Answers
Exact value: [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]
Approximate value: c = 0.08387
Round the approximate value however you need to
==============================================
Work Shown:
Let x = 1+c
[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]
We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.
Each new term is found by multiplying the previous term by 1/x.
Assuming -1 < r < 1 is true, the infinite geometric sum is
[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]
Plug in S = 11 and solve for x
[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]
Use the quadratic formula to find the two solutions
[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]
Using these x values, we find that the corresponding r values are
r = 1/x = 1/(1.08387) = 0.92262
r = 1/x = 1/(-0.08387) = -11.92321
The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387
----------------------------------------------
Using the solution that corresponds to x = 1.08387, we find the value of c is
[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]
Related Questions
please help ??? Thanks
Answers
Answer:
Each y- value is determined by adding 4
Step-by-step explanation:
simply in ratio 20:80
Answers
Answer:
I think the answers could range in anything that are GCF including 2:8
Step-by-step explanation:
Choose the SIMPLIFIED fraction that accurately represents the repeating decimal. (Each of these)
1. 0.333
2.0.454545
3.0.353535
4.242424
5.0.393939
Answers
Answer:
1) 1/3
2) 45/99
3) 35/99
4) 24/99
5) 39/99
Explanation:
1) 0.333 = 0.333/1 = 0.999/3 ≈ 1/3
2) 0.454545 ; 100x ≈ 45.45 ; x ≈ 0.45 ; 45.45-.45 = 45 ; 100x-x = 99 ; x = 45/99
3) 0.354535 ; 100x ≈ 35.35 ; x ≈ 0.35 ; 35.35-.35= 35; 100x-x = 99x ; x = 35/99
4) 0.242424 ; 100x ≈ 24.24 ; x ≈ 0.24 ; 24.24-.24 = 24 ; 100x-x = 99x ; x = 24/99
5) 0.393939 ; 100x ≈ 39.39 ; x ≈ 0.39 ; 24.24-.24 = 24 ; 100x-x = 99x ; x = 39/99
x + 4x + 4 - 8x
please help
Answers
Answer:
The answer is -13x+4
Automated electron backscattered diffraction is now being used in the study of fracture phenomena. The following information is on misorientation angle (degrees).
Class: 0−<5 5−<10 10−<15 15−<20 20−<30 30−<40 40−<60 60−<90
Rel freq: 0.179 0.168 0.174 0.135 0.193 0.071 0.051 0.029
Is it true that more than 50% of the sampled angles are smaller than 15°, as asserted by researchers?
A. Yes, the proportion of sampled angles smaller than 15° is greater than 0.50.
B. Yes, the proportion of sampled angles smaller than 15° is not greater than 0.50.
C. No, the proportion of sampled angles smaller than 15° is greater than 0.50.
D. No, the proportion of sampled angles smaller than 15° is not greater than 0.50.
Answers
Answer: A. Yes, the proportion of sampled angles smaller than 15° is greater than 0.50.
Step-by-step explanation:
Given the data :
Class: _______ relative frequency
0−<5 __________ 0.179
5−<10 __________ 0.168
10−<15 _________ 0.174
15−<20 _________ 0.135
20−<30 _________0.193
30−<40 _________ 0.071
40−<60 _________ 0.051
60−<90 _________ 0.029
Evaluating the proportion of sampled angles less than 15°. This consist of the following classes :
Class: ________frequency
0−<5 __________ 0.179
5−<10 __________ 0.168
10−<15 _________ 0.174
Summing up the relative frequency values :
(0.179 + 0.168 + 0.174) = 0.521
0.521 * 100% = 52.1%
Hence, more than 50% of the sampled angles are smaller than 15°
Gina read 120 pages in 4 days. Which reading rate is equivalent?
Answers
Answer:
Gina reads 30 pages per day.
Step-by-step explanation:
120 / 4 = 30
I hate to ask, but please give me Brainliest. I need it to level up <3.
Answer:
Gina reads 30 pages per day.
Step-by-step explanation:
In the diagram below, lines x and y are parallel. What is the relationship between angle b and e? Write an equation if it help
Answers
Answer:
there is no relationship between the two angles if E switched with D then id say corresponding but theres not
Which set of ordered pairs does not represent a function?
\{(5, -6), (-1, -2), (2, -9), (-8, -2)\}{(5,−6),(−1,−2),(2,−9),(−8,−2)}
\{(-5, 7), (-4, -9), (-5, -4), (2, -6)\}{(−5,7),(−4,−9),(−5,−4),(2,−6)}
\{(-4, 2), (-2, 8), (-1, 6), (5, 6)\}{(−4,2),(−2,8),(−1,6),(5,6)}
\{(2, 2), (-4, 9), (9, -3), (-3, 2)\}{(2,2),(−4,9),(9,−3),(−3,2)}
Answers
Answer:
the 1st, 2nd, and 4th one because those ordered pairs, the y axis is the same . sooo thats what makes it a non function .
Round the numbers to the highest place value.
