Answers
The new matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 -10 2] and R₂ = [-12 7 -13]
What is a matrix row operationRow operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.
The row operation R₁ - 6 — R₁ will be carried out as follows:
7 - 6 = 1 {row 1 column 1}
-4 - 6 = 5 {row column 2}
8 - 6 = -8 {row column 3}
Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 -10 2] and R₂ = [-12 7 -13]
Read more about matrix here:https://brainly.com/question/28979057
#SPJ1
Related Questions
what are the answers to these questions?
Answers
The values of the expression are,
⇒ x₂ = - 9.4
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Given that;
Expression is,
e²ˣ = - 2x - 1
Hence, Function is,
⇒ f (x) = e²ˣ + 2x + 1 = 0
⇒ f' (x) = 2e²ˣ + 2
Now, By newton's method;
⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))
⇒ x₂ = x₁ - f (x₁) / f' (x₁)
⇒ x₂ = - 5 - (e¹⁰ + 10 + 1)/(2e¹⁰ + 2)
⇒ x₂ = - 5 - (e¹⁰ + 11)/(2e¹⁰ + 2)
⇒ x₂ = - 5 (2.6 + 11) / ( 2 x 2.6 + 2)
⇒ x₂ = - 68 / 7.2
⇒ x₂ = - 9.4
⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))
⇒ x₃ = x₂ - f (x₂) / f' (x₂)
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Thus, The values of the expression are,
⇒ x₂ = - 9.4
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Draw n equally spaced marks between 0 and 1 on each of the x and y axes. Connect the first mark on the x-axis (closest to 0) to the last mark on the y axis (closest to 1), the second mark on the x axis to the second last on the y axis, and so on.
As n increases this process creates a curved boundary, C, as seen in this example diagram. Give an equation for this curve as n → ∞.
Answers
the equation for the curve C as n approaches infinity is y = x This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).
what is diagonal line ?
A diagonal line is a straight line that runs obliquely (at an angle) between two opposite corners of a geometric shape, such as a rectangle or a square. It is called "diagonal" because it connects two non-adjacent vertices of the shape, forming a diagonal across the interior of the shape.
In the given question,
As n increases, the process described in the question creates a set of line segments that connect the equally spaced points on the x-axis to the equally spaced points on the y-axis. The resulting curve is a piecewise linear function that converges to a continuous curve as n approaches infinity.
To derive an equation for this curve, we can start by considering the line segment connecting the first mark on the x-axis to the last mark on the y-axis. Let's call this point (0, 1) and the nth mark on the x-axis (1, 0). The slope of the line connecting these two points is given by:
m = (0 - 1) / (1 - nth mark) = (1 - nth mark)^(-1)
where the nth mark on the x-axis is given by:
nth mark = 1 - (1/n)
Substituting this expression for nth mark into the equation for m, we get:
m = (n/(n-1))
The y-intercept of the line is given by:
b = 1 - m = 1 - (n/(n-1)) = 1/(n-1)
Therefore, the equation for the line segment connecting the first mark on the x-axis to the last mark on the y-axis is:
y = (n/(n-1))x + 1/(n-1)
Similarly, the equation for the line segment connecting the second mark on the x-axis to the second last on the y-axis is:
y = (n/(n-2))x + 1/(n-2)
Continuing this process for all n line segments, we get:
y = (n/(n-k))x + 1/(n-k)
where k = 1, 2, ..., n.
To get the equation for the curve C, we need to take the limit as n approaches infinity. As n goes to infinity, the value of k becomes insignificant compared to n, and we can approximate the equation for the curve as:
y = x
Therefore, the equation for the curve C as n approaches infinity is:
y = x
This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).
To know more about diagonal line , visit:
https://brainly.com/question/9253179?
#SPJ1
Oak and Maple streets are parallel to each other. Main Street has a traffic
light at (5, 1) and is perpendicular to Oak and Maple. What is the equation
of the line representing Main Street?
Oak St.: y =
A. Y
1
22
+3 Maple St.: y = 22
C. y = -2x + 11
B.y=2x-9
D. y = -2x + 15
+6
Answers
The equation of the line representing Main Street is option C. y = -2x + 11
How did we arrive at this equation?The slope of the parallel lines is ½. The Main Street is perpendicular to Oak and Maple. So, the slope of Main Street is -2.
