e^3x.cos4x.sin2x hii please solv this you have to differentiate
Answers
Answer:
\(y = e^{3x}.cos4x.sin2x\)
\(=> y' =- 3e^{3x}.4sin4x.2cos2x=-24.e^{3x}.sin4x.cos2x\)
\(dy=y'.dx => dy = -24e^{3x}.sin4x.cos2x.dx\)
Step-by-step explanation:
The function \(e^3^x\).cos4x.sin2x on differentiating gives the solution as 2\(e^3^x\)cos2x.cos4x - 4\(e^3^x\)sin2x.sin4x + 3\(e^3^x\)cos4x.sin2x.
What is Product rule in Differentiation?Product rule in differentiation states that, for two functions f(x) and g(x),
\(\frac{d}{dx}\) [f(x).g(x)] = f(x) . \(\frac{d}{dx}\)[g(x)] + g(x) . \(\frac{d}{dx}\)[f(x)]
The question is to differentiate y = \(e^3^x\).cos4x.sin2x
We have three functions here.
Let u = \(e^3^x\) and v = cos4x.sin2x
\(\frac{d}{dx}\) [u . v] = u \(\frac{d}{dx}\)[v] + v \(\frac{d}{dx}\)[u]
= \(e^3^x\) \(\frac{d}{dx}\) [cos4x.sin2x] + cos4x.sin2x \(\frac{d}{dx}\) [\(e^3^x\) ]
= \(e^3^x\) \(\frac{d}{dx}\) [cos4x.sin2x] + cos4x.sin2x (3\(e^3^x\))
\(\frac{d}{dx}\) [u . v] = \(e^3^x\) \(\frac{d}{dx}\) [cos4x.sin2x] + 3\(e^3^x\)cos4x.sin2x
Let the above equation be equation E.
Again apply the product rule for \(\frac{d}{dx}\) [cos4x.sin2x].
Let u' = cos4x and v' = sin2x
\(\frac{d}{dx}\) [u'. v'] = u' \(\frac{d}{dx}\)[v'] + v' \(\frac{d}{dx}\)[u']
= cos4x \(\frac{d}{dx}\)[sin2x] + sin2x \(\frac{d}{dx}\)[cos4x]
= cos4x [2cos2x] + sin2x [-4sin4x]
= 2cos2x.cos4x - 4sin2x.sin4x
Substituting this is equation E, we get,
\(\frac{d}{dx}\) [u . v] = \(e^3^x\) [2cos2x.cos4x - 4sin2x.sin4x] + 3\(e^3^x\)cos4x.sin2x
= 2\(e^3^x\)cos2x.cos4x - 4\(e^3^x\)sin2x.sin4x + 3\(e^3^x\)cos4x.sin2x
Hence the function \(e^3^x\).cos4x.sin2x on differentiating gives 2\(e^3^x\)cos2x.cos4x - 4\(e^3^x\)sin2x.sin4x + 3\(e^3^x\)cos4x.sin2x.
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Related Questions
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 4. If there were 8085 total votes, how many no
votes were there?
Answers
There are 2940 no votes.
From the question, we have
there were 8085 total votes
ratio= 7 :4
No votes = 4/11*8085
=2940
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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How do you solve SSS theorem?
Answers
A SSS (side-side-side) theorem is kind of Congruence rule where two triangles with three congruent sides. So, we can solve it by showing the congruency between two triangles.
Statement: Side-Side-Side (SSS) ,the congruence theorem states that two triangles are congruent if three of their sides are equal to the corresponding sides of the other triangle.
Proof: Given, AB = DE, BC = EF, AC = DF.
To prove: ΔABC ≅ ΔDEF.
We know that the three sides of both triangles are equal in size and length. With both triangles superimposed, DE is placed on AB, EF is placed on BC, and DF is placed on AC. That is, AB = DE, BC = EF, AC = DF. Therefore, we can say that ΔABC ≅ ΔDEF.
