To evaluate the integral | cos(ina), x g to break it down to two parts: Use u-substitution method u = ln to show | cos(In a) = le = el cos udu Evaluate the integral in part (a) using Integration by Pa
The integral |cos(inx)| dx can be expressed as:
|cos(inx)| = -(1/in) sin(inx) for π/(2n) ≤ x ≤ π/n
What is integration?The summing of discrete data is indicated by the integration. To determine the functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.
To evaluate the integral ∫|cos(inx)| dx, we can break it down into two parts based on the periodicity of the absolute value function:
∫|cos(inx)| dx = ∫cos(inx) dx for 0 ≤ x ≤ π/(2n)
= -∫cos(inx) dx for π/(2n) ≤ x ≤ π/n
Now, let's focus on the first part of the integral:
∫cos(inx) dx for 0 ≤ x ≤ π/(2n)
We can use the substitution u = inx, which implies du = in dx. Rearranging, we have dx = du/(in). Substituting these values, we get:
∫cos(u) (1/in) du = (1/in) ∫cos(u) du
Integrating cos(u) with respect to u gives us sin(u):
(1/in) ∫cos(u) du = (1/in) sin(u) + C
Now, let's evaluate the second part of the integral:
-∫cos(inx) dx for π/(2n) ≤ x ≤ π/n
Using the same substitution u = inx, we can rewrite the integral as:
-∫cos(u) (1/in) du = -(1/in) ∫cos(u) du
Again, integrating cos(u) with respect to u gives us sin(u):
-(1/in) ∫cos(u) du = -(1/in) sin(u) + C
Now we have evaluated both parts of the integral. Combining the results, we get:
∫|cos(inx)| dx = (1/in) sin(inx) for 0 ≤ x ≤ π/(2n)
= -(1/in) sin(inx) for π/(2n) ≤ x ≤ π/n
Therefore, the integral |cos(inx)| dx can be expressed as:
|cos(inx)| = (1/in) sin(inx) for 0 ≤ x ≤ π/(2n)
= -(1/in) sin(inx) for π/(2n) ≤ x ≤ π/n
Note: The second part of the integral could also be written as (1/in) sin(inx) with a negative constant of integration, but for simplicity, we have used the negative sign inside the integral.
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Kyle is practicing for a 3 mile race. His normal time is 23 minutes and 26 seconds. Yesterday it took him 21 minutes and 38 seconds. How much faster was Kyle's time yesterday than his normal time?
Kyle's yesterday's time was 108 seconds, or 1 minute and 48 seconds, faster than his normal time.
How much faster was Kyle's time yesterday than his normal time?To find the difference in time between Kyle's normal time and yesterday's time, we need to subtract his normal time from yesterday's time:
(21 minutes 38seconds)−(23 minutes 26 seconds)
(21 minutes 38 seconds)−(23 minutes 26 seconds)
We can first convert both times to seconds to make the subtraction easier:
=(21×60+38)seconds
−(23×60+26)seconds
=(21×60+38) seconds−(23×60+26) seconds
=(1298 seconds)−(1406 seconds)
=(1298 seconds)−(1406 seconds)
=−108 seconds
=−108 seconds
The result is negative because Kyle's yesterday's time is faster than his normal time. To find the positive difference, we can multiply by -1:
∣−108∣ =108seconds
∣−108∣= 108 seconds
Therefore, Kyle's yesterday's time was 108 seconds, or 1 minute and 48 seconds, faster than his normal time.
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5. Write an equation of a line in standard form for the given conditions. passes through (0,0) and is perpendicular to the line 2- y=6
Answer:
69
Step-by-step explanation:
Which situation is best represented by the following equation?
45w + 123.95
753.95
Answer:
w=14
Step-by-step explanation:
753.95-123.95=630
630 divided by 45=14
So w=14
Answer:
w=14
Step-by-step explanation:
753.95-123.95=630
630 divided by 45=14
So w=14
If 52 men can do a piece of work in 35 days in how many days will 28 men to it?
28 mando the peace of work in 41 days
by divida 52 and 35 and multiiply with28
Select the methodology that would result in a subjective probability....
Dividing the number of favorable events by the number of possible events.