2 398-
56 254-
71 563-
33 021-
9 645-
Answers
Answer:
[tex]2398 = 2000[/tex]
[tex]56254 = 60000[/tex]
[tex]71563 = 70000[/tex]
[tex]33021 = 30000[/tex]
[tex]9645 = 10000[/tex]
Step-by-step explanation:
Given
[tex]2398[/tex]
[tex]56254[/tex]
[tex]71563[/tex]
[tex]33021[/tex]
[tex]9645[/tex]
Required
Round up to highest place value
[tex]2398[/tex]
Highest place value here is thousand.
So:
[tex]2398 = 2000[/tex], when approximated
[tex]56254[/tex]
Highest place value here is ten thousand.
So:
[tex]56254 = 60000[/tex], when approximated
[tex]71563[/tex]
Highest place value here is ten thousand.
So:
[tex]71563 = 70000[/tex] when approximated
[tex]33021[/tex]
Highest place value here is ten thousand.
So:
[tex]33021 = 30000[/tex] when approximated
[tex]9645[/tex]
Highest place value here is ten thousand.
So:
[tex]9645 = 10000[/tex] when approximated
MY TEACHER TEXTED ME THIS IDK WHAT TO EVEN DO:( help i luv u
Answers
Answer:
yea
same
Step-by-step explanation:
Answer:
well i hope you can figure it out
Step-by-step explanation:
How many subsets of 5 e elements can be made from a set of 7 elements?
Answers
Answer:
seems like this.
Step-by-step explanation:
From set theory, the factorial combinations are 2^N where N are the number of induvidual mambers of the set and that includes the null set. If we require that one element be the minimum to form a set, this eliminates the empty set (and there is only one empty set) so we must subtract one from the formula. The correct answer is therefore 2^N-1. In this case that is 2^5–1 = 31.
I am 15 years old right now. How many years until i turn 18 years old?? I was born on May 9, 2005. If yoi answer this one i will give you brainly
Answers
Find the slope of the line through the pair of points: (6,12) and (-6, -2)
Answers
Answer: The answer would be 1
Step-by-step explanation:
Rise over run or fall over run so the fall is 10 and run is 10 and 10/10 is 1.
5x - 12=18
Solve for x
Answers
Pls mark brainliest
Answer:
x = 6
Step-by-step explanation:
Add 12 to each side, so it now looks like this: 5x = 30Divide each side by 5 to cancel out the 5 next to x. It should now look like this: x = 6I hope this helps!
Check all true statements.
A. For all nonempty sets A, B, C, D, if A x B = C x D, then A = C and B = D.
B. For all sets A, B, the power set of the cartesian product of A and B is the cartesian product of the power sets of A and B. If A={1,2} and B={3} then A x B ={ {1,3}, {2,3} }.
C. The cartesian product has a cancellation property, i.e. if A x B = A x C for some sets A, B, C and A nonempty, then B = C. If A={1,2} and B={3} then A x B ={ (1,3), (2,3) }.
D. The cartesian product is symmetric, i.e. A x B = B x A for all sets A, B. For all sets A, B, the cardinality of A x B is the sum of the cardinalities of A and B.
E. The cartesian product is associative, i.e. (A x B) x C = A x (B x C) =for all sets A, B, C. Both sets are equal to A x B x C.
F. The cartesian product has a cancellation property, i.e. if A x B = A x C for some sets A, B, C, then B = C.
Answers
Step-by-step explanation:
the true statemnts underneath and are in bold letters
-.For all nonempty sets A, B, C, D, if A x B = C x D, then A = C and B = D.
This property is true
-The cartesian product has a cancellation property, i.e. if A x B = A x C for some sets A, B, C and A nonempty, then B = C.
This property is true
- If A={1,2} and B={3} then A x B ={ (1,3), (2,3) }.
if we have 2 non empty sets a and b if we want to get their cartesian product, it is defined as the set of all ordered pairs from a and b
we have A x B to be{(1,3)(2,3)}
therefore this is also true
Express each ratio as a fraction in the simplest form. 12 pennies to 24 pennies
Answers
Answer: 1:2
Step-by-step explanation:
24 ÷ 12 = 2
12 ÷ 12 = 1
Answer to the question is 1:2
to bake 100 of his favorite cookies, Mr.Wallis needs 350 grams of sugar. How many grams of sugar would he need to bake 10 cookies?
Answers
answer:35 grams
explication: because if he need 350 grams of sugar to make 100 cookies , we have to divide 350 by 100 so it gives 35
The number of grams of sugar would he need to bake 10 cookies will be 35 grams.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
To bake 100 of his favorite cookies, Mr.Wallis needs 350 grams of sugar.
Let x be the amount of sugar for 10 cookies.
The number of grams of sugar would he need to bake 10 cookies will be
x / 10 = 350 / 100
x / 10 = 3.5
x = 35 grams
The number of grams of sugar would he need to bake 10 cookies will be 35 grams.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ2
What is the converse of the conditional statement?
If x is even, then x + 1 is odd.
A. If x is not even, then x + 1 is not odd.
B. lf x + 1 is odd, then x is even.
C. If x + 1 is not odd, then x is not even.
D. If x is even, then x + 1 is not odd.
Answers
Answer:
If x+1 is odd, then x is even B
Step-by-step explanation:
Conditional: If p, then q
Converse: If q, then p
p= x being even
q, x+1 being odd.
y=12x^2-9x+4 does this have one two or no solution
Answers
find each sum.
