The correct answer is "lim n rightarrow infinity xn/n! = 0 for all values of x."
To determine whether the series an is absolutely convergent, conditionally convergent, or divergent, we need to apply the appropriate tests. One possible test to use is the ratio test, which compares the absolute value of consecutive terms. Applying the ratio test to the series an, we get:
|an+1/an| = |(3cos(n+1))/(n+1)| ≤ 3/|n+1|
Since the limit of 3/|n+1| as n approaches infinity is zero, the series an is absolutely convergent by the ratio test.
Moving on to the second part of the question, we want to determine for what values of x the series xn/n! is convergent. This series is also known as the power series for e^x. The series converges for all x, which means the correct answer is "x ge 0 for all x."
Finally, we are asked to draw a conclusion about the limit of xn/n! as n approaches infinity. Using the ratio test, we can show that this limit is zero for all values of x.
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For the first series, we have:
an = 2, 6cos(1), 18cos(2), 54cos(3), ...
We can use the ratio test to determine whether this series is absolutely convergent, conditionally convergent, or divergent:
|an+1/an| = 3|cos(n+1)/cos(n)|
Since the cosine function oscillates between -1 and 1, the ratio |an+1/an| is not bounded as n goes to infinity. Therefore, the series is divergent.
For the second question, we want to find the values of x such that the series
xn/n! = x/1! + x^2/2! + x^3/3! + ...
is convergent. This is the power series expansion of the exponential function e^x, so the series converges for all real values of x. Therefore, the answer is "x ge 0 for all x".
For the third question, we can use the ratio test to find that the limit of xn/n! as n goes to infinity is zero for all values of x. Therefore, the answer is "lim n rightarrow infinity xn/n! = 0 for all values of x".
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The library has 65400 art books and 9600 science books. What part of all the books are art. The fraction in the answer must be irreducible
Answer:
6.8125
Step-by-step explanation:
i goggled itttttt
Answer:
9,600/75,000, 16/125
Step-by-step explanation:
art+science=75000
9600
75000 =16/125
Travis, Devon, and Ramon have 17, 20, and 26 trading cards, respectively. Every minute, one of the three boys gives away two of his trading cards such that the other two boys get one trading card each. What is the shortest amount of time, in minutes, that it could take for the three boys to each have an equal number of trading cards?
We can start solving this problem by using the concept of greatest common divisor (GCD). The GCD of 17, 20, and 26 is 1, which means that the three numbers are relatively prime to each other. This means that there is no common divisor of the three numbers other than 1.
Since the trading cards are given away in pairs, we need to divide the GCD by 2, which gives us 0.5. This means that it would take half a minute for the three boys to each have an equal number of trading cards.
However, half a minute is not possible as time cannot be measured in fractions of a minute. Therefore, it is not possible for the three boys to have an equal number of trading cards in the shortest amount of time, because the numbers are relatively prime.
Answer: 5 minutes. ✅
PLEASEEEE GIVE BRANLIEST
y varies directly as the square root of x
y=11 when x=4
Express y as a function of x.
What is the value of x when y=44?
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
An= (4+3n^2)/(n+5n^2)
Lim n-> An =
To determine whether the sequence converges or diverges, we can use the Squeeze Theorem.
We can see that
[tex]4/(n + 5n^2) < = An < = (4 + 3n^2)/(n + 5n^2)[/tex]
As n tends to infinity, [tex]4/(n + 5n^2)[/tex] tends to 0 and[tex](4 + 3n^2)/(n + 5n^2)[/tex] tends to[tex]4/(5n^2)[/tex] which also tends to 0.
So by the Squeeze Theorem, we can say that An tends to 0 as n tends to infinity. Hence the limit of the sequence is Lim n-> An = 0
We can also see that the numerator of An is a constant and the denominator is a polynomial with degree 2. Since the denominator's degree is greater than the numerator, the limit will be zero as n -> infinity.
Therefore, the sequence converges to 0.
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Hallie and Mattie donated blue jeans to the clothing drive. Hallie donated 2 pairs of blue jeans. Mattie donated 6 pairs of blue jeans. Write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans.
Answer: your answer is 2:6 or 1:3 simplified
The ratio to represent the relationship between hallies donation of jean and Mattie's donation of jeans is 2:6
2:6 simplified is 1:3
Step-by-step explanation: Hope this helps!! :)))
What is the common denominator of Y +( y 3 3 in the complex fraction y +( y 3 3 )/ 5 9 2 3y?
