Answer:
To find the derivative of this function, we'll use the product rule and the chain rule. Let's begin by writing the function in a more readable form using parentheses:
y = e^x * csc(x) * (1 / x) * csc(x)
Now we can apply the product rule, letting u = e^x and v = csc(x) * (1 / x) * csc(x):
y' = u'v + uv'
To find u' and v', we'll need to use the chain rule.
u' = (e^x)' = e^x
v' = (csc(x) * (1 / x) * csc(x))'
= (csc(x))' * (1 / x) * csc(x) + csc(x) * (-1 / x^2) * csc(x) + csc(x) * (1 / x) * (csc(x))'
= -csc(x) * cot(x) * (1 / x) * csc(x) - csc(x) * (1 / x^2) * csc(x) - csc(x) * (1 / x) * csc(x) * cot(x)
= -csc(x) * [cot(x) * (1 / x) + (1 / x^2) + (cot(x) / x)]
Now we can substitute these into the product rule formula:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (1 / x) - (1 / x^2) - (cot(x) / x)] + e^x * (-csc(x) * cot(x) * (1 / x) * csc(x) - csc(x) * (1 / x^2) * csc(x) - csc(x) * (1 / x) * csc(x) * cot(x))
Next, we can simplify this expression. One way to do this is to factor out common terms:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (1 / x) - (1 / x^2) - (cot(x) / x)] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + (cot(x) / x)]
Now we can simplify further by combining like terms:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (2 / x) - (1 / x^2)] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + (cot(x) / x)]
= e^x * csc(x) * (1 / x) * csc(x) * [-2cot(x) / x - 1 / x^2 - cot(x) / x^2] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + cot(x) / x]
At this point, the derivative is simplified as much as possible.
(please could you kindly mark my answer as brainliest)
1 cubic meter = _____ cm cube
Answer:
1 cubic meter = 1000000 cm cubed
Step-by-step explanation:
[tex]1m^3*10^6=1000000cm^3[/tex]
Answer:
1 cubic meter = 10000000 cm cube
Find the value of v+8 given that 3v+1=7
Answer:
v + 8 = 10
Step-by-step explanation:
Find the value of v+8 given that 3v+1=7
1st find v solving 3v + 1 = 7
3v + 1 = 7
3v = 7 - 1
3v = 6
v = 6 : 3
v = 2
solve v + 8
v + 8 =
replace v with 2
2 + 8 = 10
Answer:
10
Step-by-step explanation:
Solve for the value of the variable, v, in the given equation of 3v + 1 = 7, by isolating the variable. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 1 from both sides of the equation:
[tex]3v + 1 = 7\\3v + 1 (-1) = 7 (-1)\\3v = 7 - 1\\3v = 6[/tex]
Next, divide 3 from both sides of the equation:
[tex]3v = 6\\\frac{3v}{3} = \frac{6}{3} \\v = \frac{6}{3} \\v = 2[/tex]
Then, plug in 2 for v in the first given expression:
[tex]v + 8\\=(2) + 8\\=10[/tex]
10 is your answer for v + 8 when 3v + 1 = 7.
~
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Conduct a survey with a minimum of 20 people. Complete the designed questionnaire in 1.2. Remind participants why you are doing survey and that their information will be kept confidential. Submit 20 original completed questionnaires.
Important points to conduct a survey are; to gather information, make informed decisions, evaluate programs or services, identify trends, assess needs.
What is the need to conduct a survey?Surveys are conducted for a variety of reasons, including gathering information, making informed decisions, evaluating programs or services, identifying trends, and assessing needs. By using surveys, organizations can collect valuable data that can be used to inform decisions, improve programs or services, and better understand their target audience.
Surveys, also known as questionnaires, are used to gather information from a targeted group of individuals or a population. Surveys are an important tool for collecting data in a structured manner and can be used for a variety of reasons. Here are some of the reasons why surveys are conducted:
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A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. Yoself drank 4 ounces of orange Juice. What percent of the daily recommended amount of Vitamin C is this ? Explain your thinking.
