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]
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Answers
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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.
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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
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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
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Step-by-step explanation:
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Step-by-step explanation:
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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
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Class: ________frequency
0−<5 __________ 0.179
5−<10 __________ 0.168
10−<15 _________ 0.174
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Answers
Answer:
1) 1/3
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3) 35/99
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Answers
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Step-by-step explanation:
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Answers
Answer:
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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
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Answers
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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
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This property is true
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Answers
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Step-by-step explanation:
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Answers
Answer:
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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}
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
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Answers
Answer:
yes yesss yessssssssssssssssssssssssssssssssssss
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17+(-28
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Answers
Answer:
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Step-by-step explanation:
thats the answer
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Answers
Answer:
Gina reads 30 pages per day.
Step-by-step explanation:
120 / 4 = 30
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Answer:
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Step-by-step explanation:
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