The common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y) is 5y + 6.
What makes it a denominator?The Latin word "nomen," which also appears in words like "nominate" and "nomenclature," is the root of the English word "denominator," which means "name." And that's essentially what a fraction's denominator does: it "names" or denotes the kind of fraction that is specified by the numerator (the top part).
How to calculate common denominator?step1
{y + [(y - 3)/3]}/(5/9 + 2/3y)
multiply and divide with ‘9y'
9y/9y.{y + [(y - 3)/3]}/(5/9 + 2/3y)
9y.y + 9y.y - 3/3 / 9y(5/9) + 9y(2/3y)
9y.y + 3y(y - 3) / 9y(5/9) + 9y(2/3y)
9y.y + 3y(y - 3) / y.5 + 9y.2/3y
9y2 +3y2 -9y / 5y +6
12y2 - 9y / 5y + 6
The denominator will be 5y + 6
step2
The common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y) is 5y + 6.
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exact solution:
y =?
m=?
n =?
W=?
Approximate Solution
y =?
m =?
n?
W=?
Exact solution are - 1.2, -1, -0.1, 0.75 and approximate solution are -0.012, -0.01, -0.001, 0.0075.
What is exact and approximate solution?
The solution that has no uncertainly is known as exact solution. On the other hand, the solution that has some confusion is termed as approximate solution.
What are the exact and approximate solution of the given problem?
exact solution, y = - 1.2
m = - 1
n= - 0.1
w = 0.75
approximate solution in nearest hundredth,
y = - 0.012
m = -0.01
n = - 0.001
w = 0.0075
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Hello! I need help solving this problem #2
Solving the provided questions, we can say that the exponential growth for the provided data will be 11.
What is exponential growth?The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially. The exponential function has the formula f(x)=abx where a and b are positive real values. Sketch exponential functions using the app below for different values of a and b. Describe verbally how modifying a and b changes the graph's form.
the growth rate will be
n(3) = [tex]85e^{0.l8(3)}[/tex]
n(3) = 145.86
[tex]85e^{0.l8(t)} = 600\\e^{0.l8(t)} = 7.059\\ln[e^{0.l8(t)}] = ln[7.059]\\0.18(t) = ln[7.059]\\\\t = 10.86 = 11[/tex]
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Identify a claim made by Sae and explain the reaoning underlying thi claim. Lit at leat two piece of upporting evidence from the paage, and briefly explain how they upport the claim you have identified in tak 1
As consumerism is wiping out American society, Sasse claims that young people have based their achievements and achievements on material goods.
He said parents influenced this by creating a population of young people who are empty in spirit and who will lead American society to grow without direction and positioning.
To support this claim, he provides details on how the country did not encouraged the children to have experiences, conquer and walk their paths, thereby resisting consumerism and presenting the rewards of hard work.
What is the central idea of the Vanishing American Adult?
Sasse tried to explore the causes of a generation that can't grow up in "The Vanishing American Adult" and offers a path for raising children to be active and engaged citizens.
He identifies core formative experiences that all young people should pursue: hard work to appreciate the benefits of labor, travel to understand deprivation and want, the power of reading, the importance of nurturing your body, and how parents can encourage them, and explains how they can be encouraged.
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$39.20 = 0.49m divided by 0.49
Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or theorem you used
Answer:
I can't comment, but we can't see what we are supposwd to bw doing
Without using a calculator, determine between which two integers the following surds lie (1)√5 (2) √1 (3)√107 (4)√3
Answer:
Step-by-step explanation:
Please help as soon as possible!!!
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1.
Answer:One
Step-by-step explanation:
What is StartFraction 4 Over 6 EndFraction divided by StartFraction 3 Over 12 EndFraction
The quotient is:__
PLS HELP ME IT'S A ASSIGNMENT!!!!!!
The quotient between the two fractions will give:
(4/6)÷(3/12) = 8/3
How to solve the quotient between two fractions?Here we want to find the quotient between the fractions 4/6 and 3/12.