[The product of slopes of perpendicular Lines is -1.)
y - 1 = -2 (x -5)
y - 1 = -2x +10
y = -2x + 10 + 1
y = -2x + 11
Therefore, the best choice is option C. y = -2x + 11
learn more about perpendicular lines: https://brainly.com/question/1202004
#SPJ1
Since Main Street is perpendicular to Oak and Maple, its slope will be the negative reciprocal of the slope of Oak and Maple. Let's first find the equation of Oak Street.
We don't have enough information to determine the equation of Oak Street, so we need to make an assumption about its equation. Let's assume that Oak Street passes through the point (0,3) and has a slope of 2 (since the options suggest that Oak Street has a positive slope).
Using the point-slope form of a line, we have:
y - 3 = 2(x - 0)
y - 3 = 2x
y = 2x + 3
Now we can find the slope of Maple Street by noticing that it is parallel to Oak Street. Since parallel lines have the same slope, Maple Street also has a slope of 2.
To find the equation of Main Street, we need to use the fact that it passes through the point (5,1). Using the point-slope form of a line, we have:
y - 1 = -1/2(x - 5)
y - 1 = -1/2x + 5/2
y = -1/2x + 7/2
Therefore, the equation of the line representing Main Street is y = -1/2x + 7/2. The answer is (D).
If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?
Answers
If you look at the six numbers (101, 203, 407, 512, 98, 642) you can see they range from 98 all the way to 642. the best interval to use for this group be 100.
What is the range?The right interval to utilize for this set of numbers depends on the aim of the analysis.
If we want to look on the single values and small differences between them, then using interval of 10 would be more better. This would give u room to see small changes that exist between adjacent numbers.
So, in the event that we need to look on the full range and distribution of the numbers, an interval of 100 would be more better. This would permit us to see how the numbers are shared over a larger area of values.
Learn more about range from
https://brainly.com/question/26098895
#SPJ1
See full question below
If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?
101, 203, 407, 512, 98, 642
Unit seven geometry and measurement homework to perimeter area of rectangles and parallelograms answer key
Answers
The required maximum area of the rectangle is 17.5m
How to explain the perimeterThe perimeter of a rectangle is = 70m.
We have to find The maximum area of rectangle .
A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four.
Maximum area of rectangle is = 70 / 4
= 17.5
The required value of maximum area of the rectangle is 17.5m.
Learn more about Perimeter on
https://brainly.com/question/19819849
#SPJ1
the perimeter of a rectangle is 70m. What are the dimensions that will produce the maximum area of such a rectangle
Use the quadratic formula to solve -2x^2+2x+1
Answers
The solutions for -2x²+2x+1 are x = 1 + √(3)/2 and x = 1 - √(3)/2.
To use the quadratic formula to solve -2x²+2x+1, we first identify the coefficients a, b, and c of the quadratic equation in standard form: ax²+bx+c=0. In this case, a=-2, b=2, and c=1. We then plug these values into the quadratic formula
x = (-b ± √(b²-4ac)) / 2a
Substituting the values, we get
x = (-2 ± √(2²-4(-2)(1))) / 2(-2)
Simplifying the expression inside the square root
x = (-2 ± √(4+8)) / (-4)
x = (-2 ± √12) / (-4)
Simplifying the radical
x = (-2 ± 2√3) / (-4)
Reducing the fraction
x = (1 ± √3/2)
Therefore, the two solutions are x = (1 + √3/2) and x = (1 - √3/2).
To know more about quadratic formula:
https://brainly.com/question/9300679
#SPJ1
Find the surface area of each composite figure. Use 3.14 for π. Round to the nearest tenth. 12m. 6cm. 6cm. 4cm.
Answers
The Surface area of the composite figure is calculated as approximately: 234 sq. cm
How to Find the Surface Area of a Composite Figure?The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:
Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)
Area of base = area of square = 6 * 6 = 36 sq. cm.
Surface area of the square prism = 2a² + 4ah
a = 6 cm
h = 4 cm
Plug in the values:
Surface area of the square prism = 2(6²) + 4*6*4
= 72 + 96
= 168 sq. cm.
Surface area of the square pyramid = 2bs + b²
b = side length = 6 cm
s = slant height = √(8² + 3²) = 8.5 cm
Plug in the values:
Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.
Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm
Learn more about Surface area on:
https://brainly.com/question/28178861
#SPJ1
Please help confused thank you
Answers
The solution to the inputs of the given function are:
a) f(0) = 13
b) f(2) = -1
c) f(-2) = 27
d) f(1) + f(-1) = 26
How to solve Function Inputs?The set of input values of a function is referred to as the domain of the function. Then, the set of output values of the function is referred to as the range of the function. Thus, if we possess a set of ordered pairs, we can find the domain by listing all of the input values, which are the x-coordinates.
We are given the function:
f(x) = (-x)³ - x² - x + 13
a) f(0) = (-0)³ - (0)² - 0 + 13
f(0) = 13
b) f(2) = (-2)³ - (2)² - 2 + 13
f(2) = -1
c) f(-2) = (2)³ - (-2)² + 2 + 13
f(-2) = 27
d) f(1) = (-1)³ - (1)² - 1 + 13
f(1) = 10
f(-1) = (1)³ - (-1)² + 1 + 13
f(-1) = 16
f(1) + f(-1) = 10 + 16 = 26
Read more about Function Inputs at: https://brainly.com/question/10283950
#SPJ1
A new car sells for 25000 the value of the car decreases by 15% each year what is the approximate value of the car 5 years
Answers
The answer is $11,092.63.
This could be calculated using the proportion. If the value of the car decreases by 15% each year, that means that after each year the value of the car is 85% of the value from the first year.
After 1st year:
$25,000 : 100% = x1 : 85%
x1 = $25,000 · 85% ÷ 100%
x1 = $21,250
After 2nd year:
$21,250 : 100% = x2 : 85%
x2 = $21,250 · 85% ÷ 100%
x2 = $18,062.5
After 3rd year:
$18,062.5 : 100% = x3 : 85%
x3 = $18,062.5 · 85% ÷ 100%
x3 = $15,353.12
After 4th year:
$15,353.12 : 100% = x4 : 85%
x4 = $15,353.12 · 85% ÷ 100%
x4 = $13,050.15
After 5th year:
$13,050.15 : 100% = x5 : 85%
x5 = $13,050.15 · 85% ÷ 100%
x5 = $11,092.63
Therefore, the value of the car 5 years after it is purchased is $11,092.63.
50 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
the answer for this question is x=8
1. A sample of 250 high-school students in a city results in an average number of text messages sent per month of 172.6, with a margin of error of + 4.8. If there are 3000 high-school students in the city, what is the estimated number of text messages sent in a month? between______ and____text messages
Answers
Answer:
Step-by-step explanation:
1) Find the upper bound of the confidence interval:
Upper bound = sample mean + margin of error
= 172.6 + 4.8
= 177.4
2) Find the lower bound of the confidence interval:
Lower bound = sample mean - margin of error
= 172.6 - 4.8
= 167.8
3) Estimate the total number of text messages sent in a month:
Total number of text messages sent = (number of students in the population / number of students in the sample) x sample mean
= (3000 / 250) x 172.6
= 2071.2
Therefore, the estimated number of text messages sent in a month is 2071.2, with a 95% confidence interval between 167.8 and 177.4 text messages.
Answer:
Between 503400 and 532200 text messages----------------------------
Determine the average number of text messages sent per student within the margin of errorFind lower bound:
172.6 - 4.8 = 167.8 text messagesFind upper bound:
172.6 + 4.8 = 177.4 text messages Estimate the total number of text messages for all 3000 studentsLower bound:
167.8 text messages × 3000 students = 503400 text messagesUpper bound:
177.4 text messages × 3000 students = 532200 text messagesThe estimated number of text messages sent in a month for all 3000 high-school students in the city is:
Between 503400 and 532200 text messagesWhat is the maximum possible product of two numbers that have a sum of -8?
Answers
The maximum possible product of two numbers that have a sum of -8 is 16.
How to find the maximum possible product of two numbers that have a sum of -8Let us name the two numbers "x" and "y".
We are aware of the following: x + y = -8
We're looking for the greatest possible product of x and y.
The number we're looking that are as near together as feasible and have a sum of -8.
-4 and -4 are the two numbers that are as near together as possible and have a sum of -8. As a result, x = -4 and y = -4.
The sum of these two figures is:
x * y = (-4) * (-4) = 16
So, the maximum possible product of two numbers that have a sum of -8 is 16.
