Step-by-step explanation:
4x-2y = 9 ...1
2x-y = -6 ...2
if ...2 × 2
4x-2y = -12
9 is not equal to -12
Will mark brainliest
Using the given definition and [tex]\Delta x=\frac{0-(-2)}n=\frac2n[/tex], we have
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \sum_{i=1}^n \left(7\left(-2+\frac{2i}n\right)^2 + 7\left(-2+\frac{2i}n\right)\right) \frac2n \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac2n \sum_{i=1}^n \left(14 - \frac{42i}n + \frac{28i^2}{n^2}\right)[/tex]
Recall the well-known power sum formulas,
[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + 9 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]
Reducing our sum leads to
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \frac2n \left(\frac{7n}3 - 7 + \frac{14}{3n}\right) = \lim_{n\to\infty} \left(\frac{14}3 - \frac{14}n + \frac{28}{3n^2}\right)[/tex]
As [tex]n[/tex] goes to ∞, the rational terms containing [tex]n[/tex] will converge to 0, and the definite integral converges to
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \boxed{\frac{14}3}[/tex]
if a rectangular piece of metal has 27.75 square inches what is the length and width?
We cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations.
What are the dimensions of a rectangular piece of metal?
By geometry we know that the area of the piece of metal is equal to the product of its length and width, then we must find two real numbers such that:
l · w = 27.75, where l, w > 0.
Unfortunately, we cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations. We need at least one equation to find an unique solution.
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I really need your help ASAP!
Answer:
Option 4
Step-by-step explanation:
See the attached image.
Amanda works as a waitress. She earns $50 a day plus 75% of the tips her customers leave.(The rest of the tips go to the kitchen
staff and bussers.) The table of values represents Amanda's earnings on different days. Write a linear equation that represents
the relationship between earnings and tips.
Tips ($)
20.00
50.00
100.00
Total Earnings ($)
65.00
87.50
125.00
The linear equation that represents the relationship between earnings and tips will be y = 0.75x + 50.
What is a linear equation?The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Working as a waitress is Amanda. She receives $50 every day in addition to 75% of the tips her clients leave.
Let 'x' be the tip amount and 'y' be the total earning.
y = 0.75x + 50
Check:
At (20,65), then we have
65 = 0.75(20)+50
65 = 15+50
65=65
At (50,87.5), then we have
87.5 = 0.75(50)+50
87.5 = 37.5+50
87.5=87.5
At (100,125), then we have
125 = 0.75(100)+50
125 = 75+50
125=125
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Find the solution of the system of equations
shown on the graph.
Answer: (0,6)
Step-by-step explanation:
The solution is where the graphs intersect.
Colby needs to wash the windows on the second floor of a building.
He only has a 12 ft ladder and because of dense shrubbery, he hasto put the base of the ladder 5 feet from the building. How many feet above the ground would the windows need to be in order for Colby to reach them with his 12 ft ladder?
If the length of ladder is 12 feet then the height of windows from the ground is 10.91 feet.
Given that the length of ladder is 12 feet and the base is 5 feet.
We are required to find the height of the windows from the ground.
When we graph all the things like ladder and all that we will get a right angled triangle.
We can find the height of window by using pythagoras theorem.
Pythagoras theorem says that the square of the hypotenuse is equal to sum of squares of base and perpendicular of right angled triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex]
P=[tex]\sqrt{H^{2} -B^{2} }[/tex]
Height of wall=[tex]\sqrt{12^{2} -5^{2} }[/tex]
=[tex]\sqrt{144-25}[/tex]
=[tex]\sqrt{119}[/tex]
=10.908
After rounding off it will be 10.91 feet.
Hence if the length of ladder is 12 feet then the height of windows from the ground is 10.91 feet.
