The state space is {0, 1, 2, 3},
The transition matrix is : P = [[(1-p)³, 3p(1-p², 3p²(1-p), p^3], [(1-p)², 2p(1-p)²+2p(1-p)², 2p²(1-p)+2p²(1-p), 2p³], [(1-p), p(1-p)²+2p(1-p), p²(1-p)+2p², p³], [0, p(1-p), 2p², 3p³]], the probability of one idle machine 3 nights later is 0.33554432.
The state space of (Xn : n ≥ 0) is the set of all possible states that the system can be in at the end of a given day. The state space is {0, 1, 2, 3}, where 0 corresponds to all machines being broken, 1 corresponds to one machine working and two broken, 2 corresponds to two machines working and one broken, and 3 corresponds to all machines working.
The transition matrix is given by:
P = [[(1-p)³, 3p(1-p², 3p²(1-p), p^3], [(1-p)², 2p(1-p)²+2p(1-p)², 2p²(1-p)+2p²(1-p), 2p³], [(1-p), p(1-p)²+2p(1-p), p²(1-p)+2p², p³], [0, p(1-p), 2p², 3p³]]
Given that 2 machines are idle tonight (i.e., Xn = 1), the probability of one idle machine 3 nights later (i.e., Xn+3 = 2) is given by the (1, 2) entry of P^3, where P^3 is the matrix obtained by multiplying P by itself 3 times.
Using the given value of p = 0.8, we can calculate P^3 and find the (1, 2) entry to obtain the desired probability. The (1, 2) entry of P^3 is 0.33554432, so the probability of one idle machine 3 nights later is 0.33554432.
Therefore, the answer to part c is 0.335544.
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Solve by factoring. ,3x^(2)-27x+60=0 What method of factoring did you use? If you forget how to factor on a multiple choice test, what other methods could you use to solve the quadratic?
The solution of the quadratic equation is x=24/2 and x=-6/2.
To solve the quadratic equation 3x2-27x+60=0, you can use the method of factoring. You can factor this equation by taking out the common factor of 3 from the terms.
That leaves us with x2-9x+20=0, which can be factored into (x-10)(x-2)=0. To solve, you set each factor equal to 0, so x=10 and x=2 are the solutions.
If you forget how to factor on a multiple choice test, you can use other methods such as completing the square or the quadratic formula.
For this equation, completing the square would involve adding and subtracting 92/4 to both sides, which would give us (x-9/2)2=225/4. To solve, you would then take the square root of both sides, resulting in x-9/2=±15/2, or x=24/2 and x=-6/2.
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Chrissy's age plus 5 is Maddy's age. If Maddy is 12 years old, how many years old is Chrissy?
Answer:
Chrissy is 7 years old
Step-by-step explanation:
What is the solution of the system?
2x+3y=−26
5x+3y=−29
Answer:
x = -1
y = -8
Step-by-step explanation:
2x+3y= −26
5x+3y= −29
Time the first equation by -1
-2x - 3y = 26
5x + 3y = -29
3x = -3
x = -1
Now put -1 in for x and solve for y
2(-1) + 3y = - 26
-2 + 3y = -26
3y = -24
y = -8
Let's check
2(-1) + 3(-8) = -26
-2 - 24 = -26
-26 = -26
So, x = -1 and y = -8 is the correct answer.