Studying the fraction of times in the past a particular event has happened.
Weighing the available information and assigning a probability.
Weighing the available information and assigning a probability.
A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It solely represents the subject's thoughts and prior experience and does not include any formal computations. A "gut instinct" used when making a deal is an illustration of subjective probability.
So, as per the definition of subjective probability
Dividing the number of favourable events by the number of possible events and Studying the fraction of times in the past a particular event has happened, both can be determined through calculations mathematically accurate but for Weighing the available information and assigning a probability we might use a "gut instinct". Thus
Weighing the available information and assigning a probability.
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what divided by 5/6 equals 3/5
Answer:
let the decided no. be x
Now
\( \frac{5}{6} \times \frac{1}{x} = \frac{3}{5} \)
\(5 \times 5 = 3 \times 6x\)
\(x = \frac{25}{18} or1 \frac{7}{18} \)
is a required answer.
when
no. divided by 5/6 equals 5/3
now
\( \frac{5}{6} \times \frac{1}{x} = \frac{5}{3} \)
\(5 \times 3 = 5 \times 6x\)
\(x = \frac{15}{30} \)
\(x = \frac{1}{2} \)is a required answer.
The soulution to 6+2x>32 is either x>13 or x<13. Which soulution is correct? Explain how you know - prove it with a number
Answer:
6+2x >32
2x>32-6
2x>26
divide both sides by 2
therefore, x>13
Step-by-step explanation:
this is because x don't has a negative sign or is on the other side
Alex and Thomas share 300 sweets.
They divide them in the ratio 3:2.
How many sweets does Thomas have?
Is the given value a solution of the inequality?
z + 2> -4; z+ -8
.
Step-by-step explanation:
Yum-Yum-Yum restaurant has just increased the wages they pay their employees. to help offset this added expense, Yum-Yum-Yum must mark up their meals by 12% if the average meal costs $7.99, how much will it cost after the markup?
Answer:
12% of 7.99
=0.96$
so...
The cost after Markup
=7.99$+0.96$
=8.95$answer/explanation:
carry out these steps: 12% of 7.99 = $0.96 and use fraction if u may like. therefore the new cost after the markup is $7.99 + $0.96 which is then equal to your final answer - $8.95!
x + y = 16
2y = -2x + 2
Answer:x=−y+16x=−y+1
Step-by-step explanation:
solve the initial-value problem. 2xy' y = 6x, x > 0, y(4) = 18
The solution to the initial-value problem is y =\(18x^{-3/8\) with x > 0 and y(4) = 18.
To solve the initial-value problem 2xy'y = 6x with x > 0 and y(4) = 18, we need to use the method of separation of variables.
First, we can write the equation in the form y' = f(x,y), where f(x,y) = 3/\(x^2\).
Next, we separate the variables by dividing both sides by y and multiplying both sides by dx:
(2x/y) dy = 3/\(x^2\) dx
We integrate both sides:
∫(2x/y) dy = ∫3/\(x^2\) dx
ln|\(y^2\)| = -3/x + C
where C is the constant of integration.
We can simplify this expression using the initial condition y(4) = 18:
ln|\(18^2\)| = -3/4 + C
C = ln(324) + 3/4
So the solution to the initial-value problem is:
ln|\(y^2\)| = -3/x + ln(324) + 3/4
Simplifying further:
ln|\(y^2\)| = ln(324\(x^{-3/4\))
|\(y^2\)| = 324\(x^{-3/4\)
y = ± 18\(x^{-3/8\)
Since y(4) = 18, we choose the positive sign:
y = 18\(x^{-3/8\)
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Of the 50 students in the sixth grade, 16 are girls. What percent are girls?
Answer:
Step-by-step explanation:
That is (16/50) * 100
= 16 * 100/50
= 16 *2
= 32%.
Answer: 32%
Step-by-step explanation:
put it into a fraction, 16/50 then multiply by 2 to get 32/100 now you can turn that into a percent to get 32%
PLS COME AND LOOK!!! I NEED YOU GENIUSES!!! I WILL GIVE BRAINLIEST!!!!! AT LEAST COME AND LOOK!!!! WILL FOREVER BE GREAT FULL!!! EASY IM JUST DUMB!!