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need heeeelp please
Answer:
[tex]\dfrac{3x+6}{x^2+x-6}[/tex]
Step-by-step explanation:
Notice that we can factor the expression [tex]x^2-x-2[/tex] as [tex](x-2)(x+1)[/tex]. Similarly, we can express [tex]3x+3[/tex] as [tex]3(x+1)[/tex]. Now, we can multiply the fraction together as [tex]\dfrac{(x+2)(3)(x+1)}{(x-2)(x+1)(x+3)} = \dfrac{3(x+2)}{(x-2)(x+3)} = \boxed{\dfrac{3x+6}{x^2+x-6}}[/tex].
Consider the following figure:
The value of a is
Answer:
125
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation according to this information and that will help us find the value of x:
65 + 60 = x add like terms
125 = x is the answer we are looking for.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{equation:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\huge\textsf{solving:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\large\textsf{60 + 65 = a}[/tex]
[tex]\huge\textsf{simplify it:}[/tex]
[tex]\large\textsf{a = 125}[/tex]
[tex]\huge\textsf{therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{a =} \frak{125}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
which theorem can be used to show that LJKL is the same as LMNP
a. AA similarity
b. SSS similarity
c. ASA similarity
d. SAS similarity
Which of the following statements is equivalent to 10x – 30? 10(x – 30) 10(x – 3) 10 + (x – 20) 10(x – 20)
Answer:
10(x-3) is equivalent to 10x – 30
Step-by-step explanation:
First you have to take everything of out the parentheses and then simplify if needed.
10(x – 30) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 30 is 300. So, 10(x – 30) is not equivalent to 10x – 30.10(x – 3) is equivalent to 10x – 30 because, 10 times x is 10x, and 10 times 3 is 30. So, 10(x – 3) is equivalent to 10x – 30.10 + (x – 20) is not equivalent to 10x – 30 because, 10 minis 20 plus x are -10 + x. So, 10+(x – 20) is not equivalent to 10x – 30.10(x – 20) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 20 is 200. So, 10(x – 20) is not equivalent to 10x – 30.Answer: 10(x-3) is equivalent to 10x – 30
A pail holds 3 1/2 gallons of water. How much is this in cups?
What is the equation of the line described below in slope-intercept form?
The line passing through point (-1, 5) and parallel to the line whose equation is x + y = 10
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]x + y = 10\implies y = -x+10\implies y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+10 \leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so, we're really looking for the equation of al ine whose slope is -1 and that passes through (-1 , 5)
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}( ~~ x-\stackrel{x_1}{(-1) ~~ }) \\\\\\ y-5 = -(x+1)\implies y-5=-x-1\implies y=-x+4[/tex]
CAN SOMEONE HELP PLEASE!
Answer:
None of these
Step-by-step explanation:
[tex]\frac{360}{n}=24 \implies n=15[/tex]
This is called a pentadecagon.
(a+b)² - 11(a+b) -42
pls show the work
Answer:
(a+b)² - 11(a+b) -42
Step-by-step explanation:
Thoughtfully split the expression at hand into groups, each group having two terms,
Group 1: -11b-11a
Group 2: a2+2ab
Group 3: b2-42
Pull out from each group separately :
Group 1: (a+b) (-11)
Group 2: (a+2b) (a)
Group 3: (b2-42) (1)
Looking for common sub-expressions :
Group 1: (a+b) (-11)
Group 3: (b2-42) (1)
Group 2: (a+2b) (a)
final answer:(a+b)² - 11(a+b) -42
Answer:
(a+b+3)(a+b-14)
Step-by-step explanation:
let a+b be x,
= x²-11x-42
=x²-(14-3)x-42
=x²-14x+3x-42
=x(x-14)+3(x-14)
=(x+3)(x-14))
replacing x by a+b,
=(a+b+3)(a+b-14)
Melissa is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Melissa has been adding money. Suppose that x and y are related by the equation y = 550+20x.
Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?
Check the picture below.
Solve the inequality for x.
OA.
X S
5- 2/2 x ²
x 2
28
OB. x ≤ 7
OC.