Learn more about word problems at https://brainly.com/question/21405634
#SPJ1
What is the solution of x=9y and 3y - 3x =24
Answers
Answer:
Step-by-step explanation:
The solution to the system of equations `x=9y` and `3y - 3x =24` can be found by substituting the value of `x` from the first equation into the second equation. This gives us `3y - 3(9y) = 24`, which simplifies to `-24y = 24`. Solving for `y`, we get `y = -1`. Substituting this value of `y` into the first equation, we get `x = 9(-1) = -9`. So the solution to the system of equations is `(x,y) = (-9,-1)`.
Is there anything else you would like to know?
HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
Answers
The number for which the theoretical probability matches the experimental probability is 2.
What is experimental and theoretical probability?
Experimental probability and theoretical probability are two different ways to determine the likelihood of an event occurring.
Experimental probability is determined by performing an experiment or conducting observations and collecting data to see how often an event occurs. This method involves counting the number of times an event occurs and dividing that number by the total number of trials or observations.
Theoretical probability, on the other hand, is determined by using mathematical principles and calculations to determine the likelihood of an event occurring. It is based on the assumption that all outcomes are equally likely.
In the given table;
For theoretical, P(2) = 1/4
For experimental, P(7) = 7/28 = 1/4
Learn more about experimental probability here: https://brainly.com/question/8652467
#SPJ1
A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder with a height of 5 in and a diameter of 6in . The paper label is wrapped around the can and covers only the side of the can (not the top or bottom). If the company has a total of 4521.6in^2 of paper available, how many labels can be made? Use 3.14 for n , and do not round your answer.
Answers
48 labels can be made if the company has a total of 4521.6in² of paper available.
We can calculate the number of labels by finding the surface area of the side of the can.
What is the surface area of the side of the can?The surface area of the side of the can is the circumference of the base times the height:
C = πd
C = 3.14 x 6
C = 18.84 in
Area = C x h
Area = 18.84 x 5
Area = 94.2 in²
Therefore, each label requires 94.2 in² of paper.
To find the number of labels that can be made, we divide the total amount of paper by the amount needed per label:
Number of labels = Total area of paper / Area per label
Number of labels = 4521.6 / 94.2
Number of labels = 48
Therefore, 48 labels can be made using a total of 4521.6in² of paper.
Learn more about surface area at brainly.com/question/20016182
#SPJ1
Please help quickly I'm begging!
Assignment details: In this assignment, you will create two graphs and answer questions about Bond's Gym, the business you are supporting.
Answers
The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments
Creating the functions of the Bond's GymFrom the question, we have the following parameters that can be used in our computation:
The table of values
For the membership application, we have the following features
Initial value = 600Constant rate of change = (450 - 600)/(15 - 0) = -10So, the function is
f(x) = 600 - 10x
For the membership available, we have the following features
Initial value = 0Constant rate of change = (100 - 0)/(15 - 0) = 20/3So, the function is
g(x) = 20/3x
So, the functions are f(x) = 600 - 10x & g(x) = 20/3x
Read more about linear relation at
https://brainly.com/question/30318449
#SPJ1
How do I solve this?
Answers
The 99% confidence interval estimate of the population standard deviation is [12.54, 54.62] mi/h.
What is a confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test.
x = [64, 60, 56, 60, 52, 59, 58, 59, 70, 68]
s = 5.963
n = 10
CI = [(n-1)*s²/chi2_upper, (n-1)*s²/chi2 lower]
CI = [(9*5.963^m²)/19.022, (9*5.963²)/2.700]
CI = [12.54, 54.62]
Learn more about interval on
https://brainly.com/question/15712887
#SPJ1
Write the linear equation that gives the rule for this table.
X
4
5
6
7
Y
24
30
36
42
Write your answer as an equation with y first, followed by an equals sign.
Answers
The equation of the line passing through the given points is y = 6x
Given that are the values of x and y coordinates we need to find the equation of the line using them,
So, considering the points (4, 24) and (5, 30),
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (4, 24) and (5, 30),
Therefore, the required equation is =
y-24 = 30-24/5-4 (x-4)
y-24 = 6(x-4)
y-24 = 6x-24
y = 6x
Hence, the equation of the line passing through the given points is y = 6x
Learn more about equation of the line click;
https://brainly.com/question/21511618
#SPJ1
- x²= +x +12=0 .....................................
Answers
Therefore, the solutions of the equation -x² + x + 12 = 0 are x = -3 and x = 6.