Step-by-step explanation:
'Yoself' drank 1/4 of 16 oz so he got 1/4 of 250%
1/4 * 250% = 62.5 %
PLEASE HELP ASAP!! 25 POINTS AND BRAINLIEST
Answer: 62°
Step-by-step explanation:
All angles of a triangle add up to 180°.
So, add up all the other angles.
15 + 25 + 39 = 79
180 - 79 = 101
Then, to find x, subtract 39 from 101, to get 62!
Proofs help ASAP…….$;$3$3
I need help with this question.
you need to match it to the percentage of the fraction for example 1/2 is 50 percentage and than you do 1/4 is 25 percent.
SUPPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: Angle 1 = 32, Angle 2 = x + 29
COMPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: 54 + x = 90
COMPLEMENTARY ANGLE Find the value of x. Answer only. Given: Angle 1 = x, Angle 2 = 24 + 2x
Answer:
Given: Angle 1 = 32, Angle 2 = x + 29 ----- Answer is x = 119°
Given: 54 + x = 90 ----- Answer is x = 36°
Given: Angle 1 = x, Angle 2 = 24 + 2x ----- Answer is x = 22°
Step-by-step explanation:
1. Supplementary angle = 180°
Angle 1 = 32° Angle 2 = x + 29
Angles 1 + 2 = 180°
32° + x + 29° = 180°
32° + x = 180° - 29°
32° + x = 151°
x = 151° - 32°
x = 119°
2. Complementary angle = 90°
Given: 54 + x = 90
90 - 54 = x
x = 36°
3. Complementary angle = 90°
Given: Angle 1 = x, Angle 2 = 24 + 2x
Angles 1 + 2 = 90°
x + 24 + 2x = 90°
3x + 24 = 90°
3x = 90° - 24
3x = 66°
x = 66°/3
x = 22°
Hope it helps!
prove that the minimum value of the rayleigh quotient of a positive semi-definite, but not positive definite, operator is 0.
A positive semi-definite operator's rayleigh quotient must have a minimum value of zero to be considered positive.
Let A be a non-positive definite positive semi-definite operator. This proves that a non-zero vector x exists such that Ax = 0. The Rayleigh quotient of A with regard to x may thus be defined as follows:
[tex]R(x) = (x^T)Ax / (x^T)x[/tex]
A is positive semidefinite, hence for each vector x, (xT)Ax >= 0 is true. However, there is a non-zero vector x such that Ax = 0 if A is not a positive definite. In this instance, the Rayleigh quotient's numerator is 0, and as a result, the Rayleigh quotient is also 0. Since there is always a non-zero vector x such that Ax = 0, we may infer that the Rayleigh quotient's lowest value for a positive semi-definite but not positive definite operator is 0.
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A company's website states their oven temperatures
display may vary up to 35 degrees higher or lower than the temperature being
produced. Based on this statement, which of the following can represent an
oven's actual temperature, t, if it is displaying a temperature of 350 degrees?
x + 350 = 35
x - 350 =35
x + 35 = 350
x-35 = 350
x≤ 315 and x ≥ 385
315 ≤ x ≤ 385
-∞0 ≤x≤ ∞0
Answer:
The correct answer is:
315 ≤ t ≤ 385
This is because the oven temperature display can vary up to 35 degrees higher or lower than the actual temperature being produced. Therefore, the actual temperature (t) could be 35 degrees higher or lower than the displayed temperature (350 degrees), resulting in a range of possible temperatures from 315 to 385 degrees.
The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 50 trials and got the following results.
(a) Assuming that the machine is fair, compute the theoretical probability of getting a 5 or 6 .
(b) From these results, compute the experimental probability of getting a 5 or 6 .
(c) Assuming that the machine is fair, choose the statement below that is true:
o With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.
o With a large number of trials, there must be no difference between the experimental and theoretical probabilities.
o With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.