28
9
OD. x ≥ 7
The solution to the inequality x-13<=7+4x is x >= -20/3
How to solve the inequality?The inequality expression is given as:
x-13<=7+4x
Add 13 to both sides of the inequality
x <= 20 + 4x
Subtract 4x from both sides of the inequality
-3x <= 20
Divide both sides of the inequality by -3
x >= -20/3
Hence, the solution to the inequality x-13<=7+4x is x >= -20/3
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Complete question
Solve the inequality for x
x-13<=7+4x
Brandon enters bike races. He bikes 91 half miles every1 half hour. Complete the table to find how far Brandon bikes for each time interval.
Help,
Using proportions, it is found that he bikes:
19 miles in one hour.28.5 miles in one and a hour.38 miles in two hours.47.5 miles in two and a hours.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the proportion is that he bikes 9.5 miles each half hour, hence:
In one hour, he bikes 2 x 9.5 = 19 miles.In one and a half hour, he bikes 3 x 9.5 = 28.5 miles.In two hours, 4 x 9.5 = 38 miles.In two and a half hours, he bikes 5 x 9.5 = 47.5 miles.More can be learned about proportions at https://brainly.com/question/24372153
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8 ft
10 ft
20 ft
A trapezoid has a height of 10 feet,
and base measurements of 20 feet and
8 feet. What is the area?
[?] square feet
Hint: The formula for the area of a trapezoid is: (b₁b2). h
Enter
ग
15
The area of the trapezoid is 140 square feet
What are areas?The area of a shape is the amount of space on that shape
How to determine the area of the trapezoid?The dimensions of the trapezoid are given as:
Height = 10 feet
Parallel bases = 8 feet and 20 feet
The area of a trapezoid is calculated using
Area = 0.5 * (Sum of parallel bases) * Height
Substitute the known values in the above equation
Area = 0.5 * (8 + 20) * 10
Evaluate the equation
Area = 140
Hence, the area of the trapezoid is 140 square feet
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If 4 out of 7 students at
Johnson High play sports,
about how many of the 504
students at the school play
sports?
[tex]\frac{4}{7}(504)=\boxed{288}[/tex]
What is the smallest odd number of using 9,3,6,8,1,9
Answer: well one is
Bc its the smallest besides zero, but zero is neither odd or even
Step-by-step explanation:
F(v) =2x if g(x)=5x then f(g(x)
Answer:
10x
Step-by-step explanation:
g(x)=5x
f(x)=2x
f(g(x))=f(5x)
f(g(x))=2*5x=10x
The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and point A is reflected across the x-axis to obtain point C. What are the coordinates of points B and C?
B(2, 3) and, C(−2, −3)
B(−2, −3) and C(2, 3)
B(2, −3) and C(−2, 3)
B(−2, 3) and C(2, −3)
Answer: B(2, -3) and C(-2, 3) which is choice 3
Further Explanation:
The rule for a y-axis reflection is [tex](\text{x}, \text{y}) \to (-\text{x}, \text{y})[/tex] meaning the x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.
Therefore, point A(-2,-3) moves to B(2, -3) when reflecting over the y-axis.
A similar rule is [tex](\text{x}, \text{y}) \to (\text{x}, -\text{y})[/tex] to describe an x-axis reflection. This time the y coordinate flips in sign, and the x coordinate stays the same.
In this case, we move from A(-2,-3) to C(-2, 3)
The graph of all three points is shown below. I used GeoGebra to make the graph, but Desmos is another option. I also recommend graphing by hand on graph paper to get practice that way if possible.
Perform the following mathematical operation, and report the answer tot he correct number of significant figures 0.396/0.5
Answer:
answer 0.8
Step-by-step explanation:
Solution
0.396 has 3 significant digits
0.5 has 1 significant digit.
Therefore the answer should be 1 significant digit.