The quotient between any two fractions a/b and c/d can be solved as:
(a/b)÷(c/d) = (a*d)/(b*c)
Then our quotient can be solved in the following way as:
(4/6)÷(3/12) = (4*12)/(3*6)
(4*12)/(3*6) = (48/18)
Now we can simplify that fraction, if we divide both numerator and denominator by 2, we will get:
24/9
Now we can divide both by 3, then we will get the simplified fraction:
8/3.
That is the correct answer.
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Answer: The answer is 2 2/3
Step-by-step explanation: I got it right on edge
What is the area of 8 cm triangle?
The area of a (equilateral) triangle with side 8cm is 16√3cm^2.
What is a triangle and its types?
A figure which has a three-sided closed figure is called a triangle.
Types
Equilateral Triangle
A triangle where all the sides are the same is called an equilateral triangle.
Isosceles Triangle
When two of the sides of a triangle are the same it’s called an isosceles triangle. It’s a hard one to spell, but an easy one to recognize!
Scalene Triangle
In our last triangle, none of the sides have the same length, so this is called a scalene triangle.
Acute Triangle
when the largest angle in the triangle is less than 90, that is an acute triangle. Just remember that acute angles are less than 90 degrees.
Right Triangle
When the largest angle is exactly 90 degrees. You might remember that a 90-degree angle is a right angle, so this triangle is a right triangle.
Obtuse Triangle
When largest angle is more than 90 degrees, this is an obtuse angle, so we call this triangle an obtuse triangle.
Area of an equilateral triangle whose side is 8 cm is √3/4*a^2 where
a=8
= √3/4*8^2
= √3/4*64
= √3*16
Area=16√3
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NEED HELP WITH BOTH. I WILL GIVE BRAINLIST
Find the missing length
Answer
2 =1
3=1.4
Step-by-step explanation:
hb=2A
b=2·5
10=1
hb=2A
b=2·14
20=1.4
Step-by-step explanation:
2 .) Using Pythagorean Theorem,
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]5^{2}+ 10^{2} = c^{2}[/tex]
[tex]25 + 100 = c^{2}[/tex]
[tex]125 = c^{2}[/tex]
[tex]\sqrt{125}= c[/tex]
[tex]11 . 18 = c[/tex]
3.) Using Pythagorean Theorem,
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]a^{2} + 14^{2} = 20^{2}[/tex]
[tex]a^{2}= 20^{2}- 14^{2}[/tex]
[tex]a^{2} = 400 - 196\\a^{2} = 204[/tex]
[tex]a = \sqrt{204}[/tex]
[tex]a = 14.28[/tex]
Please solve this for me and show steps that would be a big help!
Answer:
bagel: $3OJ: $2Step-by-step explanation:
You want the price of a bagel and a can of OJ if 2 bagels and 1 can costs $8, and 3 bagels and 2 cans cost $13.
EquationsYou can write an equation for the value of each purchase. The cost of a bagel can be represented by 'b', and 'j' can be used for the cost of an orange juice.
2b +1j = 83b +2j = 13SolutionThe coefficients of j are related by a factor of 2, so we can make the sum of coefficients of j be zero if we subtract the second equation from 2 times the first:
2(2b +1j) -(3b +2j) = 2(8) -(13)
b = 3 . . . . . . . . . . . . . . simplify
Now, we can use this value in the first equation to find j:
2(3) +1j = 8
1j = 2 . . . . . . . . . subtract 6
A bagel costs $3, and a can of orange juice costs $2.
19 Nimra buys a 3 kg box of sweets for £17.60
She puts the sweets into bags to sell.
Each bag contains 150g of sweets.
Nimra fills as many bags as possible.
She will sell each bag for the same price.
Nimra wants to make a profit of at least 35%
Assuming she sells all the bags,
? what is the lowest price Nimra should charge for each bag?
£
(5)
The lowest price that would yield a profit of 35% is 1.18.
What is profit and loss?A product is sold at a profit if the price is higher than the cost price. When a product is sold for less than what it costs to produce, the seller suffers a loss.
Each bag contains 150g of sweets.
