Find the differential of each function.
(a) y=s/(1+2s)
(b) y=(e^(-u))*cos(u)
Answers
For (a) Therefore, the differential of y=s/(1+2s) is dy = -2s/(1+2s)² ds. For (b) the differential of y=(e^{(-u)})×cos(u) is dy = (-e^{(-u)sin(u)} - cos(u)e^{(-u))} du.
(a) Given the function y = s/(1 + 2s), we need to find dy/ds.
Using the quotient rule, (d(u/v)/ds) = (v(du/ds) - u(dv/ds))/v²,
where u = s and v = (1 + 2s).
dy/ds = ((1 + 2s)(1) - s(2))/(1 + 2s)²
dy/ds = (1 + 2s - 2s)/(1 + 2s)²
dy/ds = 1/(1 + 2s)²
(b) Given the function y = e^{(-u)} × cos(u), we need to find dy/du.
Using the product rule, (d(uv)/du) = u(dv/du) + v(du/du),
where u = e^({-u)} and v = cos(u).
dy/du = e^{(-u)(-sin(u))} + cos(u)(-e^{(-u)})
dy/du = -e^{(-u)(sin(u)} + cos(u))
So, the differentials for each function are:
(a) dy/ds = 1/(1 + 2s)²
(b) dy/du = -e^{(-u)(sin(u)} + cos(u))
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Related Questions
hurry please thank u if u answer
Answers
Answer:
92
Step-by-step explanation:
<C = 180 - 140 = 40 deg
180 = 40 + 2x + (x+2)....... x= 46
<B = 2x = 2*46 = 92 deg ans
how is everyone's day going? Mine is okay can u help me on this question?
Solve the following system of equations. 8x +y = 23= −10x - y = −27
x=
y=
Answers
Answer:
x = 2 and y = 7
Step-by-step explanation:
We are given two equations:
1. 8x + y = 23
2. −10x - y = −27
By adding both equations with each other we get:
(1.+2.) -2x = -4
Which can be reduced to:
(1.+2. : (-2)) x = 2
We can insert x in Equation 1. (or 2) and get:
8*2 + y = 23
16 + y = 23 [-16 on both sides]
y = 7
Resulting in x = 2 and y = 7 as a possible solution for this system.
Answer:
Step-by-step explanation:
8x + y = 23
-10x - y = -27
-2x = -4
x = 2
8(2) + y = 23
16 + y = 23
y = 7
(2, 7)
according to a recent survey, voter turnout for young people is at an all-time low. from a random sample, it was found that 35% of young people voted in the last primary election. if three people are interviewed, what is the probability that none of them voted in the primary election? what is the probability that only one of them voted in the primary election? what is the probability that 2 of them voted in the primary election? what is the probability that all three of them voted in the primary election?
Answers
Probability that none of them voted in the primary election: 0.45, Probability that only one of them voted in the primary election: 0.44, Probability that 2 of them voted in the primary election: 0.18, Probability that all three of them voted in the primary election: 0.04
To calculate these probabilities, we can use the binomial distribution formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
- n is the sample size (in this case, 3)
- k is the number of "successes" (in this case, voting in the primary election)
- p is the probability of success (in this case, 0.35)
Probability that none of them voted in the primary election:
P(X=0) = (3 choose 0) * 0.35^0 * (1-0.35)^(3-0) = 0.45
Probability that only one of them voted in the primary election:
P(X=1) = (3 choose 1) * 0.35^1 * (1-0.35)^(3-1) = 0.44
Probability that 2 of them voted in the primary election:
P(X=2) = (3 choose 2) * 0.35^2 * (1-0.35)^(3-2) = 0.18
Probability that all three of them voted in the primary election:
P(X=3) = (3 choose 3) * 0.35^3 * (1-0.35)^(3-3) = 0.04
So the probabilities are:
- Probability that none of them voted in the primary election: 0.45
- Probability that only one of them voted in the primary election: 0.44
- Probability that 2 of them voted in the primary election: 0.18
- Probability that all three of them voted in the primary election: 0.04
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Identify the slope from the equation: y = 13x-5
Answers
the given expression is'
y = 13x - 5
compare this equation with the standard equation
y = mx + c
here m is slope
so m = 13
thus, the slope of the equation is m = 13
there are eight friends each friend wants five gummy bears and there are nine gummy bears and each box how many boxes will they need
Answers
At least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.