0.396 / 0.5 = 0.792
Rounded to 1 sig dig, the answer = 0.8
Line passes through the point (8,4) and a slope of 5/4. Write equation in slope-intercept
Answer:
Step-by-step explanation:
y - 4 = 5/4(x - 8)
y - 4 = 5/4x - 10
y = 5/4x - 6
what is the solution I need help
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
Square root of numbersThe square root of numbers is is expressed using the square root sign. In order to determine the square root os 0.15 given, we need need to determine the square of perfect square before and after the given number.
For the square root of √0.09
√0.09 = 0.3
Similarly for the square root of √0.16
√0.16 = 0.4
Since the resulting value is 0.3 and 0.4, hence the square root of 0.15 must be between these two values on the number line.
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
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The length and width of a rectangle must have a sum of 60. Find the dimensions of the rectangle that will have the maximum area. [Hint: Let x and 60-x be the length
and width. The area can be described by the function f(x)=x(60-x).]
The length is… and the width is…
If the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
Given that the sum of length and breadth of rectangle is 60.
We are required to find the dimensions of the rectangle that will have the maximum area. Area is basically how much part of surface is being covered by that particular shape or substance.
Let the length of rectangle be x.
According to question the breadth will be (60-x).----2
Area of rectangle=Length *Breadth
A=x(60-x)
A=60x-[tex]x^{2}[/tex]
Differentiate A with respect to x.
dA/dx=60-2x
Again differentiate with respect to x.
[tex]d^{2} A/dA^{2}[/tex]=-2x
-2x<0
So the area is maximum because x cannot be less than or equal to 0.
Put dA/dx=0
60-2x=0
60=2x
x=30
Put the value of x in 2 to get the breadth.
Breadth=60-x
=60-30
=30
Hence if the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
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Determine if the series converges or diverges. If the series converges, find its sum.
9
Σ n(n+3)
n=1
OA. The series diverges.
OB. The series converges to
11
2
7
OC. The series converges to
2
D. The series converges
15
-
2
The true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges
How to determine if the series diverges or converges?The series is given as:
[tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex]
Take the limit of the function to infinity
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)}[/tex]
This gives
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * (\infty +3)}[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * \infty}[/tex]
Evaluate the product
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty}[/tex]
Evaluate the quotient
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = 0[/tex]
Since the limit is 0, then it means that the series diverges
Hence, the true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges
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Answer:
B. The series converges to [tex]\displaystyle{\frac{11}{2}}[/tex].
Step-by-step explanation:
Before evaluating the infinite series, the expression can be decomposed as the sum of two fractions (partial fraction decomposition) as follows.
Let [tex]\textit{A}[/tex] and [tex]\textit{B}[/tex] be constants such that
[tex]{\displaystyle{\frac{9}{n\left(n+3\right)}}}} \ \ = \ \ \displaystyle{\frac{A}{n} \ \ \ + \ \ \frac{B}{n+3}}[/tex]
Multiply both sides of the equation by the denominator of the left fraction,
[tex]n\left(n+3\right)[/tex], yielding
[tex]9 \ \ = \ \ A\left(n+3\right) \ \ + \ \ B \-\hspace{0.045cm} n[/tex]
Now, let [tex]n \ = \ 0[/tex], thus
[tex]\-\hspace{0.2cm} 9 \ \ = \ \ A\left(0 + 3\right) \ + \ B\left(0\right) \\ \\ 3 \-\hspace{0.035cm} A \ = \ \ 9 \\ \\ \-\hspace{0.11cm} A \ \ = \ \ 3[/tex].
Likewise, let [tex]n \ = \ -3[/tex], then
[tex]\-\hspace{0.5cm} 9 \ \ = \ \ A\left(-3 + 3\right) \ + \ B\left(-3\right) \\ \\ -3 \-\hspace{0.035cm} B \ = \ \ 9 \\ \\ \-\hspace{0.44cm} B \ \ = \ \ -3[/tex]
Hence,
[tex]\displaystyle{\sum_{n=1}^{\infty} {\frac{9}{n\left(n+3\right)}}} \ = \ \displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right)[/tex].