The total number of bags filled with a total of 3kg sweets can be calculated as follows:
3kg = 3000g
Number of bags = [tex]\frac{3000}{150}[/tex] = 20 bags
Profit is given by the following formula:
[tex]P= \frac{SP - CP }{CP} * 100[/tex]
The Cost price, CP = 17.60 and profit is 35%, substitute the value in the formula above:
[tex]35 = \frac{SP - 17.60}{17.60} *100\\ \\\frac{(35)(17.60)}{100} = SP - 17.60\\\\6.16 = SP -17.60\\\\6.16 + 17.60 = SP\\\\SP= 23.76[/tex]
Find the cost of each 30 bags as follows:
[tex]1 \text { bag} = \frac{23.76}{20}\\ \\1 \text { bag} = 1.18[/tex]
Hence the lowest price that would yield a profit of 35% is 1.18.
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Match each function formula with the corresponding transformation of the parent function y= - (x+ 2)^2
Answer:
Step-by-step explanation:
1-6
3-2
4-1
Convert 100 in. to yards, feet, and inches.
?1 yd. 1 ft. 4 in.
?4 yd. 2 ft. 2 in.
?4 yd. 0 ft. 4 in.
?2 yd. 2 ft. 4 in.
The measure of 100 inches is given by the equations ,
100 inches = 2.77778 yards
100 inches = 8.33334 feet
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 100 inches be equation (1)
Now , the measure of 1 inch = 0.08333 feet
So , the measure of 100 inches = 100 x measure of 1 inch
Substituting the values in the equation , we get
The measure of 100 inches = 8.33334 feet
And , 1 inch = 0.0277778 yard
So , the measure of 100 inches = 2.77778 yards
Hence , the measure of 100 inches is 8.33334 feet
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find the measures of thr angles of a right triangle where one of the two acute angles measurres 8 times the other
The two angle of the right triangle are found as 30 degrees and 60 degrees.
Define the term acute angles?Less than 90 degrees is considered an acute angle. Right angles have a 90 degree angle. More than 90 degrees is found in obtuse angles.
Let one acute angle be 'x'.Then, the other actue angle will be '2x'One of the angle of right angles triangle is 90 degress.By using angle sum property of right angle triangle:
x + 2x + 90 = 180
3x = 90
x = 30 (one angle)
2x = 60 (Other angle)
Thus, the two acute angle of the right triangle are found as 30 degrees and 60 degrees.
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What type of function is f/x )= x 3?
The type of function which f(x)=x^3 is the cubic function.
What is a cubic function?
A cubic function is a function in mathematics where the variables x can take on real values and the coefficients a, b, c, and d are complex numbers. In other words, it is a real function as well as a polynomial function of degree three.
F(x) = x³ denotes the "basic" cubic function. It is depicted in the graph below. The greatest power over the x variable(s) in a cubic function is 3. The graph can be made "wider" or "skinnier" by the coefficient "a," or it can be reflected (if the value is negative): The graph's y-intercept serves as the constant "d" in the equation.
A cubic function equation is of the form f(x) = ax³ + bx² + cx + d, where a, b, c, and d are constants (or real numbers) and a ≠ 0.
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-74f = -6,142 solve for f
Determining the cause of the problem, characterizing the problem, identifying, prioritizing, and choosing potential solutions, as well as putting the solution into action, all have values of 83 for f.
What is the value of f ?-74 f = -6,142 ⇒ f = -6,142 / -74 ⇒f = 83 .
One-step equations can be solved using any one of the following four methods: adding, subtracting, multiplying, or dividing. Both sides of an equation will stay equal if the same integer is added to both sides. A mathematical expression should be evaluated according to a rule known as the order of operations.
The PEMDAS acronym can help us recall the following in that order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (from left to right). A balance scale is like an equation. The scale (or equation) will become out of balance if we add or subtract from one side. Mathematical equations must ALWAYS be balanced such that both sides are equal when the equation is completed.
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Circumference question #1 if you are good at this I’ll be posting each question! 10 points per question
Write two different equivalent forms of
the expression 2*x+3
On solving the question, The polynomial is 2x + 3 the equivalent forms are (4x- 2x + 3), (x + x +2 +1)
What is Equivalent Forms ?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Equivalent systems refer to sets of equations with the same solution. We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.
When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.
The polynomial is 2x + 3
The equivalent forms are (4x- 2x + 3), (x + x +2 +1)
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What is aspect ratio formula?
The aspect ratio is the proportional connection between the width of a video image compared to its height. It is usually expressed as width: height (separated by a colon), such as 16:9 or 4:3. The aspect ratio sets how wide a video is formatted and acts on how it will fit on your viewing screen.
