Answers
Recall the Maclaurin expansion for cos(x), valid for all real x :
[tex]\displaystyle \cos(x) = \sum_{n=0}^\infty (-1)^n \frac{x^{2n}}{(2n)!}[/tex]
Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives
[tex]\displaystyle \cos\left(\sqrt 5\,x\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt5\,x\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^{2n}}{(2n)!}[/tex]
The first 3 terms of the series are
[tex]\cos\left(\sqrt5\,x\right) \approx 1 - \dfrac{5x^2}2 + \dfrac{25x^4}{24}[/tex]
and the general n-th term is as shown in the series.
In case you did mean cos(√(5x)), we would instead end up with
[tex]\displaystyle \cos\left(\sqrt{5x}\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt{5x}\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^n}{(2n)!}[/tex]
which amounts to replacing the x with √x in the expansion of cos(√5 x) :
[tex]\cos\left(\sqrt{5x}\right) \approx 1 - \dfrac{5x}2 + \dfrac{25x^2}{24}[/tex]
Related Questions
Let's Check In
Identify the slope of the following equation.
1
4x+y=3
A. 72 = -2
B. m = 4
C = -8
D = 10
Answers
Answer:
slope (m) = -4
Step-by-step explanation:
Equation: 4x + y = 3
need to get into to y = mx + b form
m is the slope
b is the y-intercept
4x + y = 3 subtract 4x from both sides
4x - 4x + y = 3 - 4x
y = -4x - 3
m = -4
A. 72 = -2 not true expression
B. m = 4 positive 4 not negative
C = -8 ?????
D = 10 ?????
none of the choices are right
The measure of angle 1 (10x+8) and the measure of angle 3 (12x-10). What is the measure of angle 2 in degrees? 9 98 82 16
Answers
Answer: 82
Step-by-step explanation:
68.8% complete
Question
You work for a lawn service and need to prepare fertilizer for the day. The directions state that you should mix four ounces of fertilizer for every ten gallons of water. The tank holds 50 gallons of water. You want to have a full tank to start the day’s work. How many ounces of fertilizer should you add to the tank?
A.4 ounces
B.8 ounces
C.20 ounces
D.40 ounces
E.200 ounces
Answers
Answer: 20. D.
Step-by-step explanation: 10 times 5 = 50. 4 times 5 = 20.
I hope this is right.
please help me thank you
Answers
Answer:
2.5
Step-by-step explanation:
mean=sumfx/sumf
1×2+2×2+3×5+4×1/2+2+5+1
25/10
2.5
Which survey question could have been asked to produce this data display?
A. How long did it take you to walk to the waterfall and back?
B. How many times did you walk to the park last month?
C. How far did you walk today?
D. What is the length of the street you live on?
Answers
Answer:
C
Step-by-step explanation:
The only way to know if you he waked this amount of distance is to know how much they walked today! So the answer is C
Answer: Your answer is C how far did you walk today?
Step-by-step explanation: I did the k12 unit test. (For proof) it has 10 questions. Question number sevens question is Which term describes the distribution of this graph? and part of the name is Unit Test: Data Distribution - Part 1.
Hope it helped please mark me brainliest :D
Please help!! Will give brainliest if it’s the correct answer
Maggie wants to buy a car for $24,500. If she puts a down payment of $4,000 down, she will have to take out a loan for the rest of the money with an interest rate of 5.1% and pay it back over 6 years (72 months). How much will Maggie pay each month on her loan?
$299.24
$284.79
$340.27
Answers
Answer:
It's A I think
Step-by-step explanation:
hope this helps
Answer:
299.24
Step-by-step explanation:
take away the down payment from the total. multiply the interest rate then add it to the total. Then divide it by 6 to see how much she pays a year. then divide by 12 for monthly payments
Which of the following is a monomial?
O A. 4x
O B. 5x2 + 2x +3
3
O c.
oc
O D. X-1
Answers
Answer:
A. 4x
Step-by-step explanation:
Monomials are polynomials that have only one term, hence the prefix mono. Option A, 4x, is the only option with one term.
B has three terms, C has two terms, and D has two terms as well.
hope this helps!
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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Which of the following is a monomial?