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5. People Population The country of Elbonia was established in 2012. Its population at the time was 5
million and is growing at an annual rate of 3.2%. The neighboring country of Neecapia was established
at the same time. Its population was 4.1 million and is growing at an annual rate of 6.5%.
Answers
Answer:
Step-by-step explanation:
yes because the montly rate is 6.5%
CAN someone help me ):
Answers
Answer:
249.6
Step-by-step explanation:
width x height x 1/2 = area fo a triangle
12(2) x 10.4(2) x 1/2 = 249.6
I assumed this means all of the surface area. Hope this helps. Sorry if I'm wrong.
find the limit. (if the limit is infinite, enter '[infinity]' or '-[infinity]', as appropriate. if the limit does not otherwise exist, enter dne.) lim x→[infinity] 7 − x 7 2ex
Answers
The limit is 0.
We will first understand what limit is and ten calculate it :
A limit is a boundary beyond which something may not extend. Limit has many meanings such as "the point at which something stops", or "a boundary". It can also mean "to restrict" or "restrict".
We can use the word "limit" to describe what we don't want, but if it is to get used with time-sensitive items we have to make sure it's accurate.
To evaluate the limit, we can use L'Hopital's rule since we have an indeterminate form of "infinity/infinity". Differentiating the numerator and denominator with respect to x, we get:
lim x→[infinity] 7 - x / 7(2ex) = lim x→[infinity] (-1) / (14ex)
Since the denominator goes to infinity as x goes to infinity, and the numerator remains constant, we can see that the limit is equal to zero:
lim x→[infinity] 7 - x / 7(2ex) = lim x→[infinity] (-1) / (14ex) = 0
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6. (10 points) a coin with heads probability p is tossed repeatedly. what is the expected number of tosses needed to get k successive heads?
Answers
The expected number of tosses needed to get k successive heads is (2^k - 1)/p, where p is the probability of getting a head in a single toss.
Let E be the expected number of tosses needed to get k successive heads. If the first toss is tails, we have wasted one toss and must start over. If the first toss is heads, then we have one head and we need to get k - 1 more heads in the next E - 1 tosses. Thus, we have the recurrence relation: E = 1 + (p)E + (1-p)E[1] where E[1] is the expected number of tosses needed to get k successive heads after getting the first head. Since we know that the first toss is heads with probability p, we have E[1] = E. Substituting this into the recurrence relation, we get:
E = 1 + pE + (1-p)E
E = 1 + E(p + 1 - p)
E = 1 + E
Solving for E, we get: E = \((2^k - 1)/p\) Thus, the expected number of tosses needed to get k successive heads is \((2^k - 1)/p\).
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What should be the required return for a stock with a beta of 2.20 if the risk-free rate is 2% and the market risk premium is 6%? a. 10.80% b. 13.20% C. 14.39% d. 15.20%
Answers
The required return for a stock with a beta of 2.20, a risk-free rate of 2%, and a market risk premium of 6% is 14.39%. The correct option is c.
To calculate the required return, we can use the Capital Asset Pricing Model (CAPM), which relates the expected return of a stock to its beta, the risk-free rate, and the market risk premium. The formula for CAPM is as follows:
Required Return = Risk-Free Rate + (Beta × Market Risk Premium)
In this case, the risk-free rate is 2% and the market risk premium is 6%. The beta of the stock is given as 2.20. Plugging these values into the formula, we get:
Required Return = 2% + (2.20 × 6%) = 2% + 13.2% = 15.2%
Therefore, the correct answer is option C: 14.39%.
The CAPM is a widely used model in finance to estimate the required return on an investment. It takes into account the risk-free rate, which represents the return on a risk-free investment such as government bonds, and the market risk premium, which represents the additional return investors expect to receive for taking on the risk of investing in the overall market.
The beta of a stock measures its sensitivity to market movements, and multiplying it by the market risk premium gives us an estimate of the stock's additional required return. By summing this additional return with the risk-free rate, we obtain the required return for the stock.
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A green rope is 60.5 m long. Each meter of the rope has a mass of
0.052 kg. What is the total mass of the green rope? Show your work.
