The radius of Convergence for the function [tex]\frac{\[(-1)^{n} \; x^{n} }{\sqrt[3]{n} }[/tex] is 1.
What is radius of convergence?The radius of the largest disk at the center of the series in which the series converges.
Perform the ratio test for absolute convergence, which says
if [tex]\lim_{n \to \infty} \frac{a_{n}}{a_{n+1}}[/tex] =L
Then,
1) if L<1, the series is absolutely convergent
2) If L>1, the series is divergent
3) If L= 1, apply a different test.
Now, Applying test
[tex]a_{n+1}[/tex] =[tex]\frac{(-1)^{{n+1} } \; x^{n+1}}{\sqrt[3]{n+1} }[/tex]
So,
[tex]\lim_{n \to \infty} \frac{a_{n+1}}{a_{n}}[/tex] = [tex]\lim_{n \to \infty}|\frac{ (-1)^{{n+1} } \; x^{n+1}/\sqrt[3]{n+1} }{ (-1)^{n} \; x^{n} /\sqrt[3]{n} } |[/tex]
= [tex]\lim_{n \to \infty}|\frac{ (-1)^{{n+1} } \; x^{n+1}\sqrt[3]{n}}{ (-1)^{n} \; x^{n} \sqrt[3]{n+1} } |[/tex]
= [tex]\lim_{n \to \infty}|\frac{ (-1) \; x^{n}\sqrt[3]{n}}{ \sqrt[3]{n+1} } |[/tex]
= [tex]\lim_{n \to \infty}\sqrt[3]{\frac{1}{1+\frac{1}{n}} } } |x|[/tex]
Applying the limit n→∞,
= 1 x |x|
= |x|
By ratio test, the given series will be convergent if |x|< 1.
So, the radius of Convergence = 1
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8 tenths + 34 hundredths =
A 42 tenths
B 42 hundredths
c 114 tenths
D 114 hundredths
Answer:
D
Step-by-step explanation:
114 hundredths
Answer:
42 hundredths
Step-by-step explanation
Normally do 34+8 then add the hundredths since 34 hundredths is the bigger value
Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 24x – 35? 2x – 7 2x 7 3x – 7 3x 7
A factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is 2x - 7
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the polynomial:
f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35
The polynomial can be further simplified to:
f(x) = (2x - 7)(3x³ - 2x + 5)
A factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is 2x - 7
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Answer:
2x-7
Step-by-step explanation:
TLDR verified answer, correct on edge 2023
Jada's property has a shape of a parallelogram with the
dimensions shown. If the perimeter of the property is 300
feet, what is the value of x?
x + 75
X +45
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answer:
Part (a)From inspection of the diagram, the pattern is:
Step 1: 1² + 1
Step 2: 2² + 2
Step 3: 3² + 3
Let x = step number
Let y = total number of squares
Therefore, the equation that represents the relationship is:
y = x² + x
Part (b)x² relates to the large square made up of small squares (top part of the image of each step)
x relates to the rectangle of small squares (bottom part of the image of each step)
y is the total number of small squares in the image of each step.
The pattern is
1+14+29+3More simply
1²+12²+23²+3So for an integer n
y=n²+n#b
n² is pair of boxes at top side
n is boxes underneath
How much of your lawn can you mow with
one gallon of gas, if you maintain the rate
of ⅕ gallon of gas per ⅛ of a lawn?
Answer:
5/8
Step-by-step explanation:
1/5 x 5
1
1/8 x 5
5/8
a square pyramid measuring 7 in along each edge of the base with a height of 12 in
Answer:
196 in^3
Step-by-step explanation:
Volume of pyramid = 1/3 base * height
= 1/3 (7x7) (12) = 196 in^3
Shane and Abha earned a team badge that required their team to collect no less than 200020002000 cans for recycling. Abha collected 178178178 more cans than Shane did.
What is the solution set of the inequality?
The solution set of the inequality is represented as [911,∞)
How to find the solution set of the inequality?let
x be the number of cans collected by Shane.
Therefore,
Since, Abha collected 178 more cans than Shane did.
Therefore,
Abha = 178 + x
Hence,
Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.
Therefore,
x + 178 + x ≥ 2000
2x + 178 ≥ 2000
2x ≥ 2000 - 178
2x ≥ 1822
x ≥ 1822 / 2
x ≥ 911
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which fraction is equal to 5
4.5x67=
6/5x78=?