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]
4x
[tex]\blue{\textsf{\textbf{\underline{\underline{How to solve:-}}}}[/tex]
A monomial is defined as an expression with only one term.
4x is an example of a term; 5x²+2x is 2 terms (5x² and 2x)
Therefore, the monomial here is Option A. 4x
Good luck.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
A high school has 44 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players
weighing greater than or equal to 167 pounds?
Answers
The percentage of players weighing greater than or equal to 167 pounds is 75%.
What percentage of students weigh greater than 167 pounds?A box plot is used to study the distribution and level of a set of scores. On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile.
On the box plot, the lower quartile is 167.
Students that weigh greater than 167 = 100 - 25 = 75%
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Solve the division problem:
10)430
O A. 40
B. 43
C. 400
D. 403
Answers
Answer is option B.43
430÷ 10 = 43
By : Modern Einstein
What kinds of sports are played by one person?
A. Mixed
B. Individual
C. none of these
D. Team
Answers
Angel buys 6 science books and 5 marth
books. Each science book costs 45.
All math books cost the same amount in total angel spends a total of 530 buying math
and science books. find the cost of one math book.
Answers
Answer:
52$
Step-by-step explanation:
6 x 45 = 270
530 - 270 = 260
260/5 = 52
Identify the vertex, equation of the axis of symmetry, y-intercept, and zeros of the graph of a quadratic function.
Answers
Answer:
See below ~
Step-by-step explanation:
Details of Graph
Vertex = (-3, 4)Axis of Symmetry : x = -3Y-intercept : -5Zeros : (-5, 0) and (-1, 0)Question 14 of 15
What are the domain and range of the inequality ?
Answers
Answer:
we see that x must be greater then 3 and y which is the domain must be greater then 5 for the inequality to be true.
so option D is the correct option.
let me know if you need any more help!
1. List the variable costs for one of your company's products or services, with a cost estimate for each variable cost. If you have more than one product or service, choose one of them. (3.0 points)
For example, the variable costs for a company that makes t-shirts and ships them to customers might look like this:
T-shirts--$6 each
Paint--about $1.25 per shirt
Labor--about $3 per shirt (because workers earn $9 per hour and can make 3 shirts per hour, or because workers are paid by the shirt)
Shipping--$4 per shirt
2. Add the variable costs per unit to get the total cost of goods or services sold per unit. (1.0 points)
TIP: Your minimum selling price will have to be higher than this number. Next, you'll calculate fixed costs to find out how much higher it needs to be.
For example, the total cost of goods or services sold for the t-shirt company would be $14.25.
3. List the fixed costs for your company, with estimates for how much each cost will be per month. If some of your fixed costs are one-time purchases, like a computer or equipment, divide the total cost of the purchase by the number of months you expect to use the purchase. (3.0 points)
For example, the fixed costs for the t-shirt company might look like this:
Rent--$300 per month
Utilities (water and electricity)--$50 per month
Telephone and Internet service--$50 per month
Computer and printer--$1,200 total cost, divided by 60 months total expected use, is $20 per month
Office supplies--$25 per month
4. Add the fixed monthly costs to get the total fixed costs per month. (1.0 points)
TIP: Now you know that your minimum selling price has to be high enough to cover these fixed costs too. You'll calculate your break even point next.
For example, the monthly fixed costs for the t-shirt company would be $445.
5. Calculate the selling price you would need in order to break even if your company sold 100 units of your product or service, using the steps below.
a. Divide your total monthly fixed costs (from question 4 above) by 100. This is the total fixed cost per unit. (1.0 points)
For example, for the t-shirt company, this is $445 divided by 100, which is $4.45.
b. Add the total fixed cost per unit (from 5a above) to the total cost of goods or services sold per unit (from question 2 above). This is the selling price you would need in order to break even if you sold 100 units per month. (1.0 points)
For example, for the t-shirt company, this is $14.25 plus $4.45, which is $18.70. This means the t-shirt company would need a selling price of at least $18.70 to break even if it sold 100 shirts.