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.
Here,
The given equation is:
-x² + x + 12 = 0
To solve for x, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, we have:
a = -1, b = 1, and c = 12
Substituting these values into the quadratic formula, we get:
x= (-1 ± √(1² - 4(-1)(12))) / 2(-1)
x = (-1 ± √(1 + 48)) / (-2)
x = (-1 ± √(49)) / (-2)
x = (-1 ± 7) / (-2)
There are two solutions:
x = (-1 + 7) / (-2)
= -3
x = (-1 - 7) / (-2)
= 6
To know more about equation,
https://brainly.com/question/28243079
#SPJ1
Consider the following statements:
Which of the statement(s) regarding the "limit" concept in
Mathematics is/are TRUE and which is/are FALSE?
I
A limit is a point or value that a pattern, function or sum of
a series, approaches as the number of terms in the series
increases.
II A limit is a value that a function approximates for a given
input value.
III A limit is a value we get closer and closer to, but never
quite achieve.
Answers
I: TRUE - A limit is a value that a function, pattern, or sum of a series approaches as the number of terms or input value increases.
What is a Limit in Mathematics based on the given context?II: TRUE - A limit can also be a value that a function approximates for a specific input value, especially when dealing with continuity or differentiability.
III: FALSE - Although a limit might seem like a value that is never quite achieved, it can be reached or even exceeded, depending on the function and its behavior.
Read more about math limits here:
https://brainly.com/question/30339394
#SPJ1
ACTIVITY 1: Complete the table below by computing the unknown component of simple interest.
Answers
Answer:
what arecrosses on line 2
A chef has 5 containers of rice. Each container has 2 cups of rice in it. If the chef uses cup of rice for a recipe, how many cups of rice do they have left?
Answers
Answer:10-x
Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.
Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
Answers
The correct equation for the following sentence is 24 = 31.4n + (–8.4) . Option C
What are algebraic expressions?Algebraic expressions are simply described as those expressions that are made up of factors, coefficients, constants, terms and variables.
Additionally, algebraic expressions are made up of arithmetic or mathematical operations, such as;
BracketDivisionSubtractionMultiplicationParenthesesAdditionFrom the information given, we have that;
24 is the constant
Let the number be represented as n
Then, the expression is given as;
24 = 31.4(n) - 8.4
Learn about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
In circle
V
V,
V
W
=
2
VW=2 and the length of
⌢
=
2
9
π
WX
⌢
=
9
2
π. Find m
∠
W
V
X
∠WVX.
Answers
Answer:
Step-by-step explanation:
In a circle, the measure of an inscribed angle is equal to half the measure of its intercepted arc. In this case, the inscribed angle is ∠WVX and its intercepted arc is ⌢WX.
Since the length of ⌢WX is (9/2)π, its measure in degrees is (9/2)π * (180/π) = 810/2 = 405 degrees.
Therefore, the measure of ∠WVX is half the measure of its intercepted arc, which is 405/2 = 202.5 degrees.
one two 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Answers
Answer:
31
Step-by-step explanation:
the next number is 31 in this series
Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
1. Find the data using at least 10 numbers in the x column.
2. Create a scatter plot. Label the graph and show increments.
3. Write an exponential equation.
4. Interpret the meaning of the "a" and "b" in your function y=ab^x including the units.
5. Find out how long it will take before the stadium is half empty and all the way empty.
Answers
y = 92000(0.9)^x
where y is the number of fans remaining in the stadium after x minutes.
Using this formula, we can plug in x values from 0 to 30 (or more) to generate a table of values:
| x | y |
|------|---------|
| 0 | 92000 |
| 1 | 82800 |
| 2 | 74520 |
| 3 | 67068 |
| 4 | 60361 |
| 5 | 54325 |
| 6 | 48892 |
| 7 | 43903 |
| 8 | 39313 |
| 9 | 35082 |
| 10 | 31174 |
2. Here is a scatter plot based on the above data:
The x-axis represents the time in minutes, and the y-axis represents the number of fans remaining in the stadium.
3. The exponential equation that best fits the data is:
y = 92000(0.9)^x
where y is the number of fans remaining in the stadium after x minutes.
4. In the equation y = ab^x, a represents the initial value or starting point, and b represents the rate of change or growth factor. In this case, a = 92000 represents the initial number of fans in the stadium, and b = 0.9 represents the rate at which the number of fans decreases per minute. The units of a are fans, and the units of b are fans per minute.