Choose one value that is in the domain of both ( ) = 2and 2 = and that is greater than 0. Substitute that value into ( ) = 2and 2 = and then simplify. Explain how your answers help to show that the graph on the left represents a function while the graph on the right represents a relation. Show your work and use function notation where possible
(ignore the little checks on the graph lol)
Heres a Simple Answer:
1. The one on the left follows the Vertical Line test, while the one on the right doesn't
2. A function is either y = mx+b, or a Nonlinear function. The one on the right is a Parabolic Function becuase it has the x^2 on it. The right one is y^2, which is not a function.
(Not very good, but I gtg so I rushed.)
*I NEED THIS ASAP*
5. number of terms
6. degree
7. leading coefficient
8. end behavior
9. turning point(s)
10. x-intercept(s)
11. relative minimum(s)
12. relative maximum(s)
Answer:
5 terms
to the fourth degree
leading coeff of 1
3 turning points
end behavior (when x -> inf, y -> inf. When x -> - inf, y -> -inf)
x intercepts are (0,-4) (0,-2) (0,1) (0,3)
Relative min: (-3.193, -25) (2.193, 25)
Relative max: (-0.5, 27.563)
Step-by-step explanation:
The terms can be counted, seperated by the + and - in the equation given.
The highest exponent is your degree.
The number before the highest term is your leading coeff, if there is no number it is 1.
The turning points are where the graph goes from falling to increasing or vice versa.
End behaviour you have to look at what why does when x goes to -inf and inf.
X int are the points at which the graph crosses the x-axis.
The relative min and max are findable if you plug in the graph on desmos or a graphing calculator.
Kerry has an investment account which compounds interest annually at a rate of 4. 4%. After 3 years, she has $7080 in the account. How much money did she initially place in the account? round your answer to the nearest whole number. Do not include a $ in your answer.
She initially placed $6222 in the account.
With annual compound interest accruing at a rate of 4.4% after three years, she has now $7080 in the account.
From the question, we have
7080 = A * (1 + 4.4/100)^3
7080 = A * 1.1379
A = 7080/1.1379
= 6221.99 = $ 6222 (approx.)
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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You have just signed up for a broadband home internet service that uses coaxial cable. which connector type will you most likely use?
Answer:
F type connector
Step-by-step explanation:
Use an F-type connector for broadband cable connections that use coaxial cable.
The F connector is a coaxial RF connector commonly used for "over the air" terrestrial television, cable television and universally for satellite television and cable modems,
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F type connector
The F-connector is a coaxial RF connector commonly used for "wireless" terrestrial television, cable television, and common for satellite television and cable modems, usually with RG-6/U cable or with RG -59 / U.F connector is also known as threaded connector. There are two main types: 7mm (6.8mm) is the most common and used in coaxial cable, and 5mm connector is used in thin coaxial cable commonly used in satellite system.
The F-connector is an accessory that connects a coaxial cable to an electronic device or wall outlet.
Type F connectors are highly mechanical and electrically stable coaxial screw connectors for cable television (CATV), set-top boxes, cable modems and satellite television applications up to 4 GHz
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5<2y<12 where y is an integer.
Write down all the possible values of y.
Answer:
y = 3, 4, or 5
Step-by-step explanation:
Step 1; Simplify the Double Inequality
Let's first simplify this double inequality to make answering this problem a bit easier. This means getting the middle term to be just y, without any added constant or coefficients.
In this case, this is a fairly simple process, as all we have to do to get y by itself is just divide the entire inequality by 2. This means that we will also divide the 5 and 12 by 2. (Note that the signs stay the same because we are not dividing by a negative number.)
Doing so gives us the following double inequality: 2.5 < y < 6.
Step 2: Identify the Integers in this Range
Now that we have a simplified double inequality, all we need to do is find all of the integers in its range. (Recall that an integer is any number that is not a fraction when fully simplified (ex. …-1, 0, 1...).)
In other words, we need to find all of the integers in between 2.5 and 6. Note that we don't include 6 because of the "<" sign, which indicates that the 2.5 and 6 are not included in the set. These numbers are 3, 4, and 5, making them your answer. Hope this helps!