6. Calculate the number of units you would need to sell in order to break even, using a selling price of your choice. Use the steps below.
a. Choose a selling price that is higher than your total cost of goods or services sold per unit (the amount from question 2 above) but that is different from the selling price from question 5b above. Pick a price you think is reasonable. (2.0 points)
For example, the t-shirt company might decide that it is reasonable to price the shirts at $20 instead of $18.70.
b. Subtract the total cost of goods or services sold per unit (the amount from question 2 above) from the selling price. This is the gross profit per unit. (1.0 points)
For example, the t-shirt company would take its $20 price and subtract $14.25, which leaves $5.75.
c. Divide the total monthly fixed costs by the gross profit from 6b above. This tells you how many units you must sell to break even. (1.0 points)
For example, the t-shirt company would take its $445 monthly costs and divide that number by $5.75, which is 77.4. The company would round that number up to 78, so it would have to sell 78 shirts per month at the $20 price to break even.
7. Describe two things you could emphasize about your product in order to help make it attractive to your target market. What makes you think these things matter to this target market? (2-8 sentences. 2.0 points)
8. Identify a competitor to your company and find out what their prices are for similar products or services. Do you want your prices to be higher, lower, or the same as your competitors? Why? (2-6 sentences. 2.0 points)
9. Will your company use cost-based markup, or retail-based markup? Why? (2-5 sentences. 2.0 points)
10. Do you think the demand for your product will be elastic or inelastic? Why? (2-5 sentences. 2.0 points)
11. Describe at least one pricing strategy you will use and explain why you think it will be effective. (2-5 sentences. 3.0 points)
Answers
Answer:
Variable costs are expenses that vary in proportion to the volume of goods or services that a business produces. In other words, they are costs that vary
Step-by-step explanation:
i need help with this question please
Answers
Answer:
A polyhedron with 6 faces and 8 vertices has 12 edges.
Step-by-step explanation:
Euler Formula is given in the problem:
F + V = E + 2We are told that the polyhedron has 6 faces (F = 6) and 8 vertices (V = 8). The only unknown variable in Euler's Formula now is E = number of edges.
Substitute the known variables into the formula and solve for E.
6 + 8 = E + 2 14 = E + 2 12 = E E = 12A polyhedron with 6 faces and 8 vertices has 12 edges.
Number of faces = 6
Number of vertices = 8
Formula used:
Euler's formula:
F + V - E = 2
F = Number of Faces of Polyhedron
V = Number of Vertices of Polyhedron
E = Number of Edges of Polyhedron
Calculations:
Let the polyhedron have E edges,
6 + 8 - E = 2
14 - E = 2
E = 14 - 2
E = 12
Therefore:
The Polyhedron has 12 edges
Mrs. Li classroom is 24 ft wide and 40 ft long what is the area of the classroom
Answers
What is the approximate volume of a cylinder with a radius of 3 centimeters and a height of 4 centimeters?
Use 3.14 for π and round the answer to the nearest tenth.
Answers
Answer:
113.04 cm
Step-by-step explanation:
Answer:113
Step-by-step explanation:
please help and ty if u do <33
Answers
Answer:
[tex]3^{-5} =\frac{1}{3^{5} } = (\frac{1}{3} )^{5}[/tex]
[tex]5^{-3} = \frac{1}{5} *\frac{1}{5} *\frac{1}{5} = \frac{1}{5*5*5}[/tex]
Step-by-step explanation:
15 and 1/15 do not equal anything.
Hope this helped!
Determine the linear function of the line that goes through the points (2; 6) and
(6; 5).
(1) = −6,50 + 0,50;
(2) = 0,25 − 6,50;
(3) = 6,50 − 0,25;
(4) = −0,65 − 0,25x
Answers
Answer:
[tex]y=6.50-0.25x[/tex]
Step-by-step explanation:
[tex]\textsf{let}\:(x_1,y_1)=(2,6)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(6,5)[/tex]
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-6}{6-2}=-0.25[/tex]
Point-slope form of linear equation: [tex]y-y_1=m(x-x_1)[/tex]
(where m is the slope and (x₁, y₁) is a point on the line)
Substituting the found slope and a point on the line:
[tex]\implies y-6=-0.25(x-2)[/tex]
[tex]\implies y-6=-0.25x+0.5[/tex]
[tex]\implies y=-0.25x+6.5[/tex]
Rearranging the equation to match the answer options given:
[tex]\implies y=6.50-0.25x[/tex]
Edwin was evaluating the expression below when a = 3 and b = -6
Answers
Answer:
D
Step-by-step explanation:
[tex] {3}^{2} - 18 + 4( - 6) \\ 9 - 18 + ( - 24) \\ - 9 + ( - 24) \\ = - 33[/tex]
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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Evaluate the expression a²-18+4b when a=3 and b=-6
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
Substitute 3 in lieu of a and -6 in lieu of b:-
(3)²-18+4(-6)
9-18+4(-6)
On further simplification,
9-18-24
[tex]\dashrightarrow\bigstar\boxed{\boxed{\underline{\bold{-33}}}}\dashleftarrow[/tex]
Good luck.-- - - - - - - - - - - - - - - - - - -- - - ---- - - -- - - - - - - - - - - - - - - - - - - - -- - -
Which name does not apply to the angle pair that is shown.