[tex]2x + 3y = - 26 \\ \implies \: 2x + 3y + 26 = 0[/tex]
[tex]5x + 3y = - 29 \\ \implies \: 5x + 3y + 29 = 0[/tex]
For finding what sort of solution the pair of equations give , we need to check the type of equality between
[tex] \frac{ a_{1}}{ a_{2} \: } , \: \frac{ b_{1} }{ b_{2} } , \: \frac{ c_{1}}{ c_{2} } \\ [/tex]
The following results can be obtained ,
[tex]if \: \: \frac{ a_{1} }{a _{2} } \neq \: \frac{ b_{1}}{ b_{2}} \\ \\ \implies \: we \: obtain \: a \: unique \: solution[/tex]
[tex]if \: \: \frac{ a_{1} }{a _{2} } = \: \frac{ b_{1}}{ b_{2}} \: \neq \: \frac{ c_{1}}{ c_{2}} \\ \\ \implies \:we \: obtain \: no \: solution[/tex]
[tex]if \: \: \frac{ a_{1} }{a _{2} } = \: \frac{ b_{1}}{ b_{2}} \: = \: \frac{ c_{1}}{ c_{2}} \\ \\ \implies \:we \: obtain \: infinitely \: many \: \: solutions[/tex]
Considering the equations provided ,
[tex] a_{1} = 2 \: \: , \: \: b_{1} = 3 \: \: , \: \: c_{1} = 26 \\ a_{2} = 5 \: \: , \: \: b_{2} = 3 \: \: , \: \: c_{2} = 29[/tex]
[tex]\therefore \frac{ a_{1}}{ a_{2} } = \frac{2}{5} \: \: \: , \: \: \: \frac{ b_{1}}{ b_{2} } = \frac{3}{3} = \frac{1}{1} \: \: \: , \: \: \: \frac{ c_{1} }{ c_{2} } = \frac{26}{29} \\ [/tex]
Since ,
[tex] \frac{ a_{1} }{ a_{2}} \neq \: \frac{ b_{1} }{ b_{2}} \\ [/tex]
The system of equations has a unique solution .
On further calculations done by elimination method , the solution of the equations comes out to be
[tex]\boxed{x = - 1} \\ \boxed{y = - 8}[/tex]
let's have a look at how it'll be done now.
the equations given in the question are -
[tex]2x + 3y + 26 = 0 \: ...(1) \\ 5x + 3y + 29 = 0...(2) \\ \\ multiplying \: equation \: (1) \: by \: - 1 \\ \implies \: - 2x - 3 - 26 = 0...(3) \\ \\ solving \: eqs. \: (2) \: and \: (3) \\ \\ 5x + \cancel{3y} + 29 = 0 \\ \underline{ - 2x \cancel{- 3y} - 26 = 0} \\ 3x + 3 = 0 \\ \\ \implies \: 3x = - 3 \\ \implies \: \boxed{x = - 1} [/tex]
substiting the value of x in equation 1
[tex]2( - 1) + 3y + 26 = 0 \\ 3y + 26 - 2 = 0 \\ 3y + 24 = 0 \\ 3y = - 24 \\ \implies \: \boxed{y = - 8}[/tex]
hope helpful! :)
calculate the height of n of the flag pole
give your answer in meters to 1 dp
Using a trigonometric relation we will see that the height is 8.62m
How to get the height of the flag pole?On the diagram we can see a right triangle, where we know one of the angles and the adjacent cathetus and we want to find the opposite cathetus.
Then we can use the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing the values that we know we will get:
tan(72°) = n/2.8m
2.8m*tan(72°) =n = 8.62m
That is the height.
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Abbie bought 82 cases of water for her restaurant Each case had 24 bottles of water How many bottle of water did Abbie buy in all?
Answer:
1968 bottles of water
Step-by-step explanation:
24×82=1968
1968 bottles of water
How many seconds are in 5 1/2 min is it 90 or 180 or 230 or 300 or 330 or 550 0r 630
Answer:
There are 60 seconds in 1 minute, so in 5 1/2 minutes:
5 minutes x 60 seconds/minute = 300 seconds
1/2 minute x 60 seconds/minute = 30 seconds
Adding those together gives:
300 seconds + 30 seconds = 330 seconds
Therefore, there are 330 seconds in 5 1/2 minutes.
There are 330 seconds in 5 and 1/2 minutes. We find this by converting the minutes (both the whole and the half) into seconds and adding these amounts together.
Explanation:To calculate the number of seconds in 5 and 1/2 minutes, we need to know the basic fact that 1 minute equals 60 seconds. With this, we can easily convert minutes to seconds by multiplying the number of minutes by 60.
First, let's convert the 5 whole minutes into seconds: 5 minutes x 60 seconds/minute = 300 seconds.
Next, let's convert the half minute: 1/2 minute x 60 seconds/minute = 30 seconds.
FInally, add these two amounts together: 300 seconds + 30 seconds = 330 seconds. Therefore, 5 and 1/2 minutes equals 330 seconds.
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IM DESPERATE PLS HELP PLEASE
The area of the one rectangular panel is equal to 220 ft².
