Answer:
The exponential growth function for the population can be written as:
P(t) = P0 * e^(rt)
Where:
P0 = initial population = 8,000
r = annual growth rate = 4.3% = 0.043
To find the monthly rate, we need to divide the annual rate by 12 (since there are 12 months in a year):
r_monthly = r/12 = 0.043/12 = 0.00358
So the exponential growth function with monthly growth rate becomes:
P(t) = 8000 * e^(0.00358t)
To find the quarterly rate, we need to divide the annual rate by 4 (since there are 4 quarters in a year):
r_quarterly = r/4 = 0.043/4 = 0.01075
So the exponential growth function with quarterly growth rate becomes:
P(t) = 8000 * e^(0.01075t)
find the unit rate!
it would end up by costing $0.55 cents a cup
A swimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t= 0, city water containing 0.003% chlorine is pumped into the pool at a rate of 6 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.006% chlorine? What is the percentage of chlorine in the pool after 1 hour? After 1 hour the pool will be % chlorine. (Round to four decimal places as needed.)
The pool water will be 0.006% chlorine after approximately 236.5 minutes, and the percentage of chlorine in the pool after 1 hour (60 minutes) is approximately 0.674%.
Let C(t) be the amount of chlorine in the pool at time t in minutes, measured in gallons of chlorine. Since the volume of the pool is 10,000 gal and the initial concentration of chlorine is 0.01%, we have:
C(0) = 10,000 gal x 0.01% = 1 gal
As city water containing 0.003% chlorine is pumped into the pool at a rate of 6 gal/min and the pool water flows out at the same rate, the differential equation for C(t) is:
dC/dt = (0.003 - C(t)/10,000) x 6 - C(t)/10,000 x 6
Simplifying the right-hand side and solving the differential equation using separation of variables, we get:
C(t) = 30,000(1 - e^(-t/166.7)) - 180,000e^(-t/166.7)
After 1 hour (60 minutes), we have:
C(60) = 30,000(1 - e^(-60/166.7)) - 180,000e^(-60/166.7) ≈ 0.0674 gal
The percentage of chlorine in the pool after 1 hour is:
0.0674 gal / 10,000 gal x 100% ≈ 0.674%
To find when the pool water is 0.006% chlorine, we set C(t) = 10,000 gal x 0.006% = 0.6 gal and solve for t:
30,000(1 - e^(-t/166.7)) - 180,000e^(-t/166.7) = 0.6
Using numerical methods, we find that t ≈ 236.5 minutes.
After roughly 236.5 minutes, the chlorine content of the pool will be 0.006%, and after an hour (60 minutes), it will be approximately 0.674%.
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A rectangle with side lengths y and z has perimeter 2y+2z. Elizabeth bought a rectangular painting of the seashore and wants to decorate the edges with sky-blue ribbon. The painting is 2 feet long and 1.5 feet wide.
What is the perimeter of the painting?
The perimeter of the painting 7 feet.
What is Perimeter?Perimeter is the distance around the edge of a shape. To find the perimeter by adding up the side lengths of various shapes.
Given:
A rectangle with side lengths y and z has perimeter 2y+2z.
Elizabeth bought a rectangular painting whose length = 2 ft and width = 1.5 ft.
So, the perimeter of the painting
= 2l+ 2w
= 2(2)+ 2(1.5)
= 4 + 3
= 7 feet
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Use the rules of equations and Inverse operations to solve the equation.
3x² = 48
04
0 +4
0 -4
0+2
Answer:
Below
Step-by-step explanation:
3 x^2 = 48 divide both sides of the equation by 3 to get
x^2 = 16 Now, sqrt both sides
x = + 4 or -4
Graph the angle -4pi/3 in standard position :)
The point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
The angle for this problem is given as follows:
-4pi/3.
Hence the sine and the cosine are given as follows:
sin(-4pi/3) = 0.866.cos(-4pi/3) = -0.5.Hence the point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.
(the equation of the unit circle is x² + y² = 1).
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Custom Castings, Inc. pays its employees on a piece-rate basis of $1.28 for each acceptable piece produced. What gross pay was earned by an employee whose production of 483 pieces included 9 pieces
that did not pass inspection?
Question Progress
Homework Progress
19/48 Marks
The circle shown has a radius of 4 cm.
Not drawn
to scale
What is the length of the diameter of the circle?
The length of the diameter of the circle is 8 cm.
