Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
For negative exponents, you get the original number and make it into its reciprocal, and then whatever power it is to, is the power the bottom number is to, so you get:
[tex]6^{-2} = \frac{1}{6^{2} }[/tex]
Which simplifies to:
[tex]\frac{1}{36}[/tex]
So, [tex]6^{-2}[/tex] in fraction form, is [tex]\frac{1}{36}[/tex].
Hope this helped!
Please give me brainliest if possible!
In ΔKLM, k= 1.2 cm, � m∠L=93° and � m∠M=6°. Find the length of I, to the nearest 10th of a centimeter
Using the law of sines, the length of l is: 12.1 cm.
What is the Law of Sines?The Law of Sines is a theorem in triangle geometry that relates the lengths of the sides of a triangle to the sine of its angles. It states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides.
Given the following:
k = 1.2 cm
m<L = 93°
m<M = 6°
m<K = 180 - 93 - 6 = 81°
Using the law of sines, sin K/k = sin L/l:
sin 81/1.2 = sin 93/l
Find l:
(sin 81)(l) = (sin 93)(12)
l = (sin 93)(12)/(sin 81)
l = 12.1 cm
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A rocket is set to blast from the surface of Earth. What speed will it need to achieve in order to stay in orbit around the Earth at an altitude of 300 km? Note distance here to the center of the Earth is 6.7*10^6 km and the mass of Earth is 6*10^24.
Answer:
For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.
A right triangle is shown below.
ہو
60%
X
What is the sine of t?
1
The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped. Answer is 8.212°.
What does sin t mean in math?The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped.
The ratio of the opposite side to the hypotenuse is called sin(), and the ratio of the adjacent side to the hypotenuse is called cos(), when viewed from a vertex with angle.
So, the Pythagorean identity-based formula for sin is sin²x = 1 - cos²x.
Hypotenuse²=base²+perp²
(8)²=(7)²+(perp)²
64=49+(perp)²
64/49=perp²
1.306=perp²
Now taking square root on both sides
Perp=√1.306
Perp=1.142
Sin C=opposite/hypotenuse
Sin =1.142/8
Sin C=0.14285
C=Sin^-1 0.14285
C=8.212°
Answer is 8.212°.
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ange the following polynomial in column and then add 1.(9x+3y)+(5x-4y)
)????????????????????????????????????????????????
Answer:
14x - y
Steps:
(9x + 3y) + (5x - 4y)
Determine the sign:
9x + 3y + 5x - 4y
Combine as terms:
14x - y
I hope it helps you :)
Can anyone help me answer this question?
In a geometric progression, the first term is 7, the last term 448 and the sum 889. Find
the common ratio.
Answer:
Step-by-step explanation:
Given : In a GP the first term is 7
the last term is 448
and the sum 889
To find : Common ratio ? The number of terms is 7.
The common ratio is 2
Answer:
common ratio (r) = 2
Step-by-step explanation:
solution in picture
a jit system uses kanban cards to authorize movement of incoming parts. in one portion of the system, a work center uses an average of 99 parts per hour while running. the manager has assigned an inefficiency factor of .31 to the center. standard containers are designed to hold 5 dozen parts each. the cycle time for parts containers is about 105 minutes. how many containers are needed? (
The required number of containers are two.
How to solve the problem to number of container?105 minutes per process cycle.
We must first determine the utilization rate of the process in order to determine the number of containers required for the parts. Usage rate is the typical unit utilised each hour.
The scenario specifies that the procedure uses 88 components every hour.
The net cycle time per part per hour is determined as follows: (99/60) x 105 = 173.25
0.31 is the efficiency factor.
We can determine the total number of things Kanban can maintain using the information provided:
= 173.25/(1 - 0.31)
= 119.54
We may calculate the total number of containers required by dividing the container capacity by the entire number of parts after we know how many total pieces will be stored.
Each container can hold 8 dozens, or 96 pieces.
= 119.54
Consequently, two containers are required.
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The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens' answers. If there are 130,000citizens in the community, how many chose Cats, Dogs, or Birds
On solving the provided question, we can say that be equation the value we obtain Number of citizens × total percentage = 140,000 x (23%+11%) = 47,600
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
number of citizens who chose cat or fish is 47,600
Number of citizens × total percentage
140,000 x (23%+11%)
140,000 x 34%
= 47,600
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A city planner make a cale drawing of a propoed playground. The length of the actual playground i 78 feet, and the width i 42 feet. Suppoe a cale of 0. 5 inch = 6 feet i ued. Which dimenion repreent the playground on the cale drawing?