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Generally speaking, the opposites sides of a rectangle are equal;
DN = WF
12x + 4 = 20x - 8
20x - 12x = 8 + 4
8x = 12
x = 3/2.
Side DN = 12x + 4 = 12(3/2) + 4 = 22 feet.
DW = NF
5y - 5 = 2y + 4
y = 3
Side DW = 5y - 5 = 5(3) - 5 = 10 feet.
Area of rectangular panel = DN × DW
Area of rectangular panel = 22 × 10
Area of rectangular panel = 220 ft².
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9
AL MATHEMATICS
A mall charges a parking fee of
P35.00 for the first two hours and an
extra P15.00 for each hour (or a
fraction of it) after that. If you park
for more than twelve hours, you
instead pay a flat rate of P250.00.
Represent your parking fee using the
function p(t) where t is the number
of hours you parked in the mall.
p(t) = {
P35.00 if t ≤ 2
P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12
P250.00 if t > 12
} is the required function to represent given information.
What is expression ?Expressions are commonly used in programming to perform calculations, manipulate data, and make decisions based on the results of evaluations.
According to given conditions:To represent the parking fee using the function p(t), we need to consider the different rates depending on the number of hours parked. Here are the different cases we need to consider:
If t ≤ 2, the parking fee is P35.00
If 2 < t ≤ 12, the parking fee is P35.00 plus P15.00 for each hour (or fraction of it) after the first two hours. This can be represented by the equation:
p(t) = P35.00 + P15.00 × (t - 2)
If t > 12, the parking fee is a flat rate of P250.00.
We can combine these cases into a single function using a piecewise function. Here is the function p(t):
p(t) = {
P35.00 if t ≤ 2
P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12
P250.00 if t > 12
}
This function represents the parking fee in terms of the number of hours parked (t). To use it, simply substitute the number of hours parked into the function and calculate the resulting fee. For example, if you parked for 4 hours, the fee would be:
p(4) = P35.00 + P15.00 × (4 - 2) = P65.00
Therefore, p(t) = {
P35.00 if t ≤ 2
P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12
P250.00 if t > 12
} is the required function to represent given information.
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The amount of merchandise (in millions) that store A sold can be represented by A = 13x squared + 8x - 3. The amount of merchandise (in millions) that store B sold can be represented by B = 8x squared - 3x + 11. Find the total amount of merchandise that stores A and B sold.
The total amount of merchandise that stores A and B sold is 21x²+5x+8
What is equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given that, are two stores selling merchandise given by equation,
A = 13x²+8x-3 and B = 8x²-3x+11, we need to find the total amount of merchandise that stores A and B sold.
We add both the equations to find the same,
Total merchandise sold = 13x²+8x-3 + 8x²-3x+11
= 21x²+5x+8
Hence, the total amount of merchandise that stores A and B sold is 21x²+5x+8
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For each of the following polynomial find the following (3-3x^(3)-7x^(2))-(-2x^(2)-3x+7)
The result of the (3-3x^(3)-7x^(2))-(-2x^(2)-3x+7) polynomial is -3x^(3) - 5x^(2) + 3x - 4.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
To find the result of the given polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.
Step 1: Distribute the negative sign to the second polynomial:
(3 - 3x^(3) - 7x^(2)) - (-2x^(2) - 3x + 7) = (3 - 3x^(3) - 7x^(2)) + (2x^(2) + 3x - 7)
Step 2: Combine like terms:
3 - 3x^(3) - 7x^(2) + 2x^(2) + 3x - 7 = -3x^(3) - 5x^(2) + 3x - 4
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5. A right triangle has side lengths of
8 inches and 6 inches. What is the
length of the hypotenuse, in inches?
Answer:10
Step-by-step explanation:
A^2 + B^2 = C^2
8^2 + 6^2 = 100^2
take the square root since c is squared
sqrt 100 = 10
Answer:
Step-by-step explanation:
10
Use a linear approximation (or differentials) to estimate the given number. (Do not round your answer). (32. 03)4/5
Using linear approximation, we estimate that ([tex]32.03^{4/5}[/tex]) is approximately equal to 31.952. It's important to note that this is only an estimate and may not be exact.