Answers
Answer:
Answer:
4
Step-by-step explanation:
If you read it carefully then you'll get it :)
The total mass of the green rope will be the multiplication of length by per meter mass thus it will be 3.146kg.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.
Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.
As per the given,
Length of rope = 60.5 m
Mass per meter = 0.052 kg
Total mass = 60.5 x 0.052 = 3.146kg
Hence "The total mass of the green rope will be the multiplication of length by per meter mass thus it will be 3.146kg".
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1. Square of a Binomial
Symbols/Pattern:
(a + b)2 = a2 + 2ab + b2
(a - b)2 = 22 - 2ab + b2
In the pattern, if a is the first term and b is the last term, then the square
of a binomial consists of:
a) the square of the first term (a);
b) twice the product of the first and last terms (2ab); and
c) the square of the last term (54).
2. The product of the sum and difference of two terms
Answers
a street vendor sells two types of newspapers one for 25 cents and the other for 40 cents. fi she sold 100 newspaper for 28.00 how many newspapers did she sell at 25 cents
Answers
She did sell the newspapers for $.25 each at age 80. The equation is referred to as a linear equation in one variable if only one variable is present in the linear equation.
A linear equation is what?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The information provided in the issue is;
One newspaper will set you back $.25.
Other newspapers are $.40 each.
The 100 newspapers were purchased for $28.00.
x is the quantity of newspapers sold for $.25 each.
Y stands for the other newspaper's number.
The total of both newspapers is one hundred.
x+y=100
y=100-x
25x+ 40y=28.00
25x+40(100-x)=2800
25x+4000-40x=2800
-15x+4000=2800
-15x=-1200
x=80
She therefore sold 80 newspapers for $.25 each.
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Liam's bookstore sold 404040 notebooks and 202020 newspapers for a total of \$130$130dollar sign, 130. A day later, the bookstore sold 888 notebooks and 444 newspapers at the same prices, for a total of \$28$28dollar sign, 28. How much does a notebook and a newspaper cost at Liam's bookstore
Answers
By the given condition we find that to calculate the cost of the notebooks and newspaper is impossible, from the given condition we get only no solutions.
Let the cost of the notebooks and newspaper in Liam's bookstore be x and y respectively.
According to the given question.
Liam's bookstore sold total 40notesbooks and 20 newspater for $130.
⇒ 40x + 20y = 130
⇒ 20(2x + y) = 130
⇒ 2x + y = 6.5 ...(i)
And the next day,
The bookstore sold 8 notebooks and 4 newspapers for $130.
⇒ 8x + 4y = 28
⇒ 4(2x + y ) = 28
⇒ 2x + y = 7 ...(ii)
Since, if we see the two equations i and ii we find that the given conditions provide no solutions.
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Question 2
Which results in a net value of 0?
O John has $25 and spends $10
O John gives away 4 out of 5 of his canned sodas
O John buys a shirt for $20 and returns it for a refund of $20
O John makes $8 but owes Tracie $5
Answers
(8, -1) and slope m= -3 for slope intercept
Answers
Answer:
Slope-intercept Form: \(y = -3x + 16\)
Step-by-step explanation:
Point-slope: \(y- y_1 = m (x - x_1)\)
\(y + 1 = -3(x - 8)\\y \frac{+8}{-8} = -3x + \frac{+24}{-8} \\y = -3x + 16\)
Expand and simplify
(x + 1)(x + 2)(x + 3)
Answers
Im using my casio calculator :)
use the vectors in the figure below to graph the following vector
Answers
Given:
The given vector is w.
Required:
We need to draw 3w.
Explanation:
Use the Pythagorean theorem to find the magnitude AB.
Let the origin be (0,0).
Point A is (0,4) and point B is (3,0).
The magnitude of AB is (3-0,0-4)
\(w=(3,-4)\)Multiply the equation by 3 to find 3w.
\(3\cdot w=3\cdot(3,-4)\)\(3w=(3\cdot3,3\cdot(-4))\)\(3w=(9,-12)\)Consider any point on the graph and take it as the origin (0,0) and mark (9,-12) and joint them as follows.
