.96 - 3.59) / 4 = 0.8425
Using a t-value for a 99% confidence interval and 31 degrees of freedom, we have:
t = 2.750
E = 2.750 * (0.8425/√32) ≈ 0.929
So the 99% confidence interval for the true mean difference in exam score is (3.59 - 0.929, 6.96 + 0.929) = (2.66, 7.89).
To find the maximum expected increase in exam score if a student studies an extra 3 hours, we can subtract the mean difference in exam score from the previous 32 students from the mean difference in exam score between students who study for an extra 3 hours and those who do not.
Mean difference in exam score = (6.96 - 3.59) / 32 = 0.104
Max expected increase in exam score = 0.104 + 3 = 4.11
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A flagpole casts a 20-foot shadow at the same time Lexi casts a 5-foot shadow. If Lexi is 5'9", find the height of the flagpole.
Answers
The height of the flagpole is 20.3 feet.
How to find the height of the flagpole?A flagpole casts a 20-foot shadow at the same time Lexi casts a 5-foot shadow. If Lexi is 5'9", the height of the flagpole can be calculated as follows:
5 ft 9 inches = 5.075 feet's
Using proportion let's find the height of the flag,
let
height of flag = x
Therefore,
x / 20 = 5.075 / 5
cross multiply
5x = 20(5.075)
5x = 101.5
divide both sides by 5
x = 101.5 / 5
x = 20.3 feet
Hence,
height of the flagpole = 20.3 feet
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exterior angle theorem
Answers
\(m1 = 79 + 58\)
\(m1 = 137\)
Find the total surface area of this triangular prism.
10cm
6 cm
4cm
8 cm
Answers
Method:
Front: 6x8 = 48/2 = 24
Back: Also 24
Base: 8x4 = 32
Left: 6x4=24
Add your answers:
24 + 24 + 24 + 32 + 40
Answer:
TSA is 144 cm²
Brett spent $25 for a tennis racket and pays $5 each time she plays a game. What is the initial value and the slope?
Answers
In the given scenario, Brett spent $25 for a tennis racket, which can be considered as the initial value or the y-intercept. The slope represents the rate of change, which in this case is the cost per game. Since Brett pays $5 each time she plays a game, the slope is $5.
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HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr2,
Answers
Answer:
r = √(A/π)
Step-by-step explanation:
HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr²,
inverse formula
r = √(A/π)
a teacher wants to see if a new unit on factoring is helping students learn. she has five randomly selected students take a pre-test and a post test on the material. the scores are out of 20. has there been improvement? (pre-post) what value of t would you use for the 90% confidence interval? student 1 2 3 4 5 pre-test 12 14 11 12 13 post- test 15 17 15 20 13 group of answer choices 2.776 2.132 4.604 3.747 1.645
Answers
The paired t-test results suggest that there is no significant improvement in students' learning after the new unit on factoring, based on a 90% confidence level.
How to find the value of t?To determine if there has been an improvement in students' learning after a new unit on factoring, we can perform a paired t-test on the pre-test and post-test scores of the five randomly selected students.
The differences between the pre-test and post-test scores for each student are: 3, 3, 4, 8, 0.
The mean of the differences is 3.6, and the sample standard deviation is 2.39.
The t-value for a 90% confidence interval with 4 degrees of freedom is 2.776. Since the calculated t-value of 2.68 (calculated as the mean of the differences divided by the standard error of the mean of the differences) is less than the critical t-value of 2.776, we fail to reject the null hypothesis that there is no improvement in students' learning.
Therefore, there is not enough evidence to conclude that the new unit on factoring has helped students learn based on the sample data.
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pleasee help me fast
Answers
hope it will helpful to you please reply me it is correct or not
solve for x Express your answer as an integers or in simplest radical form 1-x^3=9
Answers
Answer:
\(\large\boxed{\tt x = 2}\)
Step-by-step explanation:
\(\textsf{We are asked to solve for x in the given equation.}\)
\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)
\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)
\(\textsf{both sides of the equation.}\)
\(\large\underline{\textsf{How is this possible?}}\)
\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)
\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)
\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)
\(\textsf{of once.}\)
\(\large\underline{\textsf{For our problem;}}\)
\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)
\(\textsf{both sides of the equation.}\)
\(\large\underline{\textsf{Solving;}}\)
\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)
\(\textsf{Property of Equality;}/tex]
\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)
\(\tt - x^{3} = 8\)
\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)
\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)
\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)
\(\underline{\textsf{Evaluate;}}\)
\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)
\(\textsf{*Note;}\)
\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)
\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)
\(\underline{\textsf{We should have;}}\)
\(\tt -x=2\)
\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)
\(\large\boxed{\tt x = 2}\)
The pressure in a car tire is given by p(x) = 31 - X where p is pressure in psi and x is the number of months
since the tire was filled. Describe what this function represents.