To estimate the value of ([tex]32.03^{4/5}[/tex]) using linear approximation, we start by finding the differential of the function f(x) = [tex]x^{4/5}[/tex] at the point x = 32.
[tex]f(x) = x^{4/5}[/tex]
[tex]f'(x) = 4/5x^{-1/5}[/tex]
Evaluating [tex]f'(32)[/tex], we get:
[tex]f'(32) = (4/5)(32)^{-1/5} = 0.1585[/tex]
Now, using the linear approximation formula:
[tex]f(x) ≈ f(a) + f'(a)(x - a)[/tex]
where a is the point at which we are estimating the function, we have:
[tex]f(32.03) = f(32) + f'(32)(32.03 - 32)[/tex]
[tex]= 32^{4/5} + 0.1585(0.03)[/tex]
[tex]= 31.952[/tex]
Linear approximation is a useful tool for approximating values of functions near a given point, but it has limitations and may not work well for functions that are highly nonlinear or have discontinuities.
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What is 92199+20923+29290+83292+2819+99279+38471+378143
Answer:
744416
Step-by-step explanation:
Just add everything together
Question 6
When you evaluate and simplify the expression f(a+h)-f(") what is one important detail to
ALWAYS remember
A. h must be less than or equal to x
B. the h in the denominator always cancels out with the h in f(x+h)
C. f(x + h) must be equal to f(x) + h
D. as you simplify the rational expression, the f(x) and h typically cancels out
Does anyone know the answer?
Answer:
33.7°
Step-by-step explanation:
the direction angle is calculated as
tanΘ = [tex]\frac{y}{x}[/tex] ( Θ is the direction angle ) , then
tanΘ = [tex]\frac{-4}{-6}[/tex] = [tex]\frac{2}{3}[/tex]
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{2}{3}[/tex] ) ≈ 33.7° ( to the nearest tenth )
write an algebraic expression for 24 more than the product of 2 and x
Answer:
24+2x
Step-by-step explanation:
Answer:
Step-by-step explanation:
x = 24+2x
Mike constructed a kite by attaching two congruent triangles as shown in the diagram below. Which equation can Mike use to determine the amount of material, in square inches, needed to create the kite?
F. A=[12(12)(8)]⋅2
G.A=[12(6)(8)]⋅2
H.A=[(12)(4)]⋅2
J.A=[(6)(10)]⋅2
Answer: We cannot provide a complete answer as there is no diagram attached to the question. However, based on the information provided, we can make an educated guess as to which equation Mike can use to determine the amount of material, in square inches, needed to create the kite.
Since Mike constructed the kite by attaching two congruent triangles, we can use the formula for the area of a triangle, which is:
A = (1/2) * base * height
To find the area of both triangles, we need to know the base and height of each triangle. Without a diagram, we cannot determine the exact dimensions of the triangles.
However, based on the answer choices provided, we can make an assumption that the kite is made up of two congruent right triangles, each with legs of length 6 inches and 8 inches. Using this assumption, we can determine the area of each triangle and then multiply by 2 to get the total area of the kite.
Using the formula for the area of a triangle, we get:
A = (1/2) * base * height
= (1/2) * 6 * 8
= 24
So the area of each triangle is 24 square inches, and the total area of the kite is:
A = 2 * 24
= 48
Therefore, the equation that Mike can use to determine the amount of material, in square inches, needed to create the kite is likely to be:
G. A = [12(6)(8)]⋅2
This equation corresponds to the area of two congruent right triangles with legs of length 6 inches and 8 inches.
Step-by-step explanation:
can anyone please help me with this question -2u^5(-6u^3)
The simplified expression is [tex]12u^8[/tex].
What is simplification?
Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.
Here the given expression is ,
=> [tex]-2u^5(-6u^3)[/tex]
Now simplifying the expression,
=> [tex]-2\times -6 \times u^5 \times u^3[/tex]
=> 12[tex]u^{5+3}[/tex]
=> [tex]12u^8[/tex]
Hence the simplified expression is [tex]12u^8[/tex].
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51% of a certain food is water. Out of 300 total grams, how many grams are not water?
Out of 300 grams, 147 grams of food is not water in the given food sample.