20-100=+3,000
Find the solution set of the inequality: 8x+2 > 34
x > or < or >= or =
Inequality are expressions that are not separated by an equal sign. The solution to the given system of equation is x > 4
Inequality functionInequality are expressions that are not separated by an equal sign.
Given the inequality
8x+2 > 34
Subtract 2 from both sides
8x + 2 - 2 > 34 - 2
8x > 32
Divide both sides by 8
8x/8 = 32/8
x > 4
Hence the solution to the given system of equation is x > 4
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Please help this assignment is due in 20 mins!
Jayvalyn is buying milk. She needs 4 liters. A half-liter of milk costs $2.86. A 200-milliliter container of milk costs $1.19. What should Jayvalyn buy so she gets 4 liters at the lowest price?
Answer:
the half liter
Step-by-step explanation:
200 mL :
4,000 mL in 4 liters.
4,000/200=20
20x1.19=23.8
half liter :
4x2=8
8x2.86=22.88
Calculate the value of A please ?
Which angle in this quadrilateral is an obtuse angle?
Angle J
Angle K
Angle L
Angle M
Answer:
Where is the quadrilateral? You haven't inserted a picture.
Is the sequence geometric? If so, identify the common ratio.
5, -25, 125, -625, ...
Please help quickly! Will give points to 1st right answer!
the table below represents a logarithmic function f(x)
The domain of the logarithm function is (0, ∞) and the range of the logarithm function will be (-∞, ∞)
What are domain and range?The domain means all the possible values of the x and the range means all the possible values of the y.
The table is shown below.
Let the logarithm function with the variables x and y. Then we have
y = logₐ x
At x = 25, the value of y will be 2. Then the value of a will be
2 = logₐ 25
2 = 2 logₐ 5
1 = logₐ 5
Then 1 can be written as
1 = log₅ 5
Then on comparing, the value of a will be
a = 5
Then the logarithm function will be
y = log₅ x
Then the domain of the logarithm function is (0, ∞) and the range of the logarithm function will be (-∞, ∞)
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what’s the reason? help
Answer:
adjacent exterior angles
x equals 80
casey sight the top of an 84 foot tall lighthouse at an angle of elevation of 58. if casey is 6 feet tall how far is he standing from the base of the lighthouse
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12y−15x=84
The equation in slope-intercept form is y = (5/4)x + 7.
We have,
The slope-intercept form of a linear equation is given by y = mx + b, where "m" is the slope and "b" is the y-intercept.
To write the equation 12y - 15x = 84 in slope-intercept form, simplify the fractions and solve for y:
12y = 15x + 84
y = (15x + 84) / 12
y = (5x + 28) / 4
y = (5/4)x + 28/4
y = (5/4)x + 7
Thus,
The equation in slope-intercept form is y = (5/4)x + 7.
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Help me find the area here! 6th grade math
63 cm2
hope it helps
you
63 CM answer
The price of a visit to the dentist is $25. If the dentist fills any cavities, an additional charge of $75 per cavity gets added to the bill. If the dentist finds x cavities, what will the cost of the visit be? Write your answer as an expression.
which expression represents 5 times the sum of 24 and 7?
a. 5 x 24 + 7
b. 5 x 24 x 7
c. 5 + 24 + 7
d. 5 x (24 x 7)
e. 5 x (24 +7)
Answer:
e
Step-by-step explanation:
the sum of 24 and 7 is 24 + 7 and multiplying this by 5 gives
5 × (24 + 7)
Answer:
e.
Step-by-step explanation:
24 + 7 = 31
5 * 31 = 155.
Solve by taking a square root: (x + 7)2 - 10
Answer:
2x+4
Step-by-step explanation:
Trust me
Which equation matches this graph?
Answer:
y = 4"x +2
Step-by-step explanation:
We choose negative 4 because the graph lies below the asymptote and we chose positive 2 because the horizontal asymptote is on the positive section of the y axis
The length of a rectangle is "a" inches and the width is 3 inches more than its length. find the perimeter and the area
Answer:
Step-by-step explanation:
Givens
Length = a
Width = a + 3
Formulas
P = 2L + 2w
Area = L * w
Solution
Perimeter
P = 2L + 2w
P = 2*a + 2(a + 3) Remove the Brackets
p = 2a + 2a + 6 Combine
P = 4a + 6
Area
Area = L * w
Area = a (a + 3)
Area = a^2 + 3a
HELP, I WILL GIVE YOU MANY POINTS (60)!