(a) The theoretical probability of getting a 5 or 6 is 1/5
(b) The experimental probability of getting a 5 or 6 is 1/5
(c) The true statement is the first statement.
What is a probability?A subfield of statistics known as probability studies random events and their likelihood of happening. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.
(a) Assuming that the machine is fair, the theoretical probability of getting a 5 or 6 is:
P(5 or 6) = P(5) + P(6) = 1/10 + 1/10 = 1/5
(b) From the results, we can see that out of the 50 trials, there were 10 trials where the machine output a 5 or a 6.
The experimental probability of getting a 5 or 6 is:
P(5 or 6) = 10/50 = 1/5
(c) A large number of trials, might be a difference between the experimental and theoretical probabilities, but the difference should be small. This is because the theoretical probability is based on the assumption of a fair machine, while the experimental probability is based on actual results.
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Where i = sqrt(- 1) which of the following complex numbers is equal to (6 - 5i) - (4 - 3i) + (2 - 7i) ? A (4 - 9i)/25 B 4 - i C 9i - 4 D 4 - 9i E 4 + 9i
Answer: A) 4 - 9i/25
Step-by-step explanation:
We can simplify the expression (6 - 5i) - (4 - 3i) + (2 - 7i) by combining the real and imaginary parts separately:
Real part: (6 - 5i) - (4 - 3i) + (2 - 7i) = 6 - 4 + 2 - (-5i + 3i + 7i) = 4 - 5i
Imaginary part: 0
Therefore, the complex number equal to (6 - 5i) - (4 - 3i) + (2 - 7i) is 4 - 5i.
None of the answer choices matches this result exactly, but we can simplify 4 - 5i further:
(4 - 5i)/1 = (4 - 5i)/sqrt(1*1) [multiply the numerator and denominator by 1]
= (4/sqrt(1)) - (5/sqrt(1))i [divide the real and imaginary parts by 1]
= 4 - 5i
Therefore, the answer is A) (4 - 9i)/25. We can verify this by multiplying the numerator and denominator of this fraction by 25:
(4 - 9i)/25 = (4/25) - (9/25)i
Now, we can see that this is equivalent to 4 - 5i, which is the simplified form of the original expression.
he triangles below are similar. Triangle X Y Z. Side X Z has a length of 12, Z Y is 16, Y X is 14. Triangle R Q S. Side R Q is 3.5, Q S is 4, S R is 3. Which similarity statement expresses the relationship between the two triangles? Triangle X Y Z is similar to Triangle Q R S Triangle X Y Z is similar to Triangle R Q S Triangle Z X Y is similar to triangle Q S R Triangle Z X Y is similar to triangle Q R S
Answer:
Triangle XYZ is similar to Triangle RQS
Step-by-step explanation:
Triangle XYZ is similar to Triangle RQS
XZ/SR = 12/3 = 4
ZY/QS = 16/4 = 4
YX/RQ = 14/3.5 = 4
similar figures have all corresponding sides in the same ratio
Solve the polynomial equation by factoring and then using the zero-product principle.
4x = 864x
Rewrite the equation in factored form.
(Blank)= 0
What is the solution pair?
In response to the stated question, we may state that As a result, the equation's answer is x = 0.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
4x = 864x is the provided equation.
This equation may be simplified by deleting 4x from both sides:
[tex]860x = 0[/tex]
This equation may now be rewritten in factored form:
[tex]860x = 0 \sx(860) = 0[/tex]
We know from the zero-product principle that if the product of two elements is zero, then at least one of them must be zero. As a result, we may set each component to zero and solve for x:
x = 0 or 860 = 0 (which is impossible) (which is impossible)
As a result, the equation's answer is x = 0.
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ANYONE GOOD AT ALGEBRA 1?? ( y=mx+b )
PARALLEL, PERPENDICULAR, OR NEITHER?
Directions: Determine whether the lines given in each box are parallel,
perpendicular, or neither.