Answers
Answer:
A. Vertical
Step-by-step explanation:
B. applies because the angles are next to each other, so they are adjacent.
C. applies because these angles add up to 180, so they are supplementary.
D. applies because they are 90° angles, so they are right angles.
So, in the end, the one that is left, and does not apply, is vertical.
Answer:
The answer is A.
Step-by-step explanation:
B: 1 and 2 are adjacent angles as they are adjacent to one another in the figure.
C: 1 and 2 are also supplementary angles because they add up to 180 degrees (90 degrees + 90 degrees).
D: 1 and 2 are also right angles, which is shown in the figure.
However, 1 and 2 are not vertical angles because they are not opposite to one another along the intersection of the lines.
Joanna ate 3/7 of a pizza . Michael ate 2/7 of the pizza
How much pizza did joanna and Michael eat altogether
Answers
Answer:
5/7
Step-by-step explanation:
3+2 is 5 over the same denominator because that's how many slices of pizza there are
Calculate the accumulated amount after 3 years, if R5 000 is invested at an interest rate of 10% compounded quarterly?
Answers
Answer:
R6,724.44 or so I think that's right
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &3 \end{cases} \\\\\\ A=5000\left(1+\frac{0.10}{4}\right)^{4\cdot 3}\implies A=5000(1.025)^{12}\implies A\approx 6724.44[/tex]
NO LINKS!!! Please help me with this graph part 3a
Answers
Answer:
g(x) = -|x| - 8
Step-by-step explanation:
Finding the values of a, h, and k :
a = slope of the line
a = -10 + 8 / 2 - 0a = -2/2a = -1h = any horizontal shift (left/right)
As it lies on the y-axis, we can conclude no horizontal shift has taken placeh = 0k = vertical shift (up/down)
It has shifted 8 units downk = -8Forming the equation :
⇒ g(x) = (-1)|x - 0| - 8
⇒ g(x) = -|x| - 8
Answer:
[tex]\large{\boxed{\sf y = -1|x-0| -8}}[/tex]
Explanation:
Absolute value of a graph formula:
y = a |x -h| + kIdentify the vertex : (h, k) = (0, -8)
Take two points: (0, -8), (1, -9)
[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-9-(-8)}{1-0} \ \ = \ \ -1[/tex]
Put them together : [tex]\bf y = -1|x-0| -8[/tex]
Find the distance between point P and line I
Line I contains points (3,2) and (7,-1). Point P has coordinated (2,9)
Answers
Answer: 8
Step-by-step explanation: divion
Answer:
Step-by-step explanation:
please answer this question
Answers
Given that the variables are complex numbers, the value of the complex expression [tex]\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}}[/tex] is -2
How to solve the complex expression?The given parameters are:
[tex]\alpha + \beta + \gamma = 0[/tex]
[tex]\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = 0[/tex]
Rewrite the first equation as:
[tex]\alpha + \beta = - \gamma[/tex]
Take LCM in the second equation
[tex]\frac{\alpha + \beta}{\alpha \beta} + \frac{1}{\gamma} = 0[/tex]
So, we have:
[tex]\frac{ - \gamma}{\alpha \beta} + \frac{1}{\gamma} = 0[/tex]
Rewrite as:
[tex]\frac{1}{\gamma} = \frac{\gamma}{\alpha \beta}[/tex]
Multiply through by [tex]\alpha[/tex]
[tex]\frac{\alpha}{\gamma} = \frac{\gamma}{\beta}[/tex]
Inverse both sides
[tex]\frac{\gamma}{\alpha} = \frac{\beta}{\gamma}[/tex]
Make [tex]\beta[/tex] the subject in [tex]\alpha + \beta + \gamma = 0[/tex]
[tex]\beta =-(\alpha + \gamma)[/tex]
So, we have:
[tex]\frac{\gamma}{\alpha} = \frac{-(\alpha + \gamma)}{\gamma}[/tex]
Expand
[tex]\frac{\gamma}{\alpha} = -\frac{\alpha}{\gamma}- 1[/tex]
