Answers
Answer:
L = 7/6 , and the correct option is B, the series diverges.
Step-by-step explanation:
Here we have that:
[tex]an = \frac{(3n + 3)*7^n}{6^{n+4}}[/tex]
Now we want to see the quotient test, then we need to do find the value of the quotient as n tends to infinity. Then we first need to find the quotient:
[tex]a(n + 1)/a(n) = \frac{(3(n + 1) + 3)*7^{n + 1}}{6^{n + 1 + 4}}*\frac{6^{n + 4}}{(3*(n) + 3)*7^{n}}[/tex]
We can simplify the right part to get:
[tex]\frac{(3(n + 1) + 3)*7^{n + 1}}{6^{n + 1 + 4}}*\frac{6^{n + 4}}{(3*(n) + 3)*7^{n}}= \frac{(3n + 3 + 3)*7^{n + 1}}{6^{n + 5}}*\frac{6^{n + 4}}{(3*n + 3)*7^{n}}[/tex]
[tex]\frac{(3n + 3 + 3)*7^{n + 1}}{6^{n + 5}}*\frac{6^{n + 4}}{(3*n + 3)*7^{n}}= \frac{(3n + 3 + 3)*7}{(3*n + 3)*6}[/tex]
Now we want to find the limit of this as n goes to infinity, we can see that both parts will tend to infinity, then we need to use the Lhopital rule and find the limit of the quotient of the first derivatives.
The first derivatives are:
For the denominator: (3*6)
For the numerator: (3*7)
Then we need to find the limit as n goes to infinity to:
[tex]\frac{3*7}{3*6} = \frac{7}{6}[/tex]
But this does not depend on the value of n, then the limit is just 6/7.
L = 7/6
And 7/6 > 1.
Then we can conclude that our series diverges.
Related Questions
A cable company uses the formula S = 20,000 (1 + 0.08)y to estimate the number
of subscribers, S, that use their service after y years. If there were 20,000 cable
television subscribers when the cable company began, what is the meaning of the
expression (1 + 0.08)Y?
A. Every year the number of subscribers is estimated to increase by 8 over the number
of subscribers the year before.
B. Every year the number of subscribers is estimated to increase by 8% of the original
20,000 subscribers
C. Every year the number of subscribers is estimated to increase by 8% over the
number of subscribers the year before.
D. Every year the number of subscribers is estimated to increase by 80% of the
original 20,000 subscribers.
I
Answers
Answer:
C. Every year the number of subscribers is estimated to increase by 8% over the
number of subscribers the year before.
Step-by-step explanation:
Using the formula :
S = 20,000 (1 + 0.08)^y to estimate ;
S = number of subscribers ; y = years
The expression : (1 + 0.08)^y
0.08 = 0.08 * 100% = 8%
(1 + 0.08)^y represents a continous growth or increase in the number of subcsribers by 8% over the number of subscribers the preceeding year
Find the variables
a/k+b=c/k find k
Answers
Answer:
[tex]k=-\frac{a}{b}+ \frac{c}{b}[/tex]
Step-by-step explanation:
[tex]\frac{a}{k}+b = \frac{c}{k}\\\frac{a}{k}- \frac{c}{k} = -b\\\frac{1}{k}(a-c)=-b\\a-c=-bk\\k=-\frac{a}{b}+ \frac{c}{b}[/tex]
Forty percent of the 70 buttons in the box had 5 holes
a. What fraction of the buttons did not have 5 holes?
b. How many buttons did not have 5 holes?
Answers
Answer: a. 0.6
b. 42 buttons
Step-by-step explanation:
a. What fraction of the buttons did not have 5 holes?
Since forty percent of the 70 buttons in the box had 5 holes, the number of buttons in the box that doesn't have 5 holes will be:
= 100% - 40%
= 60%
= 60/100
= 0.6
b. How many buttons did not have 5 holes?
This will be:
= 60% × 70
= 0.6 × 70
= 42 buttons
Help please! Thank you!!!!!!!!!!!!!!!!!
Answers
Answer:
[tex]7m\\ 322m^{2}[/tex]
Step-by-step explanation:
What is the value of x?
o 3
o 6
o 10
o12
Answers
Answer:
x = 6
Step-by-step explanation:
Sum of all the angles of a kite = 360
∠W + ∠Y + ∠V = 360
18x - 2 + 12x + 2 + 90 + 90 = 360 {Combine like terms}
18x + 12x -2 + 2 + 90 +90 = 360
30x + 180 = 360
30x = 360 - 180
30x = 180
x = 180/30
x = 6
Find m<YQR pls need grade gud.
Answers
Answer:
21°
Step-by-step explanation:
We can prove these two triangles congruent by the HL (Hypotenuse-Leg) theorem. Then, we know that m<YQR is congruent to m<PQY. We can then use their given values to form an equation.