Answers
Answer:
Step-by-step explanation:
Which value of x satisfies the equation
5/6 (3/8 - x)
= 16
Answers
Answer:
\(x = - 18.825\)
Step-by-step explanation:
\( \frac{5}{6}( \frac{3}{8} - x)
= 16 \\ \frac{(5)(3)}{(6)(8)} - \frac{5x}{6} = 16 \\ 15 - 40x = 768\\ 40x = 15 - 768\\ x = - 18.825\)
The value of x for the equation to be equal is- 40/753
Solution to linear equationGiven the linear equation expressed as:
5/6 (3/8 - x) = 16
Open the parenthesis
5/16 - 5/6x = 16
Collect the like terms
-5/6x = 16 - 5/16
-5/6x = 251/16
Cross multiply
1506x = -80
x = -80/1506
x = -40/753
Hence the value of x for the equation to be equal is- 40/753
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write an expression for the apparent nth term (an) of the sequence. (assume that n begins with 1.) 2, 9, 28, 65, 126,
Answers
Therefore, the apparent nth term of the expression is: aⁿ = 5n² - 3n - 2.
The given sequence is not an arithmetic or geometric sequence. However, we can notice that the sequence of differences between consecutive terms is an arithmetic sequence.
The sequence of differences is: 7, 19, 37, 61,...
To find the nth term of this sequence, we can use the formula for the nth term of an arithmetic sequence:
dn = a1 + (n-1) * d
where dn is the nth term of the sequence of differences, a1 is the first term of the sequence of differences, d is the common difference of the sequence of differences, and n is the index of the term we want to find.
So, we have:
dn = 7 + (n-1) * 12
Simplifying this expression, we get:
dn = 5n - 3
Now, we can use this formula to find the nth term of the original sequence. Let's call the nth term an:
an = an-1 + dn-1
where an-1 is the (n-1)th term of the original sequence and dn-1 is the (n-1)th term of the sequence of differences.
We know that a1 = 2 and d1 = 7, so we can use the above formula to find the next terms:
a2 = a1 + d1 = 2 + 7 = 9
a3 = a2 + d2 = 9 + 19 = 28
a4 = a3 + d3 = 28 + 37 = 65
a5 = a4 + d4 = 65 + 61 = 126
Therefore, the apparent nth term of the sequence is: aⁿ = 5n² - 3n - 2.
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What is x ?? - 2/5x- 4 = 4
Answers
Answer:
-0.05 (-1/20)
Step-by-step explanation:
Answer:
x= -20
Step-by-step explanation:
+4 on both sides
-2/5x=8
(5) on both sides
-2x= 40
/-2 on both sides
x= -20
Who can't wait for Cyberpunk to come out
Answers
Answer:
i got it, hella good game but reallllyyy buggy
Step-by-step explanation:
feel free to ask questions abt it, I know, lore, controls, gameplay, etc.
The mapping diagram shows a functional relationship. A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (8, 4), (negative two-thirds, 3), (11, negative 1), (4, one-half). Complete the statements. f(4) is . f(x) = 4 when x is?
Answers
Answer:
f(4) is 1/2 the second is 8
Step-by-step explanation:
Answer:
1: 1/2
2: 8
Step-by-step explanation:
I did the assignment
2/3 3/3 300 1,300/10 COS 20 [Got it, thanks!] 300 1 t 60 + 2 dt = 3 sin (7) - 3 sin(6) t COS 20 60 t - [2 in (+2) = 3 60 = 3 sin(7) - 3 sin(6) In conclusion, between t = 240 and t = 300 the number of daylight hours increases by 3 sin (7) - 3 sin(6) hours. + 2 dt 300 240
Answers
The time found as between t = 240 and t = 300 the number of daylight hours increases by 3 sin (7) - 3 sin(6) hours is the conclusion.
The given problem is about the time duration of the daylight between two specified times.
The given values are:
t = 240
t = 300
t COS 20 = COS 20
= 3001,
300/10 = 1302/3
= 2/33/3
= 1
The problem can be written in the following manner:
60 t + 2 dt = 3 sin (7) - 3 sin(6)
From the above problem, the solution can be obtained as follows:
60 t + 2 dt = 3 sin (7) - 3 sin(6)
The problem is an integration problem, integrating with the given values, the result can be obtained as:
t COS 20 60 t - [2 in (+2)
= 3 60
= 3 sin(7) - 3 sin(6)
The above solution can be written as follows:
Between t = 240 and t = 300 the number of daylight hours increases by 3 sin (7) - 3 sin(6) hours. + 2 dt
Therefore, between t = 240 and t = 300 the number of daylight hours increases by 3 sin (7) - 3 sin(6) hours is the conclusion.
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At Bayshore, the ratio of girls to boys is 5:6. If there are 30 girls in the food court, how many boys can we expect to find?