The dimensions size on the scale drawing is 6.5 inches by 3.5 inches.
Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.
In Geometry we can have different dimensions, The number of dimensions is how many values are needed to locate points on a shape.
Multiplying the actual dimensions by the scale gives the scale dimensions:
(0.5 in)/(6 ft) × {78 ft, 42 ft}
= {39/6 in, 21/6 in}
= {6.5 in, 3.5 in}
Therefore, the dimensions size on the scale drawing is 6.5 inches by 3.5 inches.
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refer to exercise 75. how surprising would it be for more than 4 elk in the sample to survive to adulthood? calculate an appropriate probability to support your answer.
According to the given possibility the event of more than 4 elk surviving to adulthood is not surprising and the appropriate probability is 0.1402.
Here we have given that it be for more than 4 elk in the sample to survive to adulthood.
Then the probability is calculated by using the binomial probability,
And here we have to use the addition rule for mutually exclusive event, then we get,
=> P(AUB) = P(A or B) = P(A) + P(B)
At the possibility of k = 5 we have the binomial probability to be evaluated as follows:
=> P(X = 5) = 21 (0.44)⁵ (0.56)² ≈ 0.1086
At the possibility k = 6 then the binomial probability to be calculated as,
=> P(X = 6) = 7(0.44)⁶ (0.56)¹ ≈ 0.0284
Finally at the value of k = 7 then the binomial probability to be evaluated as,
=> P(X = 7) = 1 (0.44)⁷(0.56)° ≈ 0.0032
Therefore the two different numbers of successes are impossible on same simulation is by applying the addition rule for mutually exclusive events is calculated as,
=> P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)
=> 0.1086 +0.0284 + 0.0032
=> 0.1402
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If h(x) = -x(1 - x), find h(-3).
Answer:
12
Step-by-step explanation:
h(-3)= -(-3)(1-(-3))=
3(4)=12
question 6 a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales. the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less. what function can they use?
The required function,which best describe the problem is split function.
What is Split function?By designating one of the given string's sub-strings as the delimiter, the split() method can be used to divide a given string or line. The output is the string that comes before and comes after the substring that was supplied as a delimiter.
According to question:a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales.
the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less.
This situation is defined for split function, which is best describe it.
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What is the 4 in front of the formula called?
The 4 in front of the formula is called a coefficient.A coefficient is a number that is multiplied by a variable or a constant in an algebraic expression.
In this case, the 4 is being multiplied by the formula, which makes it a coefficient.
A coefficient is a numerical value that is used in an algebraic expression or equation. It is placed in front of a variable or a constant, and it is multiplied by that particular element. The coefficient is used to adjust the value of the expression or equation, and it can be any number, including fractions, negative numbers, and decimals. For example, if a formula were written as 4x + 2 = 10, then the 4 in front of the x is the coefficient. This number is used to adjust the value of the expression, and it can be changed to any other number in order to alter the equation. Coefficients are very useful in mathematics, and they can be used to solve many types of equations and problems.
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10. Your little brother borrows
$5.50 from you. You now have
$20. Which equation shows how
much money you had before you
let your brother borrow money?
Answer:x-5.50=20
Step-by-step explanation:
3 times what equals 5?
Answer: its 1.6667.
Answer:
Step-by-step explanation
3*X=5
X=5/3
X=1.67
Zell invested $80,000 in two different types of stocks. The first type earned 9% and the second type earned 12%. If the profit on the 12% stocks was $150 more than the profit on the 9% stocks, how much did Zell invest in the 9% stock?
Zell invested $80,000 in two different types of stocks. Solving for x gives us the amount invested in the 9% stock:
x = $45000
What is stock?Generally, Let x be the amount invested in the 9% stock.
Then (80,000 - x) is the amount invested in the 12% stock.
The profit on the 9% stock is 0.09 * x and the profit on the 12% stock is
0.12 * (80,000 - x).
We know that the profit on the 12% stock is $150 more than the profit on the 9% stock.
So we can set up the following equation:
0.12 * (80,000 - x)
= 0.09 * x + 150
x=45000
Therefore, Zell invested $80,000 in two different types of stocks. the amount invested in the 9% stock is $45000
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Answer:
$45,000
Step-by-step explanation:
A school has a square courtyard and wants to create diagonal walkways. the length of
each side of the courtyard is 25 meters. approximately how long is each walkway?
The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.
In the given question, a school has a square courtyard and wants to create diagonal walkways.
The length of each side of the courtyard is 25 meters.
We have to find how long is each walkway.
By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.