Final answer:
Evaluate this table.
X 5 10 15 25 40
Y 1 2 3 5 8
The table represents a(n) _____ relationship.
A. additive
B. multiplicative
Answers
The given table represents the additive property of the relation.
What about additive property?
In mathematics, the additive property refers to the property that allows the addition of two or more numbers to produce a sum or total. It states that the order in which the numbers are added does not affect the result.
The additive property can be expressed mathematically as follows:
⇒ a + b = b + a
For example, the additive property of integers states that if you add any two integers, the order in which you add them does not matter. So, 3 + 4 is the same as 4 + 3, and both equal 7.
The additive property can be extended to other mathematical operations as well, such as addition of vectors, matrices, and complex numbers. In all cases, the order in which the elements are added does not affect the final result.
According to the given information:
When we check in case of (X) we have that ,
5 + 10 = 15 , 10 + 15 = 25 , 15 + 25 = 40 that follow additive property
In the same way for (Y)
1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8 that also follow additive property of the given condition.
So, the both condition follow additive property .
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Can someone help me please!!!!!
Answers
Answer:-4
Step-by-step explanation:
Answer:
forgive me if I'm wrong, but I believe that a is -2.25. someone, please comment if I'm incorrect.
Step-by-step explanation:
I subtracted 3.25a from both sides and got
0.75a+5=2
then I subtracted both sides from 5 and got
0.75a=-3
divided both sides by 0.75
and I got a= -2.25
A payday loan company charges 4.4 percent interest for a two-week period. What would be the annual interest rate from that company
Answers
The annual interest rate from the payday loan company would be 114.4%.
The annual interest rate from a two-week payday loan, the number of periods in a year.
Since there are 52 weeks in a year, the loan term of two weeks corresponds to 26 periods in a year (52 weeks divided by 2 weeks).
The payday loan company charges an interest rate of 4.4 percent for a two-week period. To calculate the annual interest rate, the number of periods in a year:
Annual interest rate = Interest rate per period ×Number of periods in a year
Annual interest rate = 4.4% × 26
Annual interest rate = 114.4%
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What is the percent if we go from 12 to 23?
Answers
Answer:
91.67%
Step-by-step explanation:
find diff between 12 and 23 as a number
divide that number from step on by 12
multiply the result from step 2 by 100
What calculations should I do to find the side lengths of the new rectangle?
Answers
The side lengths of the new triangle would be = 35⅖ and 15⅖.
How to calculate the new length of the rectangule?To calculate the new lengths the formula for scale factor should be used;
That is;
Scale factor = Bigger dimensions/smaller dimensions.
Scale factor = 2/5
Smaller dimension length = 35
Smaller dimension width = 15
The bigger dimension length = 35×⅖ = 35⅖
The bigger dimension width = 15×⅖ = 15⅖
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If x+4/4 = y+7/7 then x/4 =___.
(Number 9 is the one I need an answer for)
Answers
Answer:
4th answer is correct
Step-by-step explanation:
First, let us make x the subject.
\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)
Use cross multiplication.
\(\sf 7(x+4)=4(y+7)\)
Solve the brackets.
\(\sf 7x+28=4y+28\)
Subtract 28 from both sides.
\(\sf 7x=4y+28-28\\\\\sf7x=4y\)
Divide both sides by 7.
\(\sf x=\frac{4y}{7}\)
Now let us find the value of x/4.
To find that, replace x with (4y/7).
Let us find it now.
\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)
how many feet is the actual height of the tree?
Answers
Given data:
The given scale is 2 cm= 6 ft.
The given height of the tree is h= 7.8 cm.
The given scale can be written as,
\(\begin{gathered} 2\operatorname{cm}=\text{ 6 ft} \\ 1\text{ cm= 3ft} \end{gathered}\)The actual height of the tree is,
\(\begin{gathered} H=7.8\times\text{3 ft} \\ =23.4\text{ ft} \end{gathered}\)Thus, the actual height of the tree is 23.4 ft.
calculate the margin of error of a confidence interval for the difference between the two population means.