What is Division by Sharing?
A technique used to introduce the idea of division is sharing equally. It entails dividing a sum equally across groups, one at a time, until each group has the same amount. When teaching division by sharing, physical objects like counters are frequently used.let the number of gummy bears bag = x
9x/8 = 5
9x = 40
x = 4.4
Thus, at least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.
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FIRST ANSWER GETS BRAINLIEST!
Calculate the mean of
0,0,0,8,30,90,120,138,240,240,300,420,1800,2530,2940,5040
Calculate the Median of
0,0,0,8,30,90,120,138,240,240,300,420,1800,2530,2940,5040
Answers
Answer:
Answer would be 868.5
Answer:
Mean; 868.5
Median; 189
Step-by-step explanation:
Data set:0,0,0,8,30,90,120,138,240,240,300,420,1800,2530,2940,5040
To calculate the mean you add all the values in the data set, the divide by the amount of values.
Add them;
13,896
Divide by 16
868.5
To calculate the median of the data set is find the center of the data,
0,0,0,8,30,90,120,(138 , 240),240,300,420,1800,2530,2940,5040
Now that we know this is the center we add these two values together than divide by 2.
138 + 240 = 378
378 / 2 = 189help me please question in picture
Answers
Answer:
the answer is 3x as that is the slope
Answer:
3
Step-by-step explanation:
yeah < 3
Which graph shows a system of equations with a solution at (2, -1)?
Answers
Graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is
Which graph shows a system of equations with a solution at (2,-1)?
The graph is in the picture, please refer to the attached picture.
As we can see in the graph there are two graphs of a function shown.
The first one is a parabola and the second one is a linear graph.
From the graph, the intersection point of the two groups is at (2, -1)
The intersection point is shown in graph fourth.
Thus, graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.
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Answer:
Graph 4
Step-by-step explanation:
Help! I’m confused. Select all the rates that are unit rates
Answers
Answer:
The ones you have chosen are correct
Step-by-step explanation:
:)
for all m, n ∈ a, m r n ⇔ 5|(m2 − n2). it is a fact that r is an equivalence relation on a. use set-roster notation to list the distinct equivalence classes of r. (enter your answer as a comma-separated list of sets.)
Answers
To find the distinct equivalence classes of the relation "r," we need to determine the sets of elements in set "a" that are related to each other based on the given condition. In this case, the condition is that for any "m" and "n" in set "a," "m r n" if and only if "5|(m^2 - n^2)."
To list the distinct equivalence classes using set-roster notation, we need to identify sets of elements that are related to each other under the relation "r." Let's proceed with finding these sets:
Start by picking an arbitrary element "x" from set "a."
Identify all elements "y" in set "a" such that "x r y." In other words, find elements that satisfy the condition "5|(x^2 - y^2)."
Repeat steps 1 and 2 until all elements in set "a" have been considered.
Group all elements found in step 2 for each iteration into distinct sets.
For instance, let's assume set "a" contains the elements {1, 2, 3, 4, 5}. We will go through the steps mentioned above:
Pick 1 from set "a."
Identify elements related to 1: 1 r 4 (since 5|(1^2 - 4^2)), and 1 r 3 (since 5|(1^2 - 3^2)).
Repeat steps 1 and 2 for the remaining elements: 2 r 5 (since 5|(2^2 - 5^2)).
Group the elements found in step 2 into sets: {1, 4, 3}, and {2, 5}.
Therefore, the distinct equivalence classes of "r" are {1, 4, 3} and {2, 5}. The distinct equivalence classes of the relation "r" on set "a" are {1, 4, 3} and {2, 5}. To find the distinct equivalence classes, we need to determine sets of elements in set "a" that are related to each other under the relation "r." The relation "r" is defined as "5|(m^2 - n^2)." This means that for any elements "m" and "n" in set "a," "m r n" if and only if "5" divides the difference between the squares of "m" and "n." Using the set-roster notation, we can list the distinct equivalence classes as {1, 4, 3} and {2, 5}. These sets represent elements that are related to each other based on the given condition. To find these sets, we follow the steps outlined above. Starting with an arbitrary element from set "a," we identify all elements related to it. We repeat this process for all elements in set "a" and group the related elements into distinct sets.