If 51% of a certain food is water, then 49% of it must be something other than water. To find out how many grams of the food are not water, we can first calculate how many grams of water there are,
300 grams x 51% = 153 grams of water
Then we can subtract this from the total weight to find the amount of food that is not water -
300 grams - 153 grams = 147 grams of food that is not water
Therefore, out of 300 grams of nutrition, 153 grams are water and 147 grams are not.
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How many rebounds should your team expect to have in 15 missed shots?
It is unlikely that the projected rebounds in 15 shots will actually happen.
Explain about the term probability?A probability is a scaled version of the likelihood or chance that a specific event will take place. Both percentages with values ranging from zero to one and percentages extending from 0% to 100% can be used to describe probabilities.Total shots fired equals 10.
To find that there were 15 shots total.
Consider S to be the likelihood that your team will rebound and miss a shot.
P(S) = Number of rebounds / Total Number of outcomes
P(S) = 7/15
P(S) = 0.46
Consequently, it is unlikely that the projected rebounds in 15 shots will actually happen.
Thus, it is unlikely that the projected rebounds in 15 shots will actually happen.
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The complete question is-
During a basketball game, you record the number of rebounds from missed shots for each team. How many rebounds should your team expect to have in 15 missed shots?
Picture for question is attached.
Year 1 Y = 1000+ 0.03 (1000) - 1030.00 Start with the expression for year 1. Recall the identity property of 1 (1000) + 0.03 (1000) = [ ] (1+[ ]) fill in the blanks
The expression by using property is 1000(1+0.03)
What is Number system?A number system is defined as a system of writing to express numbers.
Using the distributive property, we can factor out 1000 from the expression for year 1:
Y = 1000 + 0.03(1000) - 1030.00
= 1000(1 + 0.03) - 1030.00
Using the identity property of 1, we can rewrite (1 + 0.03) as:
(1 + 0.03) = 1.03
Substituting back into the expression for year 1, we get:
Y = 1000(1.03) - 1030.00
Hence, the expression by using property is 1000(1+0.03)
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Suppose you place $2,500 in an account that will pay annual
interest of 6% compounded quarterly. What will be your balance in
your account after 5 years?
After 5 years, the balance of your account with an initial investment of $2,500, 6% annual interest compounded quarterly, will be $3,325.81. This can be calculated using the following formula:
Balance = P(1 + r/n)nt
Where:
P = Principal Amount
r = Annual Interest Rate
n = Number of Compounding Periods
t = Number of Years
Therefore, for your given example, the equation would be:
Balance = 2500(1 + 0.06/4)4 x 5
Balance = 2500(1.015)20
Balance = 2500(1.32581)
Balance = $3,325.81
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1larr, Solve the inequality symbolically. Express the solution set in interval notation. (6x+4)/(8)>(22)/(3)
The solution set of the given inequality is (164/18, ∞).
To solve the inequality symbolically, we first need to isolate the variable x on one side of the inequality. We can do this by multiplying both sides by 8 and then subtracting 4 from both sides. Finally, we can divide both sides by 6 to solve for x. Here are the steps:
(6x + 4)/8 > 22/3
6x + 4 > (22/3)(8)
6x + 4 > 176/3
6x > (176/3) - 4
6x > 164/3
x > (164/3)(1/6)
x > 164/18
Now we can express the solution set x > 164/18 in interval notation: (164/18, ∞)
So the solution set is all values of x greater than 164/18.
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give the new coordinates of the ordered pair(7,-4) after a 180 degree rotation
The new coordinates of the point (7, -4) after a 180-degree rotation are (-7, 4).
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
To find the new coordinates of the ordered pair (7, -4) after a 180-degree rotation,
Following the trasformation of 180-degree rotation,
(x, y) ⇒ (-x, -y)
So,
(7, -4) ⇒ (-7, 4)
Therefore, the new coordinates of the point (7, -4) after a 180-degree rotation are (-7, 4).
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The scale factor of two similar hexagons is 3:7.
The area of the smaller hexagon is 18 m2.
What is the volume of the larger hexagon
Possible answers
98 m2
324 m2
42 m2
36 m2
5832 m2
Answer:
Since the hexagon is a 2D shape, it does not have volume. We can find the area of a hexagon but not its volume.