According the Pythagorean Theorem
[tex]a^2+b^2 = c^2[/tex]
[tex](25)^2+(25)^2=c^2[/tex]
Now solving,
625 + 625 = [tex]c^2[/tex]
[tex]c^2[/tex] = 1250
Taking square root on both side, we get
c = 35.36 meters.
Hence, 35.36 meters long is each walkway.
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Which statement is true of table A and table B shown below?
Table A represents a function because there is only one output for
each input value.
Table B represents a function because there is only one output for
each input value.
Table A represents a function because there is only one input for each
output value.
Table B represents a function because there is only one input for each
output value.
Table A represents a function, but Table B does not represent a function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.
As, each element of X is associated with unique element of Y, so this is a function.
Table A
X Y
3 1
2 0
1 0
As, each element of X is associated with a unique element of Y, so this is a function.
Table B
X Y
3 -2
5 1
5 2
Hence, Table A represents a function, but Table B does not represent a function.
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Help w number 1 please super confused
An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
How do you identify congruent angles?An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.An equilateral triangle always has angles that are 60° in length.
It is referred to as an isosceles triangle when a triangle's two sides are identical. When the corresponding sides and angles of two angles match, the angles are said to be congruent.
When stacked, two angles are also congruent if they match.
If they line up with each other after turning or moving it, then.
Also creating equivalent vertex angles are a parallelogram's diagonals.
Congruent sides - L and X, G and Y, and F and T.
Congruent angles - ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
ΔLGF ≅ ΔXYT
Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
Congruent sides are L and X, G and Y, and F and T.
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what is the maximum of the sinusoidal function? enter your answer in the box.
Answer:
Step-by-step explanation:
B
give the equation of the line in slope intercept form of the line with a slope of -4/3 and that passes through the point (3,-3)
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \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}{(-3)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +3= -\cfrac{4}{3} (x -3) \\\\\\ y+3=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x+1 \end{array}}[/tex]
Please Help me out!!
The solution to f(g(h(x))) = [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
f(x) = [tex]x^{4} + 6[/tex]
g(x) = [tex]x-3[/tex]
h(x) = [tex]\sqrt{x}[/tex]
Therefore to find f(g(h(x))),
fogoh(x) = f(g(h(x)))
We first substitute the value of h(x) as above,
f(g([tex]\sqrt{x}[/tex] )) ....... as h(x) = [tex]\sqrt{x}[/tex]
Now, we substitute the value of g(x) where x is [tex]\sqrt{x}[/tex]
f([tex]\sqrt{x} -3[/tex]) ....... as g(x) = [tex]x-3[/tex]
Then we substitute the value of x in f(x) with [tex]\sqrt{x} -3[/tex]
[tex](\sqrt{x} -3)^{4} + 6[/tex]
Now we further solve to find a simpler form of the equation,
[tex](\sqrt{x} -3)^{4} + 6[/tex]
= [tex](x^{2} -12x^{3/2} +54x- 108\sqrt{x} +81) + 6[/tex]
= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
Therefore, fogoh(x) = f(g(h(x))= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
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Wyatt has $780 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax.
he buys a new bicycle for $398.35.
he buys 2 bicycle reflectors for $19.41 each and a pair of bike gloves for $35.27.
he plans to spend some or all of the money he has left to buy new biking outfits for $46.60 each.
write and solve an inequality which can be used to determine oo, the number of outfits wyatt can purchase while staying within his budget.
The inequality which can be used to determine too, the number of outfits Wyatt can purchase while staying within his budget is:
780 ≥ 472.44 + 46.60x
Inequality:
In mathematics, equations are not always balanced on both sides using equal signs. It can also be about "not equal" relationships, such as one being greater than the other or less than the other. In mathematics, an inequality refers to a relationship in which two numbers or other mathematical expressions do not compare equally. These formulas belong to algebra and are called inequalities.
An inequality means that two things are not the same. One of them may be less than, greater than, less than or equal to, greater than or equal to the other.
p ≠ q means p is not equal to qp < q means p is less than qp > q means p is greater than qp ≤ q means p is less than or equal to qp ≥ q means p is greater than or equal to qAccording to the question:
As based on the information,
he can't spent more than $780.
Four cycle reflector cost = 2 × $19.41
= $38.82
Let maximum number of outfit = x
and Cost = 46.60x
and the the pair of glove is for $35.27.