The distinct equivalence classes of the relation "r" on set "a" are {1, 4, 3} and {2, 5}. These sets represent elements that are related to each other based on the given condition "5|(m^2 - n^2)."
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9.9 minus 11.8 as a decimal
Answers
Answer:
-1.9
Step-by-step explanation:
LOL IM ON ECSTACY
PLS AWNSER IS LOTS OF POINTS
Johnny pays $5 a month to use an online ordering service for his company. He has to pay an additional $2 for each order placed. Graph the
equation y=2x+5 to model this equation
Answers
In the coordinate plane, which of the following functions dilates by a factor of 3
about the point (9, 6)?
A. (, ) = (3 + 9, 3 +6)
B. (, ) = (3( + 9), 3( + 6))
C. (, ) = (9+ 3( − 9), 6 + 3( −6))
D. (, ) = (9+ 3(9− ), 6+ 3(6 − ))
Answers
Mario is filling a fish tank with water at a rate of 1 gallon every 30 seconds. Which graph shows the relationship between the number of gallons in the tank and time in minutes?
Answers
Answer:
X-axis
Step-by-step explanation:
Maybe
A rectangular tank with a square base, an open top, and a volume of 10,976 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
Answers
Answer:
Dimensions to minimize surface are is 28 ft x 28 ft x 14 ft
Step-by-step explanation:
The Volume of a box with a square base of say;x cm by x cm and height
h cm is;
V = x²h
Now, the amount of material used is directly proportional to the surface area, hence we will minimize the amount of material by minimizing the surface area.
The formula for the surface area of the box described is given by;
A = x² + 4xh
However, we need A as a function of
only x, so we'll use the formula;
V = x²h
V = x²h = 10,976 ft³
So,
h = 10976/x²
So,
A = x² + 4x(10976/x²)
A = x² + 43904/x
So, to minimize the area, it will be at dA/dx = 0.
So,
dA/dx = 2x - 43904/x² = 0
Factorizing out, we have;
2x³ = 43904
x³ = 43904/2
x³ = 21952
x = ∛21952
x = 28 ft
since, h = 10976/x²
h = 10976/28² = 14 ft
Thus,dimension to minimize surface are is 28 ft x 28 ft x 14 ft
A paratrooper bails out of an airplane at altitude 15,000 ft, then falls freely for 30 seconds, then opens a parachute.
Answers
The speed of the parachute is 50ft/s
How to calculate the speed of an objectThe formula for calculating speed is expressed as:
Speed = Distance/Time
Given the following parameters
Distance = 15,000 feet
Time = 30 seconds
Substituting into the formula;
Speed = 1500ft/30s
Speed = 50ft/s
Hence the speed of the parachute is 50ft/s
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Which item is discounted by more than 15%
A. $199.99 smartphone on sale for $167.99
B. $28,100 car on sale for $24,750
C. $58 jeans on sale for $50
D. $1.99 song download on sale for $1.75
Answers
Answer:
A
Step-by-step explanation:
2x + 9y = -7
6x - 3y = 9
Answers
Answer:
Add the equations together
Step-by-step explanation:
The reason why I know this is because they are all like terms so that would be the smartest choice to do first.
If this answer helped you then please mark it as brainliest so I can get to the next rank
what kinds of numbers are exact? check all that apply. what kinds of numbers are exact?check all that apply.
Answers
Option A: defined quantities, option C: integers that are part of a mathematical equation, and option D: measurements that can be counted, are all kinds of numbers that are exact.
A value that is known with 100 percent confidence is called an exact number. In other terms, an exact integer has an infinite number of significant digits and zero uncertainty. It is impossible to simplify or reduce an exact number. Defined quantities like volume in liters, integers that are a part pf mathematical equation like 4π\(r^{3}\), and countable measurements such as the number of students is exact number that can be quantified.
Determining if a particular unit is an exact number can be challenging because not all units and their conversions have clear definitions. Since the SI base units have all been specified, they are all precise integers. Imperial units that are defined in accordance with the SI base units are likewise precise numbers.
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Complete question is:
What kinds of numbers are exact?
Check all that apply.
A) Defined quantities (e.g., 1000 mL in 1 liter).
B) The readings of the thermometer.
C) Integers that are part of a mathematical equation (e.g., 4πr33)
D) Measurements that can be counted, such as the number of students in class.