What is Diameter?The diameter of a circle is the distance measured through its centre. The radius of a circle is the distance from the center to any point on the edge. The diameter is divided by the radius.
Given:
Radius = 4 cm
As, the radius is the point which starts from center and reach to point on the surface of the Circle.
and, the Diamter is the two times of the radius.
So, Diameter = 2 x radius
D= 2 x 4
diameter = 8 cm
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Please help me I’ll give you the best rating nO lie Trust
The distance the cyclist travelled during the time are as follows;
4 meters, 18 m and 45 etc.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
Distance = speed x time
Distance = 5 x 0.8
= 4 meters
Distance = 10 x 1.8
= 18 meters
Distance = 15 x 3
= 45 meters.
Here Segment shows as time is increasing, distance is also increasing. Which means the cyclist is moving forward at a speed.
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Allergy Sufferer #1 must take one capsule every 6 hours. Allergy Sufferer #2 must take one capsule every 12 hours. Together, how many hours will it take them to consume 45 capsules?
180 hours will it take them to consume 45 capsules.
What is least common multiple ?
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the given numbers. In other words, it is the smallest number that is divisible by all the given numbers without leaving a remainder.
To find the LCM of two or more numbers, you can list their multiples and look for the smallest number that appears in all the lists. However, this can become time-consuming for large numbers. There are various methods and algorithms to find the LCM efficiently, such as using prime factorization or the Euclidean algorithm.
According to the question:
Allergy Sufferer #1 takes 1 capsule every 6 hours, so in 45 capsules, they will need to take 45 * 6 = 270 hours.
Allergy Sufferer #2 takes 1 capsule every 12 hours, so in 45 capsules, they will need to take 45 * 12 = 540 hours.
To find the total time it will take them together to consume 45 capsules, we need to find the least common multiple (LCM) of 6 and 12.
The prime factors of 6 are 2 and 3.
The prime factors of 12 are 2, 2, and 3.
To find the LCM, we take the highest power of each prime factor that appears in either factorization. In this case, that's 2^2 * 3 = 12.
So, the LCM of 6 and 12 is 12.
This means that every 12 hours, Allergy Sufferer #1 will have taken 2 capsules (since 12/6=2), and Allergy Sufferer #2 will have taken 1 capsule.
Therefore, in 12 hours, they will have taken a total of 2+1=3 capsules.
So, to consume 45 capsules, it will take them 45/3 = 15 lots of 12 hours, which is 180 hours in total.
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Show that the quadrilateral with the vertices $H(1,\ 9),\ J(4,\ 2),\ K(5,\ 2),\ L(8,\ 9)$H(1, 9), J(4, 2), K(5, 2), L(8, 9) is a trapezoid. Then decide whether it is isosceles.
The midpoints of the given quadrilateral, AB = CD and AD = BC, are equal.
What is meant by quadrilateral vertices?Vertices are the angular intersections of two sides or edges. The four vertices of a quadrilateral are A, B, C, and D. (iii)Angles. A quadrilateral's angle is the inclination between its two sides.A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. Four non-collinear points are joined to create it. Quadrilaterals' interior angles add up to a constant 360 degrees.A polygon's vertex is a point where the sides or edges of the object or two rays or line segments meet. Vertices is the plural of a vertex.Let P represent the quadrilateral's vertices (-4,2) Q (2,6): Let A, B, C, and D be the midpoints of P(-4,2) and Q. R(8,5) and S (9,-7) (2,6)
Consequently, A's coordinates are
[tex]$\left(\frac{-4+2}{2}, \frac{2+6}{2}\right)=\left(\frac{-2}{2}, \frac{8}{2}\right)=(-1,4)$[/tex]
Coordinates of B are
[tex]$\left(\frac{2+8}{2}, \frac{6+5}{2}\right)=\left(\frac{10}{2}, \frac{11}{2}\right)=\left(5, \frac{11}{2}\right)[/tex]
Coordinates of c are
[tex]$\left(\frac{8+9}{2}, \frac{5-7}{2}\right)=\left(\frac{17}{2}, \frac{-2}{2}\right)=\left(\frac{17}{2},-1\right)[/tex]
coordinates of D are [tex]$\left(\frac{9-4}{2}, \frac{7+2}{2}\right)=\left(\frac{5}{2}, \frac{-5}{2}\right)$[/tex]
Distance between A and B
[tex]$& d(A, B)=\sqrt{(-1-5)^2+\left(4-\frac{11}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]
Simplify,
[tex]$& d(C, D)=\sqrt{\left(\frac{17}{2}-\frac{5}{2}\right)^2+\left(-1+\frac{5}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]
Then,
[tex]$& d(A, D)=\sqrt{\left(-1-\frac{5}{2}\right)^2+\left(4+\frac{5}{2}\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}} \\[/tex]
We get,
[tex]$& d(B, C)=\sqrt{\left(5-\frac{17}{2}\right)^2+\left(\frac{11}{2}+1\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}}[/tex]
As a result, the given quadrilateral's midpoints, AB = CD and AD = BC, are equal.