Therefore,
New bicycle + Bicycle reflectors + Biker gloves + Biking Outfit ≤ 780
⇒ $398.35 + $ 38.82 + $ 35.27 + $46.60 x ≤ 780
⇒ 472.44 + $ 46.60x ≤ 780
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suppose car gas mileage is normally distributed with a mean of 25 miles per gallon. if 67% of cars get at least 23 miles per gallon, what percentage of cars get less than 30 miles per gallon? a
So, on solving the provided question, we can say that percentage = 1/15 X 100 = 15%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
car gas mileage is normally distributed with a mean of = 25 miles per gallon
67% of cars get at least 23 miles per gallon
percentage of cars get less than 30 miles per gallon
25-23/30
2/30
1/15
percentage = 1/15 X 100 = 15%
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Area under the curve
f(x) = x 2 + 2x
g(x) = x + 2
Answer: The area under the curve refers to the area between the curve of a function and the x-axis. To find the area under the curve of a function, you would typically integrate the function with respect to x and then evaluate the definite integral between a set of limits.
For example, to find the area under the curve of f(x) = x^2 + 2x from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x^2 + 2x) dx = (1/3)x^3 + x^2 evaluated from x=0 to x=a,
Similarly, to find the area under the curve of g(x) = x + 2 from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x + 2) dx = (1/2)x^2 + 2x evaluated from x=0 to x=a
It's important to note that the definite integral is only defined if the function is continuous and has no vertical asymptotes on the interval.
Step-by-step explanation:
A torch and a battery cost 2. 50 altogether. The torch costs 1. 50 more than the battery. What fraction of the total price is the torch?Give your answer in its simplest form
The fraction of the total price that the torch is is 4/5.
Let x be the cost of the battery.
We know that the torch cost is 1.50 more than the battery cost. So, the cost of the torch is
x + 1.50
The total cost is the sum of the cost of the battery and the torch, so:
x + (x + 1.50) = 2.50
2x + 1.50 = 2.50
Solving this equation we get,
x = 0.50
Therefore the cost of the battery is 0.50 and the cost of the torch is 2.00.
To find the fraction of the total price that the torch is, we divide the cost of the torch by the total cost:
= (2.00) / (2.50)
= 4/5
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In the diagram, if PW = 12 and PT = 9, find PX.
The length of segment PX in this problem is given as follows:
PX = 9.
How to obtain the length of segment PX?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
In this problem, all the horizontal lines are parallel, hence the side is divided proportionality, as the resulting triangles in the context of this problem are all similar.
PX is three-fourths of the length of the segment PW = 12, hence it's length is given as follows:
PX = 3 x 12/4
PX = 3 x 3
PX = 9 units.
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Ishi walked a total of 2 miles on a treadmill. He walked at a constant rate of 4 miles per hour. Which expression shows how long, in minutes, Ishi walked on the treadmill? 2.5 miles : 4 moles/hour x 60 minutes/1 hour 2.5 miles : 4 mmoles/hour x 60 minutes/1 hour 2.5 miles : 4 mom/10 mg x 60 minutes/1 hour 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.
Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
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Convert 17 cm to decimeters
Answer: 1.7
Step-by-step explanation: First, let's see how many decimeters are in 1 cm. To find it, we must divide the cm by 10. So, we can do 17 / 10 or move the decimal one spot left. They should both = 1.7. I hope this helped!
what are the four calculator operations that a student is expected to be able to perform on the ap test?
While some College Board math sections permit all students to use a calculator, other math portion do not. Students can prayer the use of a four-function calculator for use on Non calculator sections.
Four-function calculators are basic calculators that have functions limited to subtraction, addition, multiplication, square roots, division, and percentage.
Four-function calculators can only be used on test portion that need math calculations.
They must be put away during non-mathematical part.
Board policy on use of a calculator may vary by exam. Check by reading calculator rules for the PSAT/NMSQT and PSAT 10 and the SAT or visiting AP Students to read calculator policies for specific AP exams.
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a lawn sprinkler located at the corner of a yard rotates through 80 degrees and sprays water of 20 ft. what is the length of the arc of the sector watered?
The length of the arc of the sector watered is 0.89π.
In the given question, a lawn sprinkler located at the corner of a yard rotates through 80 degrees and sprays water of 20 ft.
We have to find the length of the arc of the sector watered.
From the given question,
r = 20 ft, θ = 80 degree
A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends.
The formula for the length of the arc of the sector watered is
L = [tex]\frac{\theta}{360^{o}}\times 2\pi r[/tex]
Now putting the value
L = [tex]\frac{80^{o}}{360^{o}}\times 2\times\pi \times20[/tex]
Now simplifying the length
L = [tex]\frac{320^{o}}{360^{o}}\pi[/tex]
L = 0.89π
Hence, the length of the arc of the sector watered is 0.89π.
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