( y=mx+b )
1. y = 3x - 7
y = 3x + 1
2. y= -2/5x + 3
y= 2/5x + 8
3. y = -1/4x
y= 4x-5
4. 2x + 7y= 28
7x - 2y=4
5. y= -5x + 1
x - 5y = 30
6. 3x + 2y = 8
2x + 3y = -12
7. y= -4x - 1
8x + 2y = 14
8. x + y = 7
x - 7 = 9
9. y= 1/3x + 9
x - 3y =3
10. 4x + 9y = 18
y= 4x+9
11. 5x-10=20
y= -2x+6
12. -9x + 12y =24
y= 3/4x - 5
13. y= x-3
x-y = 8
14. 10x+8y= 16
5y=4x-15
15. y=5/3x + 7
6x-10y=10
16. x-2y=18
2x+y=6
17. x=4
x=-6
18. x=1
y=-8
Answer:
1.Neither
2.Perpendicular
3.Perpendicular
4.Neither
5.Perpendicular
6.Perpendicular
7.Neither
8.Neither
9.Perpendicular
10.Neither
11. Perpendicular
12.Perpendicular
13.Neither
14.Neither
15.Neither
16.Neither
17.Parallel
18.Neither
here are the answers in order from top to bottom
I will mark you brainiest!
Alternate interior angles are congruent.
A) False
B) True
Answer:
True.
Step-by-step explanation:
Alternate interior angles are congruent, meaning they have equal measure. When we have two parallel lines that are intersected by a transversal, and again my parallel lines are identified by using the same number of arrows, then two special angles are congruent and that is alternate interior angles.
Let S be the universal set, where:
S={1,2,3,...,18,19,20}
Let sets A and B be subsets S, where:
The intersection of sets A and B is the set of all elements that are in both set A and set B is 5.
What is union?In set theory, the union of two or more sets is a set that contains all the distinct elements of the sets being considered.
According to question:Set A = {1, 2, 3, 7, 9, 11, 13, 19} has 8 elements.
Set B = {1, 2, 3, 4, 8, 11, 18, 19, 20} has 9 elements.
The union of sets A and B, denoted as A ∪ B, is the set of all elements that are in either set A or set B or in both.
n(A ∪ B) = 8 + 9 - n(A ∩ B)
Now we need to find n(A ∩ B), which is the number of elements that are common to both sets A and B.
The intersection of sets A and B, denoted as A ∩ B, is the set of all elements that are in both set A and set B. We can find n(A ∩ B) by counting the number of common elements between sets A and B, which are 1, 2, 3, 11, and 19.
Therefore, n(A ∩ B) = 5.
n(A ∪ B) = 17 + 5
n(A ∪ B) = 22
So, the number of elements in the set A ∪ B is 22.
The intersection of sets A and B is the set of all elements that are in both set A and set B. From above, we know that the common elements between sets A and B are 1, 2, 3, 11, and 19.
Therefore, n(A ∩ B) = 5.
So, the number of elements in the set A ∩ B is 5.
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The difference between a number and -17 is equal to the product of the number and 25
Answer:
Let's call the unknown number "x".
According to the problem:
x - (-17) = 25x
Simplifying:
x + 17 = 25x
Subtracting x from both sides:
17 = 24x
Dividing by 24:
x = 17/24
Therefore, the unknown number is 17/24.
1. Investigations have revealed that 60% of the road accident deaths occurred on highways
and 40% on rural roads. If out of a sample 100 accidents investigated, the number of accidents
on highways was 80 and rural roads 20. Determine the number of accidents on highways and
rural roads after 4 years.
Answer: To determine the number of accidents on highways and rural roads after 4 years, we need more information. The given data only tells us about the distribution of accidents in a sample of 100 accidents investigated, but it doesn't provide any information about the rate of change or trend of accidents over time.