This gives
[tex]\frac{\gamma}{\alpha} +\frac{\alpha}{\gamma} = - 1[/tex]
Make [tex]\gamma[/tex] the subject in [tex]\alpha + \beta + \gamma = 0[/tex]
[tex]\gamma = -(\beta + \alpha)[/tex]
So, we have:
[tex]\frac{\gamma}{\alpha} +\frac{\alpha}{-(\beta + \alpha)} = - 1[/tex]
Split
[tex]\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}} + \frac{\alpha}{\alpha} = - 1[/tex]
Evaluate the quotient
[tex]\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}} + 1 = - 1[/tex]
Subtract 1 from both sides
[tex]\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}} = - 2[/tex]
Hence, the value of [tex]\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}}[/tex] is -2
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If p varies jointly as q and the cube
of r, and p
= 270 when q = 6 and
r = 3, find p when q = 3 and r = 5.
Answers
Answer:
625
Step-by-step explanation:
p= Kqr³
where K is the constant
K = p/qr³ = 270/6•3³
K= 5/3
p = 5/3• qr³
p = 5/3• 3• 5³
p = 5⁴
p= 625
Hope it helps! :)
Please help !!! 50 points!!!!!!
Answers
Step-by-step explanation:
I could not see the entire question
if the question was 6√5²×6√5³×6√5⁴
the answer would be 5√5
if the question was 6√5²×6√5³×6√5
without exponent 4
5²×5³×5=15625
6√15625
the answer will be 5
When Maddy was born, her aunt opened a certificate of deposit in her
honor to help send her to college some day. Now at the age of 18, there is
$39,322 in Maddy's account. How much did her aunt originally invest if
the interest rate was 5.5%? Round to the nearest dollar.
Answers
Given the final amount of money available in Maddy's account, the interest rate and the time elapsed, the initial money her aunt invested was $15,000.
What is an interest in banking?Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.
The formular for calculating compound interest is expressed as;
A = P(1 + r/n)^(n*t)
Where A is final amount, P is initial principal balance, r is interest rate, n is number of times interest applied per time period and t is number of time periods elapsed.
Given the data in the question;
Interest rate r = 5.5% anuually = 5.5/100 = 0.055Final amount A = $39,322 Time r = 18 yrsInitial principal balance P = ?We substitute our given values into the expression above.
$39322 = P(1 + 0.055/1)^(1*18)
$39322 = P(1 + 0.055)^(18)
$39322 = P(1.055)^(18)
P = $39322 / (1.055)^(18)
P = $39322 / 2.621466
P = $15,000
Therefore, given the final amount of money available in Maddy's account, the interest rate and the time elapsed, the initial money her aunt invested was $15,000.
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Help me solve equations
2=2+g/4
Answers
Answer:
g = 0.Step-by-step explanation:
Solve:
2 = 2 + g/4g/4 = 2 - 2= g/4 = 0.g = 0.Answer is g = 0.[tex]\rule{250}{2}[/tex]
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Solve 2=2+g/4
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
When solving an equation, we need to make sure all variables are on the left-hand side, and all numbers are on the right.
Since we have numbers on both sides, we need to move them to one side, as follows:-
[tex]\Longrightarrow\sf{2-2=g/4}[/tex]
[tex]\longrightarrow\sf{0=g/4}[/tex]
Now, we multiply by 4 on both sides to get rid of the fraction:-
[tex]\longrightarrow\sf{0\times4=g/4\times4}[/tex]
[tex]\longrightarrow\sf{0=g}[/tex]
So we conclude that g=0.
Good luck with your studies.
[tex]\rule{300}{3}[/tex]