When it comes to shooting video, the aspect ratio is tied to what resolution the camera records the image size in, with most DSLRs recording in a 16:9 aspect ratio.
The most popular aspect ratios for videos on the web are:
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How do you find C?? Thank you!
The value of c would be 4.
What are similar triangles?
Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, the angles of similar triangles are congruent (congruent means the angles are equal in measure) and the corresponding sides are in proportion.
In the given figure, ΔGHF and ΔGDE,
∠G ≅ ∠G ---- Common angle
Side GH ≅ Side GH ---- Corresponding side
∠F ≅ ∠E -----Each 90°
so ΔGHF ~ ΔGDE-----ASA Test
sides of similar triangles are in proportion
GH/HF = GD/DE
5/c=10/8
c=5*8/10
c = 4
Hence, the value of c would be 4.
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natalia orders 5 chocolate chip cookies for every 2 sugar cookies.She needs 42 cookies in all. Chocolate chip cookies cost $1.50 each and sugar cookies cost $0.75 each. How much will natalie spend in all on her cookies?
Therefore , the solution of the given problem of unitary method comes out to be $54.
A unitary method is defined.A single or distinct unit variable is referred to as being "unitary". Therefore, the goal of this technique is to define values in favor of a finite unit. For instance, the unitary method can be used to calculate how many kilometers a car will travel on one litre of gas if it goes 44 on two.
Here,
Given :
In place of every two sugar cookies, Natalie orders five chocolate chip cookies.
In total, she needs 42 cookies. Each sugar cookie costs $0.75, while each chocolate chip cookie costs $1.50.
thus ,
total cost is : 30 * 1.50 + 0.75*12
=> 54
Therefore , the solution of the given problem of unitary method comes out to be $54.
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4. Find the equation of opened downward parabola which contains the points (0,5), (2,5), and (-2,-5).
Equation of opened downward parabola is (x - 1) ²= - 4/5 (y - 25/4)
What is parabola?Parabola is a curve created by the intersection of a cone and a plane. Generally, parabola is U shaped and either open in downward or opened in upward direction.
What will be the equation of opened downward parabola contains the points given in question?
The formula for opened downward parabola is given by (x - h) ² = - 4p (y - k)
as the parabola contains the points (0, 5) (2, 5) and (- 2, -5)
so, the equation can be (0 -h) ² = - 4p(5 - k) [ put the value (0, 5)]
h² = - 20p+4pk ..... equation 1
while putting the value (2, 5) we have the equation of parabola.
(2 - h) ² = - 4p(5 - k)
4 - 4h + h ² = - 20p + 4pk .... equation 2
from the equation 1 and 2, the right-hand side is similar.
hence, 4 - 4h +h² = h²
4 = 4h
h = 1
put h =1 in the equation 1 we get, 1 = - 20p + 4pk .... equation 3
when we put the value ( -2, -5) in the formula.
(- 2- h) ² = - 4p ( -5 -k)
( -2 -1) ² = 20p +4pk
9 = 20p +4pk ....... equation 4
from equation 4 and equation 3
we get, 9 = 20p +4pk
1 = - 20p+ 4pk
- + -
solve by addition method and we get, 8 = 40p
p = 1/5
from h = 1 and p = 1/5 we get the value of k from equation 3
1 = - 20/5 + 4/5k
k = 25/4
now the equation of opened downward parabola will be.
(x - 1) ² = - 4/5 (y - 25/4)
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What are the 4 steps to solve an equation?
The 4 steps to solve an equation:
Identify the terms and coefficients in the equation.Use inverse operations to isolate the variable.Check your answer by substituting the value back into the original equation.Interpret the solution within the context of the problem.How to solve an equation?When solving an equation, the first step is to identify the terms and coefficients in the equation. This means looking for any constants, variables, and coefficients and understanding their relationship to one another. Once the terms have been identified, inverse operations such as addition, subtraction, multiplication, and division can be used to isolate the variable and solve for the unknown. After the equation has been solved, it is important to double check the answer by substituting the answer back into the original equation. If the equation is still true, then the answer is correct. Finally, the solution must be interpreted within the context of the problem. This means determining the meaning of the answer and how it can be used to solve the overall problem.Learn more about equations: https://brainly.com/question/22688504
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