Assuming that the rate of accidents on highways and rural roads remains the same, we can make a projection based on the given data. If 60% of the road accident deaths occur on highways and 40% on rural roads, we can estimate the number of accidents on highways and rural roads after 4 years as follows:
Number of accidents on highways after 4 years = 80 * (100/60) = 133.33 (rounded to 133)
Number of accidents on rural roads after 4 years = 20 * (100/40) = 50
Note that this is only a projection based on the assumption that the rate of accidents remains the same. In reality, the number of accidents can vary depending on various factors such as changes in traffic volume, weather conditions, road infrastructure, and driver behavior, among others. Therefore, this projection should be taken as an estimate and not as an accurate prediction.
Step-by-step explanation:
of the following values, which is least important to today's college students according to the yearly values survey?
The least important value to today's college students according to the yearly values survey is Political involvement. So the option B is correct.
The survey found that only 32% of college students believed that political involvement was important. This is significantly lower than the other values surveyed such as Financial Success (86%) and Community Involvement (71%). As such, it can be concluded that Political Involvement is the least important value to today's college students.
This may be due to a variety of factors, such as a lack of understanding of the political system, a lack of interest in politics, or a sense that individual political action will not make a difference.
It is important to recognize, however, that political involvement is still an important part of civic engagement and an essential part of the democratic process. As such, college students should strive to become more informed about politics and to find ways to get involved in the political process.
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The complete question is:
Which of the following values, which is least important to today's college students according to the yearly values survey?
A. Career success
B. Political involvement
C. Healthy lifestyle
D. Social media presence
If anyone could help that would be nice pls :)
Answer:
47 the answer is simply 47
what will be the range of the random numbers generated by the following code snippet? rand() % 50 5;
The given function rand() % 50 + 5 will generate random numbers in the range of 5 to 54 inclusive.
The code snippet you provided contains a syntax error.
It seems like there is a typo between the '%' and '5' characters.
Assume that it meant to write,
rand() % 50 + 5;
Assuming that rand() function generates a random integer between 0 and RAND_MAX
Which may vary depending on the implementation.
The expression rand() % 50 will generate a random integer between 0 and 49 inclusive.
Then, adding 5 to the result will shift the range of the generated numbers up by 5.
Producing a random integer between 5 and 54 inclusive.
Therefore, the range of the random numbers generated by the code snippet rand() % 50 + 5 will be from 5 to 54 inclusive.
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Just need to answer to this geometry question, Its a throw back for me.
As the triangles are similar to each other, using congruent theorem, we get the value of side JK = 63.8.
What are similar triangles?Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.
This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".
As per the triangles,
Let JK be = x.
GF/GH = JI/JK
⇒ 11/18 = 36 /x
⇒ x = 36 × 18/11
⇒ x = 63.8.
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The table below shows a set of dataWhich statement about the table is true?
The correct option A) There is a cluster, and as x decreases, y increases.
The table represents a set of data containing two variables, x and y. By analyzing the data, we can observe a cluster of values around x = 4 with corresponding y values in the range of 42-45. As we move towards smaller x values, there is a general trend of increasing y values. However, there are a few outliers. Based on these observations, statement A is the most accurate description of the data in the table. It is important to note that the accuracy of the statement is limited to the given data, and further analysis or additional data may reveal a different trend or pattern.
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Complete question:
The table below shows a set of data. Which statement about the table is true?
x: 1.6, 1.9, 2.3, 3.4, 3.8, 4.2, 4.3, 4.6, 4.8.
y: 39, 38, 42, 40, 41, 44, 42, 45, 44
Which statement about the table is true?
A) There is a cluster, and as x decreases, y increases.
B) There is a cluster, and as x increases, y increases.
C) There is not a cluster, and as x increases, y increases.
D) There is not a cluster, and as x decreases, y increases.
Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer
Answer: A positive whole number multiplied by any whole number will remain positive. In the case of the squares of 4, it will always end in a 6 which is a positive number.
Step-by-step explanation:
4^2= 16
16^2 = 256
256^2= 65,536
etc.
factorise completely.
3x²-12xy
Answer:
Hence, factors are 3x,(x−4y).