It is a parallel gramme as a result.
The complete question is :
A quadrilateral has the vertices at the point (−4,2),(2,6),(8,5) and (9,−7). Show that the mid-point of the sides of this quadrilateral are the vertices of a parallelogram.
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please help
question 10!
The note Micah made for the test on right triangles is correct by the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
so by Pythagoras rule we can write:
For the first right triangle;
(x/√2)² + (x/√2)² = x²...(1)
from the left hand side of equation (1): (x/√2)² + (x/√2)²
x²/2 + x²/2
2(x²)/2 = x² {the right hand side of equation (1)}
and for the second right triangle;
(x√3/2)² + (x/2)² = x²...(2)
from the left hand side of equation (2): (x√3/2)² + (x/2)²
x²(3)/4 + x²/4
3x²/4 + x²/4
(3x² + x²)/4
4x²/4 = x² {the right hand side of equation (2)}
Therefore by Pythagoras rule the note Micah made for the test on right triangles is correct
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The change in the number of students at a high school in Naples was the same from 2007 to 2013 as it was from 2013 to 2019.
Which type of function best models the data?
Answer: The type of function that best models the data would depend on the actual change in the number of students and the specific data points for each year. However, if the change in the number of students was the same for each time period, a linear function would be a good candidate for modeling the data. This function would have the form y = mx + b, where m represents the rate of change (the change in the number of students over a certain time period) and b is the y-intercept (the number of students at the starting year).
Step-by-step explanation:
I need help with this please and thank you.
The standard form of the Polynomial would be [tex]x^{4}[/tex] -x³ /2 -8
What is polynomial?The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial.
We must consider each term's degree in order to write any polynomial in standard form.
Given the polynomial -8 -x³ /2 -xx³ with the highest degree comes first, followed by x raise to power 4, and then the constant, -8, comes last.
Thus, we would have:
[tex]x^{4}[/tex] -x³ /2 -8
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Which one of these ordered pairs show a combination of 12 coins from the graph?
Which one of these ordered pairs show a combination of 12 coins from the graph?
(10, 2)
(5, 5)
(10, 5)
(10, 10)
The ordered pair that show a combination of 12 coins from the graph is (10, 2)
How to determine the ordered pairfrom the question, we have the following parameters that can be used in our computation:
The graph
The purple line represents the combination of 12 coine
Using the above as a guide, we have the following:
The equation is
x + y = 12
From the list of options, we have
(10, 2): 10 + 2 = 12
Hence, the ordered pair is (10, 2)
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The table shows some information about the dress sizes of 100 women.
Dress size Number of women
a) Find the median dress size.
16
38
27
19
(1)
10
12
14
16
10 of the 100 women have a shoe size of 6
Sue says that if you choose at random one of the 100 women, the probability
that she has either a shoe size of 6 or a dress size of 16 is 0.29 because
0.1 +0.19 = 0.29
b) Is Sue correct?
State the answer, Yes or No and give a reason for your answer.
(
The solution is the median dress size = 12.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
here, we have,
given that,
from the given data we get,
dress sizes are, 10, 12 , 14, 16
no. of dresses, 16, 38, 27, 19
Hence, using the formula we get, the median dress size = 12.
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Find the area of a circle with diameter 27.2m, both in terms of r and to the nearest tenth. Use 3.14 for r
We have to find the area of a circle which has a diameter of 27.2 m
We know that the area of the circle is:
A = πr², where A = area of the circle and r = radius
Given Diameter = 27.2 m
We know that Radius = Diameter/2,
So, Radius = [tex]\frac{27.2}{2}[/tex]
Radius = 13.6 m
Now, area of circle = 3.14 * 13.6 * 13.6
Area = 580.77
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What happens when a distribution is skewed to the right?