Step-by-step explanation:
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths. In this case, since the figures are hexagons, we can use the ratio of their corresponding side lengths to find the ratio of their areas.
Since the scale factor of the hexagons is 3:7, we know that the ratio of their side lengths is also 3:7. Therefore, the ratio of their areas is:
(3/7)^2 = 9/49
We are given that the area of the smaller hexagon is 18 m^2, so we can use this to find the area of the larger hexagon:
(area of larger hexagon) = (area of smaller hexagon) x (ratio of areas)
(area of larger hexagon) = 18 x (9/49)
(area of larger hexagon) = 3.28 m^2 (rounded to two decimal places)
Since the hexagon is a 2D shape, it does not have volume. We can find the area of a hexagon but not its volume.
What is the step-by-step way to get the remaining 5 trigonometric values?
Answer:
If sin = 1⁄2 and lies in the second quadrant, the remaining five trigonometric values are cos = √3/2, tan = 1/√3, cot = √3, sec = 2/√3, and csc = 2. These values can be derived from the basic trigonometric identities and the given value of sin. For example, the cosine of an angle in the second quadrant is the same as the sine of the same angle in the first quadrant, and vice versa. Therefore, since sin = 1⁄2 in the second quadrant, cos = √3/2 in the first quadrant. The other values can be derived in a similar manner
Step-by-step explanation:
Andrew had a piece of foam in the shape of a rectangular prism as shown below. Thebase is a square with sides 3 Inches long, and the piece is 5 Inches taill. He out the
foam along the diagonal plane shown by the shaded area.5 inches 3 inches Which of the following is closest to the area of the shaded diagonal plane? 19.3 square inches 12 square Inches 15.8 square inches 17.5 square inches
The area of the shaded diagonal plane is 17.5 square units.
What is the area of the shaded diagonal plane?The area of the shaded diagonal plane is calculated as follows:
Using Pythagoras' theorem, let the hypotenuse formed by the diagonal be x
x² = 3² + 5²
x² = 9 + 25
x² = 34
x = √34
The shape of the shaded plane is a rectangle.
The area of the rectangle will be:
Area = length * width
Area = √34 * 3
Area do the shaded plane = 17.5 square units
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Solve the equation. 4(x - 2) = 2(2x + 6) 4x – [?] = [__] + [__] First we must use the distributive property to expand our equations. Hint: Calculate and enter the value of 4•2. ______________
The equation 4(x - 2) = 2(2x + 6) has no solution.
To solve the equation 4(x - 2) = 2(2x + 6), we must first use the distributive property to expand the equations. The distributive property states that a(b + c) = ab + ac.
Using the distributive property, we can expand the equation as follows:
4(x - 2) = 2(2x + 6)
4x - 8 = 4x + 12
Next, we must isolate the variable on one side of the equation. We can do this by subtracting 4x from both sides of the equation:
-8 = 12
This equation is not true, so there is no solution to the equation 4(x - 2) = 2(2x + 6).
In conclusion, the equation 4(x - 2) = 2(2x + 6) has no solution.
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4.) The table shows some ingredients in lasagna. If you make three times the recipe, how many cups of cheese are needed?
Answer: 8
Step-by-step explanation:
2*3= 6
[tex]\frac{2}{3}[/tex]*3= 2
A right circular cylinder has the dimensions shown below.
r = 5 cm
h = 9 cm
Find the exact surface area of the cylinder.
Include correct units.
Show all your work.
Answer:
The surface area of a right circular cylinder consists of three parts: the top and bottom circular faces, and the curved lateral surface.
The area of each circular face is given by the formula A = πr^2, where r is the radius. Therefore, the total area of the two circular faces is:
2A = 2πr^2
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Therefore, the lateral surface area of the cylinder is:
A = 2πrh
Substituting the given values, we get:
A = 2π(5 cm)(9 cm)
Simplifying, we get:
A = 90π cm^2
Adding the areas of the circular faces and the lateral surface, we get the total surface area:
Total surface area = 2A + A = 3A
Substituting the value of A, we get:
Total surface area = 3(90π cm^2) = 270π cm^2
Therefore, the exact surface area of the cylinder is 270π square centimeters.