Answers
A 95% confidence interval with a 4% margin of error suggests that your statistic will be 95% of the time within 4 percentage points of the true population value.
A survey, may reveal that the 98% confidence interval is between 4.88 and 5.26. So, if the poll is repeated using the same methods, the true population parameter (parameter vs. statistic) will fall 98% of the time within the interval estimates (i.e. between 4.88 and 5.26).
The formal definition, on the other hand, includes a little more information. The margin of error in a confidence interval is defined as the range of values below and above the sample statistic. The confidence interval is a tool for demonstrating the level of uncertainty associated with a certain statistic (i.e. from a poll or survey).
In 2012, a Gallup poll (incorrectly) predicted that Romney would win the election, with Romney polling at 49% and Obama polling at 48%. The declared level of confidence was 95%, with a margin of error of 2. We can conclude that the results were computed to be 95% accurate within 2 percentage points.
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ursesRead bar graphsBella counted the number of students who play various instruments in her school's marching band and graphedthe results.file48) 1 34032ASCNumber of students24As16MY80TATUSCoFlute Saxophone DrumsTromboneTrumpetMYInstrumentProWhich instruments did the same number of students play?ProChoose 2 answers:ТеаFluteTrombone
Answers
SOLUTION:
We are to find the instruments that same number of students play?
Considering the given bar-chart, 32 students played each of Saxophone and Drums.
Therefore the answer is Saxophone and Drums.
What does multiplicity mean in math?
Answers
The phrase "number of values for which a certain condition holds" is referred to as multiplicity. The phrase, for instance, can be used to describe the magnitude of the totient valence function or the frequency with which a given polynomial equation has a root at a specific location.
Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,
f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,
and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.
This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.
Hence ,Multiplicity means the quality or state of being multiple or various. and
the number of components in a system (such as a multiplet or a group of energy levels)
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Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,
f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,
and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
10. The model below represents an equation.
What is the solution to the equation?
A. X= 3
B. X= 4 1/3
C. 13
D. 19
!!!!WILL GIVE BRAINLIEST!!!!
Answers
the model shows the equation 3x+2=11.
you subtract 11-2 and get 9.
therefore you have 3x=9.
then you divide 9 by 3 and get x=3.
hope this helps!
Multiply the Polynomials:
(2x+3) (-x+2y-4)
Answers
The result of multiplying the polynomials is (2x + 3) (-x + 2y - 4) = -2x² + 4xy - 11x + 6y - 12
How to multiply the polynomials?The polynomial expression is given as
(2x + 3) (-x + 2y - 4)
Expand the brackets in the above polynomial expression
So, we have
(2x + 3) (-x + 2y - 4) = 2x * (-x + 2y - 4) + 3 * (-x + 2y - 4)
Open the brackets in the above polynomial expression
So, we have
(2x + 3) (-x + 2y - 4) = -2x² + 4xy - 8x + -3x + 6y - 12
Evaluate the like terms in the above polynomial expression
So, we have
(2x + 3) (-x + 2y - 4) = -2x² + 4xy - 11x + 6y - 12
Hence, the solution is -2x² + 4xy - 11x + 6y - 12
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Why does nobody care about may the 4th be with you (star wars day)
Answers
There are 35 attendees in a seminar. The ratio of men to women is 3 : 4. How many women attended the seminar?
Answers
Answer:
20 women
Step-by-step explanation:
Men : Women = 3 : 4
Total attendees = 35
\(Number \ of \ women = \dfrac{4}{7}*35 = 4*5 = 20\)
Solve for the value of s.
(s+1)°
(2S-1)°
Answers
Answer
90*
Step-by-step explanation:
Answer:
s = 30
Step-by-step explanation:
The three angles lie on a line.
The sum of angles on a line are supplementary, meaning they add up to 180 degrees.
s + 1 + 90 + 2s - 1 = 1803s = 90s = 30