First and foremost, write the nth partial sum (first nth terms) of the series,
[tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ - \frac{3}{4} + \ \frac{3}{2} \ - \frac{3}{5} \ + \frac{3}{3} \ - \frac{3}{6} \ + \frac{3}{4} \ - \frac{3}{7}} \\ \\ \\ \-\hspace{3.58cm} + \ \displaystyle{\frac{3}{5} \ - \ \frac{3}{8} \ + \ \frac{3}{6} \ - \ \frac{3}{9} \ + \ \frac{3}{7} \ - \ \frac{3}{10}} \\ \\ \\ \-\hspace{3.58cm} + \ \ \dots[/tex]
[tex]+ \ \ \displaystyle{\frac{3}{n-3} \ - \ \frac{3}{n} \ + \ \frac{3}{n-2} \ - \ \frac{3}{n+1}} \\ \\ \\ \ + \ \frac{3}{n-1} \ - \ \frac{3}{n+2} \ + \ \frac{3}{n} - \ \frac{3}{n+3}}[/tex].
Notice that the expression forms a telescoping sum where subsequent terms cancel each other, leaving only
[tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ + \ \frac{3}{2} \ + \frac{3}{3} \ - \ \frac{3}{n+1}} - \ \frac{3}{n+2} \ - \ \frac{3}{n+3}}}[/tex].
To determine if this infinite series converges or diverges, evaluate the limit of the nth partial sum as [tex]n \ \rightarrow \ \infty[/tex],
[tex]\displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \lim_{n \to \infty} \left(\displaytstyle{\frac{11}{2} \ - \ \frac{3}{n+1} \ - \ \frac{3}{n+2} \ + \ - \ \frac{3}{n+3}\right) \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2} \ - \ 0 \ - \ 0 \ - \ 0} \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2}[/tex]
Simplify [tex]\frac{6a^2 b^-^2}{8a^-^3 b^3}[/tex] Assume a≠0 and b≠0
Answer:
sorry i thought i knew it
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
using the rules of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] : nm > n
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] : n > m
[tex]\frac{6a^2b^{-2} }{8a^{-3b^3} }[/tex] ← separate the variables
= [tex]\frac{6}{8}[/tex] × [tex]\frac{a^2}{a^{-3} }[/tex] × [tex]\frac{b^{-2} }{b^3}[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2-(-3)}[/tex] × [tex]\frac{1}{b^{3-(-2)} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2+3}[/tex] × [tex]\frac{1}{b^{3+2} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{5}[/tex] × [tex]\frac{1}{b^{5} }[/tex]
= [tex]\frac{3a^{5} }{4b^{5} }[/tex]
1+r+r²+...........+r^n+1=1-r^n/1-r
mathematical induction mesthod
Answer + Step-by-step explanation:
the correct question:
For r ≠ 1 ,Prove using the mathematical induction method that :
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
………………………………………………………………………………………………………………
for n = 0 :
1⁰ = 1 and (1 - r⁰⁺¹)/(1 - r) = (1 - r)/(1 - r) = 1
Then the property is true for n = 0.
For n ≥ 0 :
Suppose
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
And prove that
[tex]1+\cdots+r^{n+1} =\frac{1-r^{n+2}}{1-r}[/tex]
Since :
[tex]1+\cdots+r^{n+1} =(1+\cdots+r^n)+r^{n+1}[/tex]
Then
[tex]1+\cdots+r^n+r^{n+1} =\frac{1-r^{n+1}}{1-r}+r^{n+1}[/tex]
[tex]= \frac{1-r^{n+1}+r^{n+1}(1-r)}{1-r}[/tex]
[tex]= \frac{1-r^{n+2}}{1-r}[/tex]
Then according to the mathematical induction method
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
Where n is a natural number and r ≠ 1.
Please help! Which linear system has this matrix of constants? `[[12],[11],[4]]` A, B, C, or D
IMAGE ATTACHED
Check the picture below.