5x+6=16x-27
Continue to solve . . .
33 = 11x
x=3
Therefore, we can plug this value of 3 into the expression for the value of m<YQR, and you will get
(16 x 3) - 27, which is equal to 21°.
The diameter of the wheels on xavires bicycle is 80 cm . Calculate the circumference of the wheels
Answers
Answer:
80*3.14
Step-by-step explanation:
let diameter d=80cm
circumference c = d*pi = d*3.14 = 80*3.14
(04.05)
The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k? (1 point)
A. 3
B. 7
C. 10
D. 13
Answers
Answer:
i think that is is 10 please make me brainliest
Step-by-step explanation:
Beyonce is solving a system of equations: 2x – 3y = -2
4x + y = 24
She decides to use the elimination method to find the solution. She multiplies the second equation by 3 and adds it to the first equation to find 14x = 70, showing her that x = 5. Beyonce finds that y = 4.
Step 3: 4x + y = 24
4(5) + y = 24
20 + y = 24
-20 -20
y = 4
Step 1: 3(4x + y = 24) → 12x + 3y = 72
Step 2: 2x – 3y = -2
Solution: (5, 4)
+ 12x + 3y = 72
14x = 70
→ x = 5
Thinking about this process, Beyonce says out loud, “There are lots of ways I could go about solving this problem. I could do the method above or I could multiply the first equation by -2 and add the second.
Step 3: 4x + y = 24
4x + 4 = 24
-4 -4
4x = 20
x = 5
Step 1: -2(2x – 3y = -2) → -4x + 6y = 4
Solution: (5, 4)
Step 2: -4x + 6y = 4
+ 4x + y = 24
7y= 28
→ y = 4
“I seem to find that there is only one solution to the two equations, but I wonder if I will get the same solution if I use a different method?”
If Beyonce uses a different method, would she get the same solution? Be sure to show work or explain your reasoning.
Answers
Answer:
Step-by-step explanation:
I have to solve this: (2x + 2/5)+(5x-4/5) and then simplify it.
Answers
Answer:
35x - 2
———————
5
i hope this helps
Step-by-step explanation:
Answer:
7x + 6/5 or 7x + 1 1/5
Step-by-step explanation:
Ya welcome.
what is the answer for this
Answers
Answer:
∠B = 141
Step-by-step explanation:
n - > number of sides
n = 7
Sum of all interior angles = (n -2 ) * 180
= 5 * 180 = 900
∠B + 148 + 90 + 142 + 130 + 129 + 120 = 900
∠B + 759 = 900
∠B = 900 - 759 = 141
What is the percent equivalent to 3/2?Use a pattern like the one in the table to support your answer
Answers
Solve the inequality: y - 18 < 55
Answers
Answer:
y < 73
Step-by-step explanation:
y−18+18<55+18
y < 73
The area of a rectangle is 14 square units. It has side lengths a and b. Given the following values for a, find b.
a=4 1/5
Answers
ab = 14
(21/5)b = 14
b = 14(5/21) = 10/3 = 3⅓
What is the variables in the expression
x2 + y - 2 - 16
Answers
Answer:
The variables in your equation are x and y;
the numbers in your equation are 2, -2, and -16
The value of 3 expo3 + 4 expo2
Answers
Answer:
43
Step-by-step explanation:
[tex]3^{3}[/tex]+[tex]4^{2}[/tex]=
Solve:
[tex]3^{3}[/tex]= 3*3*3= 9*3= 27
[tex]4^{2}[/tex]= 4*4= 16
Then add them together:
27+16= 43
Hope this helps!
2. Which equation is equivalent to 2 + 4x = 5 - 3(x + 1)? A. 2 + 4x = 2x - 3 B. 2 + 4% = 5 - 3 -3. C. 6x = 5-(+ 1). D. 2 + 4 = 2/5 1).
Answers
Answer:
B) 2 + 4x = 5 - 3 - 3x
Step-by-step explanation:
By simplifying JUST the right side and re-arranging them
2 + 4x = 5 - 3(x + 1),
2 + 4x = 5 - 3x -3,
2 + 4x = 5 -3 - 3x
Describe how you know whether an equation will be true for all values of x or true for no values of x.
Answers
Answer:
Substitute your answer for the variable x. If the equation looks accurate or is correct, then the value of x is the right answer. Not sure if this makes sense
Determining whether an equation is true for all values of x or true for no values of x requires simplifying the equation, determining its domain, checking for variable restrictions, and evaluating the equation for different values of x.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Simplify the equation as much as possible using algebraic manipulations such as combining like terms, factoring, and expanding.
Evaluate the equation for a few different values of x to see if it holds true. If the equation is true for all values of x within the domain, then it will be true for all values of x. If there are any values of x within the domain that make the equation false, then it will be false for no values of x.