Answers
Answer:
so the number of boys is 36
Step-by-step explanation:
let the number of boys be x
by using ratio and proportion rule
5:6=30:x
\(\frac{5}{6}=\frac{30}{x}\)
by cross-multiplication
5×x=6×30
5x=180
x=36
i hope this will help you :)
Answer:
There are 36 boys
Step-by-step explanation:
girls : boys = 5 : 6
Number of girls = 5x
5x = 30
x = 30/5
x = 6
Number of boys = 6x = 6*6 = 36
9. Consider the matrix A=2 5
3 1
. a.) Find the unique x,y∈R such that A2=xA+y1
b.) Use a.) to find z,w∈R such that A3=zA+y1
where 1=1 0
0 1
is the identity matrix. 10. Let a,b,c,d∈R and let
A=a b
c d
Show that
A2−(a+d)A+(ad−bc)1=0 where 0 is the zero matrix. 11. Consider the rotation matrix
R(θ)=cosθ −sinθ
sinθ cosθ
Show that
a.) R(θ1)R(θ2)=R(θ1+θ2),∀θ1,θ2∈R
b.) R(θ)R(−θ)=1,∀θ∈R
Answers
a.) For the matrix \(A=\left[\begin{array}{ccc}2&5&\\3&1&\end{array}\right]\), we can find the unique values of x and y such that A² = xA + yI, where I is the identity matrix. The values of x and y are x = 7 and y = 2.
b.) Using the result from part a, we can find the values of z and w such that A³ = zA + wI. The values of z and w are z = 26 and w = 8.
a.) To find the values of x and y such that A² = xA + yI, we need to calculate A² and compare it to xA + yI. First, calculate A²:
A² = A * A = \(\left[\begin{array}{ccc}2&5&\\3&1&\end{array}\right]*\left[\begin{array}{ccc}2&5&\\3&1&\end{array}\right]\) =\(\left[\begin{array}{ccc}19&15&\\9&8&\end{array}\right]\)
Now, set up the equation xA + yI = \(\left[\begin{array}{ccc}2x&5x&\\3x&x&\end{array}\right]+\left[\begin{array}{ccc}y&0&\\0&y&\end{array}\right]\) and equate it to A²:
\(\left[\begin{array}{ccc}2x&5x&\\3x&x&\end{array}\right]+\left[\begin{array}{ccc}y&0&\\0&y&\end{array}\right]=\left[\begin{array}{ccc}19&15&\\9&8&\end{array}\right]\)
By comparing corresponding entries, we get the following equations:
2x = 19, 5x = 15, 3x = 9, x = 7, y = 2
Therefore, the unique values of x and y that satisfy A² = xA + yI are x = 7 and y = 2.
b.) Using the result from part a, we can find the values of z and w such that A³ = zA + wI. To do this, we multiply both sides of the equation A² = xA + yI by A:
A * A² = A * (xA + yI)
A³ = xA² + yA
Substituting the values of A², x, and y, we have:
A³ = 7A + 2I
Substituting the values of A and I, we get:
\(\left[\begin{array}{ccc}19&15&\\9&8&\end{array}\right]=7*\left[\begin{array}{ccc}2&5&\\3&1&\end{array}\right]+2*\left[\begin{array}{ccc}1&0&\\0&1&\end{array}\right]\)
Simplifying the equation, we find:
\(\left[\begin{array}{ccc}19&15&\\9&8&\end{array}\right]=\left[\begin{array}{ccc}14&35&\\21&7&\end{array}\right]+\left[\begin{array}{ccc}2&0&\\0&2&\end{array}\right]\)
\(\left[\begin{array}{ccc}19&15&\\9&8&\end{array}\right]=\left[\begin{array}{ccc}16&35&\\21&9&\end{array}\right]\)
By comparing corresponding entries, we get the following equations:
19 = 16, 15 = 35, 9 = 21, 8 = 9
Since the equations are satisfied, we can conclude that z = 26 and w = 8, and thus A³ = 26A + 8I.
In summary, for the given matrix A, the unique values of x and y that satisfy A² = xA + yI are x = 7 and y = 2. Using this result, we can determine that A³ = 26A + 8I.
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What is 3,150 divided by 9
Answers
Answer:
350
Step-by-step explanation:
3,150 divided by 9 is 350
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. ) x2 x2 x 6
Answers
Answer:
The answer is "\(\frac{A}{(x-2)} + \frac{B}{(x+3)}\)"
Step-by-step explanation:
Let the given value is: \(\frac{x-6}{x^2+x-6}\)
\(\to \frac{x-6}{x^2+x-6}=\frac{x-6}{x^2+(3-2)x-6}\\\\\)
\(=\frac{x-6}{x^2+(3-2)x-6}\\\\ =\frac{x-6}{x^2+3x-2x-6}\\\\ =\frac{x-6}{x(x+3)-2(x+3)}\\\\ =\frac{x-6}{(x+3)(x-2)}\\\\=\frac{A}{(x-2)} + \frac{B}{(x+3)}\)