While using a skipping rope, Emily jumps 52 times in 60 seconds. Jumping at this
same rate, how many times does Emily jump in 75 seconds?
Answer:
65 times in 75 seconds
Step-by-step explanation:
52 × 75 = 3,900
3,900 ÷ 60 = 65
What is the circumference of a circle that has a diameter of 12 feet?
Solve the following system of equations. Show all work and solutions.
y = 3x^2 + 6x + 4
y = −3x^2 + 4
Answer:
y = 4, x = 0
y = 1, x = -1
Step-by-step explanation:
[tex]y = 3 {x}^{2} + 6x + 4[/tex]
[tex]y = - 3 {x}^{2} + 4[/tex]
[tex] \: [/tex]
Since both of them are equal to y, we can just equate them and solve.
[tex] \: [/tex]
[tex]3 {x}^{2} + 6x + 4 = - 3 {x}^{2} + 4[/tex]
[tex]3 {x}^{2} + 6x + 4 + 3 {x}^{2} - 4 = 0[/tex]
[tex]6 {x}^{2} + 6x = 0[/tex]
[tex]6x(x + 1) = 0[/tex]
[tex]6x = 0[/tex]
[tex]x = 0[/tex]
[tex] \: [/tex]
[tex]x + 1 = 0[/tex]
[tex]x = - 1[/tex]
[tex] \: [/tex]
[tex]for \: x = 0[/tex]
[tex]y = 3( {0})^{2} + 6(0) + 4[/tex]
[tex]y = 4[/tex]
[tex] \: [/tex]
[tex]for \: x = - 1[/tex]
[tex]y = 3( { - 1})^{2} + 6( - 1) + 4[/tex]
[tex]y = 1[/tex]
[tex] \: [/tex]
[tex]values \: of \: x \: and \: y \: for \: the \: system \: of \: equations \: are[/tex]
y = 4, x = 0
y = 1, x = -1
The system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).
What is a system of equation?A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
The first equation given as,
y = 3x² + 6x + 4
The second equation given as,
y = -3x² + 4
Equate the value of y from both equation as,
3x² + 6x + 4=-3x²+4
3x²+3x²+6x+4-4=0
6x²+6x=0
6x(x+1)=0
x=0:x=-1
Put these values of x, in first equation,
y = 3(-1)^2 + 6(-1) + 4
y = 3 - 6 + 4
y=1
Put 0 on the place of x,
y = 3(0)^2 + 6(0) + 4
y = 0 +0+ 4
y=4
Thus, the system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).
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Which graph represents the function?
f(x)=x(x+2)
Answer:
The bottom graph on the right, check the image below:
Explanation:
Substitute the x value with 1,
f(1)=1(1+2)=3
f(2)=2(2+2)=8
f(-1)=-1(-1+2)=-1
f(-2)=-2(-2+2)=0
Can a right triangle have the side lengths 4 mm, 13 mm, and 10 mm?
Justify your reasoning.
Answer:
No, because the given values do not produce a correct equation when plugged into the Pythagorean Theorem.
Step-by-step explanation:
To solve this question, we can use the Pythagorean Theorem. (Also called Pythagoras Theorem)
The Pythagorean Theorem is true for ALL right triangles, meaning that if the side lengths don't work for it, the given triangle can not be a right triangle.
The theorem simply states that the sum of the squares of the two legs must add up to the square of the hypotenuse.
Note that the hypotenuse of a triangle is the side opposite to the right angle.
The Pythagorean Theorem can be easily written as the following expression:
a^2+b^2=c^2
This is where a and b are the legs and c is the hypotenuse.
We can plug our given values in to see if it's correct.
If it is a right triangle, the longest side will always be the hypotenuse, so we can safely set c as 13.
4^2+10^2=13^2
Simplify to see if it's true
16+100=169
116≠169
Therefore, a right triangle can not have these given side lengths.
Hope that helps, please let me know if you have any further questions!
Pleease help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!