5. To find out how long it will take before the stadium is half empty, we need to solve the equation y = 0.5a for x:
0.5a = 92000(0.9)^x
0.5(92000) = 92000(0.9)^x
0.5 = 0.9^x
Taking the logarithm of both sides, we get:
log(0.5) = x log(0.9)
x = log(0.5) / log(0.9)
x ≈ 7.72 minutes
Therefore, it will take approximately 7.72 minutes for the stadium to be half empty.
To find out how long it will take for the stadium to be completely empty, we need to solve the equation y = 0 for x:
0 = 92000(0.9)^x
Taking the logarithm of both sides, we get:
log(0) = x log(0.9)
This equation has no real solution, which means that the stadium will never be completely empty (in theory). However, in practice, the number of fans will eventually become small enough that it can be considered empty for all practical purposes.
I need some assistance with this ? Please
Answers
Answer:
I am sorry this is just so new for me like what even is an "imaginary" solution, i am in 6th grade wth
Last week Kristen spent 4 hours gardening over a period of 7 days .she spent the same amount of time gardening each day.about how much time did she spend gardening each day last week
Answers
Answer:
28
Step-by-step explanation:
i did 7 times 4
How do you find area?
Answers
The area of a shape is calculated by calculating the amount of space on the shape
How do you find area?By definitinon, the area of a shape is the amount of space on the shape
using the above as a guide, we have the following:
Area of rectangle = Length * WidthArea of square = Length²Area of triangle = 1/2 * base * heightArea of circle = π * radius²Area of parallelogram = base * heightThere are several formulas to calculate area
The formula to use is dependent on the shape whose area is being calculated
This means that the area of trapezoid cannot be calculated using the area of parallelogram
Read more about area at
https://brainly.com/question/24487155
#SPJ1
PLS HELP ME WITH THIS QUESTION PLS
PLS SHOW YOUR WORKING OUT
Answers
The value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.
How did we get these values?Let the first term of the arithmetic series be a, and the common difference be d = 3. Then, we have:
a = 2t + 1
n-th term = a + (n-1)d = 2t + 1 + 3(n-1) = 3n + (2t - 2)
(Notice that the second equation can be found by substituting the expression for a into the formula for the n-th term and simplifying.)
We also know that the n-th term is given by (14t - 5), so we can equate the two expressions:
3n + (2t - 2) = 14t - 5
Simplifying and solving for n, we get:
n = (12t + 3)/3 = 4t + 1
So, the n-th term can also be expressed as:
3n + (2t - 2) = 3(4t + 1) + (2t - 2) = 14t - 5
Simplifying, we get:
14t - 5 = 14t - 5
This confirms that our expressions for the first term, common difference, and n-th term are all consistent with each other.
Now, we can use the formula for the sum of an arithmetic series to find the sum of the first n terms:
S_n = (n/2)(2a + (n-1)d) = (n/2)(4t + 4t + 1 + 3n - 3) = (3/2)n^2 + (5/2)t - 3n/2 + 1/2
We want to rewrite this expression in the form p(qt - 1)^r. To do this, we can try to complete the square in the n term, like this:
S_n = (3/2)[n^2 - 2n(t+1) + (t+1)^2] + (5/2)t - (3/2)(t+1)^2 + 1/2
S_n = (3/2)[n - (t+1)]^2 - (1/2)(t+1)^2 + (5/2)t + 1/2
Let u = n - (t+1), so that:
S_n = (3/2)u^2 - (1/2)(t+1)^2 + (5/2)t + 1/2
We want to rewrite this in the form p(qt - 1)^r, so let's try to match the terms:
p = -3/2
q = -1/(t+1)
r = 2
Therefore, the value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.
Note that the assumption that t is greater than 0 was not necessary for the derivation of the sum formula, but it is necessary for the existence of the arithmetic series (since otherwise the first term would be negative).
learn more about arithmetic series: https://brainly.com/question/6561461
#SPJ1
The text format of the question in the picture:
22. The first term of an arithmetic series is (2t + 1) where t is > 0 The nth term of this arithmetic series is (14t - 5)
The common difference of the series is 3
The sum of the first n terms of the series can be written as p(qt - 1)^r where p, q and r are integers.
Find the value of p, the value of q and the value of r Show clear algebraic working.