If the area of triangle is 1200 sq m and its length is 60 m , find the breadth .
Answers
Answer:
20 m
Step-by-step explanation:
The area of a triangle is 120 sq m
The length is 60 m
We are required to find the breadth
Therefore to find the breadth of the traingle the formular below will be applied
Area= length × breadth
120= 60 × breadth
Breadth= 120/60
= 20 m
Hence the breadth of the traingle is 20 m
I'm stuck here, please help
Answers
Answer:
Are you stuck step-sis?
Step-by-step explanation:
Let f:ℝ→ℝf:R→R be defined by f(x)=3−3xf(x)=3−3x. Is ff a linear transformation?
Answers
No, the function f(x) = 3 - 3x is not a linear transformation.
A linear transformation is a mapping between vector spaces that preserves addition and scalar multiplication. For a function to be a linear transformation, it must satisfy two properties: additivity and homogeneity. Additivity means that f(u + v) = f(u) + f(v), where u and v are vectors in the domain of the function. Homogeneity means that f(cu) = cf(u), where c is a scalar and u is a vector in the domain.
In the given function f(x) = 3 - 3x, let's test these properties. Consider f(1 + 2). According to additivity, f(1 + 2) should be equal to f(1) + f(2). However, f(1 + 2) = f(3) = 3 - 3(3) = -6, while f(1) + f(2) = (3 - 3(1)) + (3 - 3(2)) = 0. Since f(1 + 2) ≠ f(1) + f(2), the additivity property is not satisfied.
Similarly, let's consider f(2) and f(3). According to homogeneity, f(2) should be equal to 2f(1) and f(3) should be equal to 3f(1). However, f(2) = 3 - 3(2) = -3 and 2f(1) = 2(3 - 3(1)) = 0. Similarly, f(3) = 3 - 3(3) = -6 and 3f(1) = 3(3 - 3(1)) = 0. Since f(2) ≠ 2f(1) and f(3) ≠ 3f(1), the homogeneity property is not satisfied.
Since the function f(x) = 3 - 3x fails to satisfy both the additivity and homogeneity properties, it is not a linear transformation.
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35/20+3/20=35/20+3/20=
Answers
35/20 + 3/20 = 35/20 + 3/20 = 19/10
Answer:
a
Step-by-step explanation:
a
Can anyone help me with this plz
Answers
I need this in school
Fill out the table, reporting all the sample means and standard deviations.PreAlg: 1.32 (Mean), 0.96 (SD)ElemAlg: 3.18 (Mean), 0.75 (SD)InterAlg: 4.42 (Mean), 2.78 (SD)Finish the list of all three possible comparisons.1. PreAlg compared to ElemAlg2. PreAlg compared to InterAlg3. ElemAlg compared to InterAlgFind the corrected value for the significance level by dividing 0.05 by the number of comparisons.The corrected significance level is 0.0167.We have assumed that the conditions for two-sample t-tests are met. For all tests, the null hypothesis is that the two population means are the same, and the alternative hypothesis is that the two population means are different. Complete the table below. For a significant difference, the p-value must be less than the Bonferroni-corrected value for the significance level.PreAlg and ElemAlg: 5.08 (t-value), 0.000 (p-value), different (conclusion)PreAlg and InterAlg: 3.64 (t-value), 0.003 (p-value), different (conclusion)ElemAlg and InterAlg: 1.49 (t-value), 0.163 (p-value), not different (conclusion)Write a clear conclusion based on what you found. Which groups have sample means that are significantly different, and how do they differ?Ans: PreAlg students spend less time doing homework than the others.
Answers
PreAlg students spend significantly less time doing homework compared to ElemAlg and InterAlg students, while there is no significant difference in homework time between ElemAlg and InterAlg students.
What is significantly ?
Significantly" is the keyword that indicates a notable or meaningful difference or result in the context of statistical analysis. It is often used to describe findings that have a high level of confidence and statistical significance, indicating that the observed difference or relationship is unlikely to have occurred by chance.
Based on the given data and statistical analysis, the conclusion is as follows:
PreAlg compared to ElemAlg:
The sample mean for PreAlg (1.32) is significantly different from the sample mean for ElemAlg (3.18) with a t-value of 5.08 and a p-value of 0.000. Therefore, we can conclude that PreAlg students spend significantly less time doing homework compared to ElemAlg students.