17+(-28
12+(-9)
-2+7
-14+(-10)
-9+(-2)
Answers
Answer:
-2834
Step-by-step explanation:
thats the answer
At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of silk and cotton fabrics for a dress. Silk is $16.90 per yard and cotton is $4 per yard.
Find the solution of the system of equations. Explain or show your reasoning
{x+y=4.25} ; {16.90x+4y=36.35}
Answers
Answer:
The number of yards of silk = x = 1.5 yards
The number of yards of cotton = y = 2.75yards
Step-by-step explanation:
At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of silk and cotton fabrics for a dress. Silk is $16.90 per yard and cotton is $4 per yard.
Find the solution of the system of equations. Explain or show your reasoning
{x+y=4.25} ; {16.90x+4y=36.35}
Let the number of yards of silk = x
The number of yards of cotton = y
We are given the system of equations:
{x+y=4.25} ......Equation 1
x = 4.25 - y
{16.90x+4y=36.35}....... Equation 2
4.25 - y for x in Equation 2
16.90(4.25 - y) + 4y = 36.35
71.825 - 16.90y + 4y = 36.35
71.825 - 36.35 = 16.90 - 4y
35.475 = 12.90y
y = 35.475/12.90
y = 2.75 yards.
The number of yards of cotton = y
{x+y=4.25} ......Equation 1
x = 4.25 - y
x = 4.25 - 2.75
x = 1.5 yards
The number of yards of silk = x = 1.5 yards
The yards of silk bought is 1.49 yards and the yard of cotton bought is 2.76 yards.
The two equations are known as simultaneous equation. They would be solved using elimination method.
x + y = 4.25 equation 1
16.90x + 4y = 36.25 equation 2
where:
x = yards of silk bought
y = yards of cotton bought
In order to determine the value of x, multiply equation 1 by 4.
4x + 4y = 17 equation 3
Subtract equation 3 from 2
19.25 = 12.90x
Divide both sides of the equation by 12.90
x = 1.49 yards
In order to determine the value of y, substitute for x in equation 1
1.49 + y = 4.25
y = 4.25 - 1.49
y = 2.76 yards
To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults
Someone, please help me.
Answers
CAN SOMEONE PLEASE DOUBLE CHECK IF THIS IS RIGHT!!! Please
Answers
Answer:
yes yesss yessssssssssssssssssssssssssssssssssss
6 divided by the sum of x and 4 equals the quotient of 2 and the difference of x and 4
Answers
Answer:
6
Step-by-step explanation:
k bik k,k h
if solving x=8
In each case below, we describe a study to determine whether exercise helps increase certain mood enhancing chemicals in the brain. Indicate whether each describes an experiment or an observational study.
a). Using a random sample of 100 people, we randomly assign half of them to participate in a regular exercise program for a six-week period while the other half makes no changes. At the end of the time period, we measure the brain chemicals.
b). We contact a random sample of 100 people and record how much each person exercises and also measure the chemicals in the brain for each person.
Answers
Answer:
A)Experimental Study
B)Observational Study
Step-by-step explanation:
Observational Study : A study where researchers simply collect data based on what is seen and heard and infer based on the data collected.
Experimental Study: A study which involve the random assignment of -participants into different groups in order to determine the causal effect of a certain condition on a certain outcome .
A) In this case we are randomly classifying the subjects into two groups, where one group participate in a regular exercise program for a six week period, while the other half makes no changes. In this Part we are not observing the data . we are doing experiment over here and comparing those two different groups.
So, By definition It is an experimental study
B) In this case we are recording the data of each person and decision will be based on data
So, By definition It is an observational study
angle 4 and angle 5 are ??? angles will mark brainiest
Answers
Answer:
Alternate interior
Step-by-step explanation:
They are inside making them interior angles and they are on opposite sides making them alternate angles as well.
Hope this helps!
Answer:
alternate interiorStep-by-step explanation:
alternate interior angles are congruent if and only lines are parallel.
∠4 ≅ ∠5
Solve the system of equations 2x-4y=-2 and -x+8y=-23 by combining the equations.
Answers
Answer:
(−9,−4)
Step-by-step explanation:
help plz explain how to use discributive property
Answers
1.Identify the fractions. Using the distributive property, you’ll eventually turn them into integers.
2.For all fractions, find the lowest common multiple (LCM) -- the smallest number that both denominators can fit neatly into. This will allow you to add fractions.
3.Multiply every term in the equation by the LCM.
4.Isolate variables adding or subtracting like terms on both sides of the equals sign.
5.Combine like terms.
6.Solve the equation and simplify, if needed.
What is the slope of the line that passes through the points (1, 1) and (7, 5)?
Answers
Answer:
The slope of the line is
[tex] \frac{2}{3} [/tex]
4/5 of the cake was left, but after Brian ate some only 1/4 of the cake was left. Which fraction of the cake did Brian eat?
Answers
Answer:
3/4
Step-by-step explanation:
there was 4/5 you just had to minis 3and 4