Answer:
Step-by-step explanation:
A distribution is said to be skewed to the right (also known as positively skewed) if it has a longer tail on the positive side of the mean or median, indicating that the majority of the data values are on the lower end and there are a few large values on the higher end. This results in a mean that is larger than the median.
In other words, the right skew occurs when the tail of the distribution is located to the right side of the peak, which pulls the mean to the right as well. The presence of outliers or extreme values on the right side of the distribution can cause right skew.
Right-skewed distributions are common in data sets that represent measurements or quantities that have a minimum value of zero or a natural lower limit, but can increase without bound, such as income, wealth, and height.
In summary, when a distribution is skewed to the right, it has a higher mean and lower median compared to a symmetrical distribution, and the majority of the data is concentrated on the left side.
Which statements are true about the median? Check all that apply.
1. Put the values in numerical order before trying to find the median.
2. Median is a number that is much lower or much higher than the rest of the numbers.
3. The median is always greatly impacted by outliers.
4. The median is the number in the middle of an ordered set of values.
5. The median must be calculated by finding the mean of the two middle points when
there is an even number of data points.
what is 3/4+1/2 answer
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3}{4} + \dfrac{1}{2}}[/tex]
[tex]\mathsf{= \dfrac{3}{4} + \dfrac{1\times2}{2\times2}}[/tex]
[tex]\mathsf{= \dfrac{3}{4} + \dfrac{2}{4}}[/tex]
[tex]\mathsf{= \dfrac{3 + 2}{4 + 0}}[/tex]
[tex]\mathsf{= \dfrac{5}{4}}[/tex]
[tex]\mathsf{= 1 \dfrac{1}{4}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{5}{4}\ or \ 1 \dfrac{1}{4}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A standard volleyball court is in the shape of a rectangle. It has an area of 2100 square feet. If the length of the court is 22.4 feet, then what will be the height?
Answer: The height of the court is 93.75 feet.
Step-by-step explanation:
We know that the area of a rectangle is given by :-
Area = length x width/height (1)
Given : A standard-size volleyball court has an area of 2,100 square feet.
The length of the court is 22.4 feet.
To find : The width of the court.
According to (1) , we have
[tex]2100=22.4*height[/tex]
Then,
[tex]Height=\frac{2100}{22.4} =93.75[/tex]
Hence, the height of the court is 93.75 feet.
The freshman class at Arlington High school is made up of 480 female students. This represents 65% of the freshman class. How many total students are freshmen?
The number of freshmen that are students is 738
How to calculate the number of freshmen that are students?
Let y represent the number of students that are freshmen
The freshmen class is made up of 480 female students
This number represents 65% of the freshmen class
Therefore the total number of students that are freshmen can be calculated as follows
y × 65/100= 480
65y/100= 480
Cross multiply both sides
65y= 480 × 100
65y= 48000
y= 48000/65
y= 738.4
≅ 738
Hence 738 students are freshmen
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What time is 2330 in military time?
The first two digits represent hours, and the last two digits represent minutes. 00:00 is midnight and 12:00 is noon. 0001 to 1159 defaults to "A.M." hour.
11:30 PM in regular time on a 12-hour clock.
1. 23:30 represents afternoon time, so we add 12 hours to the given time.
2. 11 + 12 hours = 23 hours
3. minutes is always the same no matter which time format is used.
4. Remove PM and colon.
5. conversion 11:30 23:30 war time
Step 1
First divide the given time into hours and minutes. For wartime 2330, this is 23 hours and 30 minutes.
Step 2
Then check if the set time is greater than 1300. Since 2330 is greater than 1300, we use the hour subtraction rule (23 - 12 = 11 hours).
Step 3
Military time minutes are the same as standard time, so 30 minutes is still 30 minutes.
Step 4
Add a colon between the calculated hours and minutes, and the result is 11:30.
Step 5
2330 is greater than 1200, so according to the mentioned rules, adding the PM after the expected time gives 23:30 regular time.
The correct answer is 23:30 standard time.
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What is Residual sum of square?
Residual sum of squares (RSS) is a measure of the total amount of variance in a given data set that is not explained by a model.
It is equal to the sum of squared differences between the observed data values and the predicted values from the model. This measure is commonly used in regression analysis to evaluate the performance of a model. The formula for RSS is RSS = Σ(y_i - ȳ)², where y_i is the observed value and ȳ is the predicted value.For example, let's say we have a data set of 10 observations (y_1, y_2, ...,y_10). We fit a linear regression model to the data set which predicts a value ȳ_i for each observation. The RSS for this model is calculated by summing the squared differences between the observed values (y_i) and the predicted values (ȳ_i) for each of the 10 observations. This yields the RSS, which is a measure of how much of the variance of the data set is not explained by the model.