PreAlg compared to InterAlg:
The sample mean for PreAlg (1.32) is significantly different from the sample mean for InterAlg (4.42) with a t-value of 3.64 and a p-value of 0.003. Hence, we can conclude that PreAlg students spend significantly less time doing homework compared to InterAlg students.
ElemAlg compared to InterAlg:
The sample mean for ElemAlg (3.18) is not significantly different from the sample mean for InterAlg (4.42) with a t-value of 1.49 and a p-value of 0.163. Therefore, we fail to reject the null hypothesis, and we cannot conclude a significant difference in homework time between ElemAlg and InterAlg students.
In summary, the PreAlg students have significantly lower homework time compared to both ElemAlg and InterAlg students. However, there is no significant difference in homework time between ElemAlg and InterAlg students.
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big box have 1/4 of 20
gigabytes of ram
Answers
Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Big boxes have 1/4 of 20 gigabytes of ram.
Then the multiplication of the numbers 1/4 and 20 will be given by putting a cross sign between them. Then we have
⇒ (1/4) x 20
⇒ 20 / 4
⇒ 5 gigabytes
Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.
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how long will it take to get to 280 kilo. at a rate of 70 kilo./per hour
Answers
what is the answer please
Answers
Answer:
A
Step-by-step explanation:
please help.
2 years ago, age of brother was 3 times less than sister's age. this year his age is just 2 times less than his sister's. how old is brother? how old is sister?
Answers
Answer:
\(The\ brother's\ present\ age= 4\ years\\The\ sister's\ present\ age=8\ years\)
Step-by-step explanation:
\(Let\ the\ brother's\ present\ age\ be\ x\\Hence\ we\ are\ given,\\His\ sister's\ present\ age=(2x)\\Now,\\The\ brother's\ age\ before\ two\ years=(x-2)\\The\ sister's\ age\ before\ two\ years=3(x-2)\\Also,\\His\ sisters\ age\ before\ two\ years=2x-2\\Hence,\\3(x-2)=2x-2\\3x-6=2x-2\\3x-2x=6-2\\x=4\\Hence,\\The\ brother's\ present\ age= 4\ years\\The\ sister's\ present\ age=2x=2*4=8\ years\)
Answer:
The sister's present age is 8 years old, and the brother's present age is 4 years old.
Step-by-step explanation:
Let \(b =\) present age of the brother, \(s =\) present age of the sister
\(s-2 = (b-2)\) × \(3\)
\(s-2\) = \(3b - 6\)
\(s = 3b - 4\)
\(s = b\) × \(2\)
\(= 2b\)
\(sb-4 = 2b\) (proved from above equations)
\(b = 4\)
\(\because s = 3b - 4\)
\(\therefore\)\(s = 3\)×\(4 - 4\)
\(= 8\)
\(\therefore\) the brother's present age is 4 years old, and the sister's present age is 8 years old.
Hope this helps :)
Select all of the TRUE statements (you may select more than one) A. We use the robust option in Stata when the variance of the error term is not constant i.e. when var(u;) ‡ 0² B. The estimated standard error using the robust option is always larger than the estimated standard error that does not use the robust option. C. Heteorskedasticity affects our ability to conduct statistical inference D. All of the above statements are false.
Answers
The correct answer is: C. Heteroskedasticity affects our ability to conduct statistical inference. Heteroskedasticity refers to the situation where the variance of the error term in a regression model is not constant across different levels of the independent variables.
It violates one of the assumptions of classical linear regression, namely homoscedasticity, which assumes constant variance.
Heteroskedasticity can affect statistical inference because it can lead to inefficient and biased estimates of the regression coefficients. Specifically, standard errors of the coefficients may be incorrect, leading to incorrect hypothesis tests and confidence intervals. Therefore, when heteroskedasticity is present, it is important to use appropriate methods to account for it, such as robust standard errors, which provide consistent estimates of standard errors even in the presence of heteroskedasticity.
Statements A and B are incorrect. The robust option in Stata is used to estimate robust standard errors that account for heteroskedasticity, but it is not specifically for cases when the variance of the error term is not constant. Additionally, whether the estimated standard error using the robust option is larger or smaller depends on the specific data and model, so it cannot be stated that it is always larger than the estimated standard error without the robust option
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