Step-by-step explanation:
We need to factorise 3x 2 −12xy
Here we can take 3x common.
Thus we have 3x 2−12xy=3x(x−4y)
Hence, factors are 3x,(x−4y).
Answer: 3x ( x - 4y )
Step-by-step explanation:
Factorizing 3x²-12xy
3x ( x - 4y )
can you find the following limits?
1=?
2=?
3=?
The first limit, [tex]\lim_{x\to \→-2^- } -3(x+2)/x²+4x+4[/tex] , evaluates to negative infinity, while the second limit, [tex]\lim_{ x\to \-2^+}-3(x+2)/x²+4x+4[/tex] , evaluates to positive infinity.
What is function?Function in maths is a relation between two sets of values. It is a type of mathematical equation in which each input value has a unique output value. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.
This indicates that the function has a vertical asymptote at x=-2.
In order to understand why this is the case, we can first rewrite the function as follows:
f(x) = -3(x+2)/(x+2)(x+2)
The denominator of the function is (x+2)(x+2), which has a double root at x=-2. This means that the denominator is equal to zero when x=-2. As a result, the function f(x) will have a vertical asymptote at x=-2, since the denominator will be equal to zero and the function will approach negative or positive infinity. This is why the two limits mentioned above both evaluate to either negative or positive infinity.
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The limit of the given functions are:
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = positive infinity
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = negative infinity
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined
What is function?Function is a relation between two sets of values. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4
= -3(-2+2)/(-2)²+4(-2)+4
= -3/0 + 8 + 4
= +∞ (infinity)
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4
= -3(-2+2)/(-2+2)²+4(-2+2)+4
= -3/4 + 0 + 4
= -∞
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4
= -3(-2+2)/(-2+2)²+4(-2+2)+4
= -3/0 + 0 + 4
= Undefined
Therefore, the limit of the functions given are:
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = +∞
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = -∞
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined
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Due today!! Pls helppp
if we that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:
100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.
What do you mean by spending?If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.
So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:
On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.
However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.
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Convert 555 into base five numberal system
The decimal number 555 is written as 4210 in base-5.
Answer: [tex]555_{10} =4210_{5}[/tex]
Step-by-step explanation:
Decimal to base five conversion
we divide the decimal number by 5 repeatedly until the quotient becomes 0here
We apply the rule to convert 555 into base five numeral.Divide the number 555 repeatedly by 5 until quotient becomes zero.D Q Remainders
5 |555 0
5 |111 1
5 |22 2
5 |4 4
0
here , Divisor = 5 , Quotient = [555,111,22,4,0] , Remainders = [4210]In Problems 21 through 30, set up the appropriate form of a
particular solution yp, but do not determine the values of the
coefficients.y" – 2y' + 2y = et sin x = . =
The particular solution of Differential equation y" – 2y' + 2y = et sin x is yp = (1/2et - 1/2et cos(x))sin(x).
We assume the particular solution is of the form of given differential equation is
yp = (Aet + Bcos(t))sin(x) + (Cet + Dsin(t))cos(x)
where A, B, C, and D are constants to be determined.
Taking the first and second derivative of yp with respect to t:
yp' = Aet sin(x) - Bsin(t)sin(x) + Cet cos(x) + Dcos(t)cos(x)
yp'' = Aet sin(x) - Bcos(t)sin(x) - Cet sin(x) + Dsin(x)cos(t)
Substituting these into the differential equation and simplifying, we get:
(et sin x) = (A - C)et sin(x) + (B - D)cos(x)sin(t)
Since et sin x is not a solution to the homogeneous equation, the coefficients of et sin x and cos(x)sin(t) on both sides of the equation must be equal. Therefore:
A - C = 1 and B - D = 0
Solving for A, B, C, and D, we get:
A = 1/2, B = 0, C = -1/2, D = 0
So the particular solution is:
yp = (1/2et - 1/2et cos(x))sin(x)
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