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What is the value of x in the triangle?
45° + 45 + 90
12 squared 2 + 12 squared 2 + x
The value of x is 24.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Given is a right angled triangle since one of the angle is 90 degrees.
Length of leg 1 = 12√2
Length of leg 2 = 12√2
Length of hypotenuse = x
By Pythagoras theorem,
Hypotenuse² = (leg 1)² + (leg 2)²
x² = (12√2)² + (12√2)²
x² = 2 × (12√2)²
= 576
x = √576
x = 24
Hence the value of x is 24.
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Your question seems incomplete. Probably, the complete question is as follows.
What is the value of x in the triangle?
a 45-45-90 triangle with a leg of length 12 times the square root of 2 and hypotenuse of length x
Does someone mind helping me with this problem? Thanks!
By evaluating the linear equation we can see that the complete table is:
x| -4 -2 0 2 4
y| 17 13 9 5 1
How to compete the table?Here we have a linear function:
y = -2x + 9
And we want to complete the given table, to do so, we just need to evaluate the linear function in the given values of x.
if x = -2
y = -2*-2 + 9 = 4 + 9 = 13
if x = 0
y = -2*0 + 9 = 9
if x = 2
y = -2*2 + 9 = 5
if x = 4
y = -2*4 +9 = 1
Then the complete table is:
x| -4 -2 0 2 4
y| 17 13 9 5 1
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can you help me with this question
Answer:
No, Tony should have rounded up to 38.
Step-by-step explanation:
Tony solved the inequality correctly; however, he rounded incorrectly.
8c+200≥500
Subtract 200 from both sides
8c≥300
Divide each side by 8
c≥37.5
Tony cannot wash 37.5 cars, because in the context it is impossible to wash half of a car. We round the answer up because rounding down would give us a value less than $500 (the inequality is greater than or equal to).
Therefore, the answer is 38. Tony is incorrect.
55/135 in simplest form
Answer:
11/27
Step-by-step explanation:
55/135 (divide by 5)
11/27
Find two consecutive whole numbers that \sqrt(139) lies between.
Answer:
11 and 12
Step-by-step explanation:
11^2<139
but
12^2>139
therefore
it lies between 11 and 12
From 1995 to 2005, the tuition at a college increases by about 7% per year. If this trend continues......
a. Write an exponential growth function that models the tuition over time.
b. What will the tuition be in 2020?
c. What was the tuition be in 1995?
d. What was the tuition in 2011?
a) An exponential growth function that models the tuition which increased from 1995 to 2005 by 7% annually, is y = 8,000 (1.07)^t.
b) If the trend of annual increase in tuition continues, the tuition in 2020 will be $43,419.20.
c) The tuition in 1995 was $8,000.
d) If the trend of annual increase in tuition continues, the tuition in 2011 will be $23,617.28.
What is an exponential growth function?An exponential growth function is one of the two types of exponential functions.
The exponential growth function is marked by an increasing constant rate and modeled as f(x ) = a (1 + r)^x , where r is the growth rate.
The other exponential function is known as an exponential decay function because it shows a constant rate of decrease.
The tuition in 1995, y = $8,000
Annual increase = 7% = 0.07
Time from 1995 = t
Time from 1995 to 2020 = 25 years
Time from 1995 to 2011 = 16 years
Exponential function:y = 8,000 x (1 + 7%)^t
y = 8,000(1.07)^t
When t = 25 years, y = 8,000 x (1.07)^25 = 8,000 x 5.4274 = $43,419.20
When t = 16 years, y = 8,000 x (1.07)^16 = 8,000 x 2.95216 = $23,617.28
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Question Completion:Tuition in 1995 = $8,000
Learn what an identity matrix is and about its role in matrix multiplication. ... How do you find the multiplicative inverse of a given matrix?
Answer:
See below
Step-by-step explanation:
[tex]I_1=[1],\, I_2=\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right],\,I_3=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right],\,...[/tex] and so on are examples of identity matrices.
The multiplicative inverse of a 2x2 matrix is [tex]\displaystyle A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex] where ad-bc represents the determinant. Multiplying this with the original matrix will produce the identity matrix as described previously. Usually, you'll mostly deal with 2x2 matrices when it comes to this topic, but don't worry too much.