If the equation cannot be simplified or the domain cannot be determined, then it may require further analysis, such as graphing or using calculus techniques to determine its behavior.
Thus, determining whether an equation is true for all values of x or true for no values of x requires simplifying the equation, determining its domain, checking for variable restrictions, and evaluating the equation for different values of x.
Learn more about the equation here:
brainly.com/question/10413253
#SPJ2
Javier was training for a half-marathon and ran a total of 260 miles. If he ran exactly 8 1/8 miles each day how many days did it take him to run 260
Answers
Answer:
32 days
Step-by-step explanation:
260 ÷ 8 1/8 =
convert the fraction to a decimal
1 ÷ 8 = 0.125
260 ÷ 8.125 = 32
A bag is filled with red,blue,and green marbles.
Red-70
Blue-120
Green-60
Marble is pulled out of random from the bag. What REDUCED fraction and percent represent the probability that the marble will be green?
HELPpppppp!!!!
Answers
Prob of green = 60/250
Reduced fraction = 6/25
Percentage = 24%
Add the integers.
-6 + (-4) =( ?
B-2
C 2
D 10
Answers
Answer:
-10
Step-by-step explanation:
Triangle QRS has the angle measures shown.
What is the measure of the obtuse angle?
m2Q=(1x)
mZR= (3x)
m25 = (6x)
O 18
54
108
© 216
Answers
Answer:
108 degrees
Step-by-step explanation:
Given the following angle measures in triangle QRS
m<Q = 1x
m<R = 3x
m<S = 6x
Note that the largest angle is the obtuse angle since they are always greater than 90 and less than 180 degrees
The sum of angle in a triangle is 180 degrees
m<Q + m<R + m<S = 180
1x + 3x + 6x = 180
10x = 180
x = 180/10
x = 18
The obtuse angle is 6x
Measure of the obtuse angle = 6x
Measure of the obtuse angle = 6(18)
Measure of the obtuse angle = 108 degrees
Hence the measure of the obtuse angle is 108 degrees
Why is 40x-16 not equivalent?
Please help (i’m in 7th grade)
Answers
Answer:
40x-6 is not equivalent because 16 is not a multiple of 40
Step-by-step explanation:
if you write the multiples of 4o you will see that 16 is not one of them so that means 40x-16 is not equivalent
* Indique 4 ejemplos
en los cuales aparezca
un nivel de medicion diferente
Answers
Answer:
1. En las competencias de atletismo se miden los kilómetros que se van a correr.
2.Al comprar tela en un almacén te dicen cuántos metros quieres.
3.En la obra los arquitectos y diseñadores miden las distancias que hay entre paredes para poder saber cuánta pintura se les va en la decoración.
4.Al cambiar una puerta tenemos que medir la altura y el ancho del hueco donde va a irinstalada.
Given b(x) - 1X+4. what is b(-10)?
-10
-6
6
14
Answers
Answer:
D. 1×10⁻⁸ M
Explanation:
[H⁺] [OH⁻] = 10⁻¹⁴
(1×10⁻⁶) [OH⁻] = 10⁻¹⁴
[OH⁻] = 1×10⁻⁸
Indicate below whether the equation in the box is true or false.4/8 = to 6/10
Answers
Answer:
Not equal. So, false.
Step-by-step explanation:
Just cross multiply
40 and 48
so no, they're are not equal.
Answer:
False
Step-by-step explanation:
Part
The point (-3, 6) is on a line with a slope of 4. What are all the points you would also find on the line.
Answers
Step-by-step explanation:
THANK YOU AND PLZ MARK AS BRAINLY AND GIVE RATING ALSO
PLSSSSSSSSSS HEEEEEEEEEEEEEEEELLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
\sqrt(x^(2)-14x+49)=x-7
Answers
Answer:
infinite solutions
Step-by-step explanation:
note the expression inside the radical is a perfect square, that is
x² - 14x + 49 = (x - 7)², then
[tex]\sqrt{x^2-14x+49}[/tex] = x - 7
[tex]\sqrt{(x-7)^2}[/tex] = x- 7, that is
x - 7 = x - 7
Since both sides are the same then any value of x will make the equation true.
The equation has infinite solutions
I NEED HELP!! WILL GIVE BRAINLEST!!!
Solve the system below by GRAPHING:
Y=5x-8
Y=1/3x+6
Answers
Answer:
I promise you the app Math. way will save you it will do it for u and show you where to put it on the graph just download it
PLEASE HELP ITS DUE AT 11:59
Solve for the value of y.
(9y-6)° 51°
Answers
Answer:
5
Step-by-step explanation:
This is a right angle which means it is equal to 90. The angle is separated into two parts as shown - the sum of these two parts is equal to 90.
Calculations:
9y - 6 + 51 = 90
9y + 45 = 90
9y = 45
y = 5
habsjsjs jkjk