A company manufactures and sells shirts the daily profit. The company makes depends on how many shirts they sell the profit in dollars when the company sells X shirts can be found using the function F (X)equals 6X -90 find the interpret the given function values and determine inappropriate domain for the function f(-9)
profit of
of the problem.
=
f(27)
profit of
of the problem.
=
f(17.5) =
profit of
of the problem.
meaning if the company sells |
dollars. This interpretation
meaning if the company sells
dollars. This interpretation
, meaning if the company sells
dollars. This interpretation
shirts, they would make a
in the context
shirts, they would make a
in the context
shirts, they would make a
in the context
The increase in earnings brought on by producing one extra unit is known as the marginal profit. The proper domain for functions is the integers (0, 1, 2, ...).
Explain about the Marginal profit?By dividing marginal revenue by marginal cost, one can compute marginal profit. Because it can help determine whether to raise or lower the level of output, marginal profit analysis is useful.
Any quantity of output below the one at which marginal profit equals zero has a positive marginal profit, meaning that profit can be increased by producing more of that quantity. Conversely, any quantity of output above the one at which marginal profit equals zero has a negative marginal profit, meaning that profit can be increased by producing less of that quantity.
A company that manufactures and sells shirts. Daily profit of...
A company that manufactures and sells shirts. The daily profit the company makes depends on the number of shirts sold. The profit in dollars if a company sells x shirts can be found using the function f(x)=7x-40. Locates and interprets given function values to determine the appropriate domain for the function.
f(-10) = -110, which means that if the company sells -10 shirts, it will make a profit of -$110. This interpretation makes no sense in the context of the problem.
f(10) = 26.5, so if the company sells 9.5 of his shirts, he makes a profit of $26.5. This interpretation makes no sense in the context of the problem
f(9.5) = 26.5, so if the company sells 9.5 shirts, it makes a profit of $26.5. This interpretation makes no sense in the context of the problem.
Therefore, based on the above observations, it is clear that the proper domain for functions is the integers (0, 1, 2, ...).
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need someone to answer as soon as possible!
Please please with proof too
The solutions to the system of equations are x=5, z=1,y=-3
What is system of equations?
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where each of these equations crosses, are the solutions of systems of equations.A system of equations in algebra consists of two maybe more equations and looks for common answers to the equations.Given equations:
x+y+z=3
3x+(y/3)-2z=12
-5x-6y+3z=-4
Solving by using the substitution method:
\(\begin{bmatrix}x+y+z=3\\ 3x+\left(\frac{y}{3}\right)-2z=12\\ -5x-6y+3z=-4\end{bmatrix}\)
Substitute x=3-y-z
\(\begin{bmatrix}3\left(3-y-z\right)+\frac{y}{3}-2z=12\\ -5\left(3-y-z\right)-6y+3z=-4\end{bmatrix}\)
Substitute z={8y+9}/{15}
\(\begin{bmatrix}-y+8\left(-\frac{8y+9}{15}\right)-15=-4\end{bmatrix}\)
simplify
\(\begin{bmatrix}\frac{-79y-72}{15}-15=-4\end{bmatrix}\)
Substitute y=-3
\(z=-\frac{8\left(-3\right)+9}{15}\)
z=1
For x=3-y-z
Substitute z=1,y=-3
x=3-(-3)-1
x=5
The solutions to the system of equations are:
x=5, z=1,y=-3
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Select the correct answer. the dimensions and number of animals are given for different corrals. corral length width number of animals 1 50 meters 40 meters 110 2 60 meters 35 meters 115 3 55 meters 45 meters 125 4 65 meters 40 meters 130 the population constraints state that each corral should have at least 20 square meters for each animal. which corral meets this requirement? a. corral 1 b. corral 2 c. corral 3 d. corral 4
The corrals that satisfies the population constraint that requires at least 20 square meters of area per animal is option (d) corral 4
To determine which corral meets the population constraints of at least 20 square meters for each animal, we need to calculate the area of each corral and divide it by the number of animals in that corral. If the result is at least 20 square meters, then the corral meets the requirement.
Corral 1: Area = length x width = 50 x 40 = 2000 square meters. Number of animals = 110. Area per animal = 2000/110 = 18.18 square meters. Therefore, Corral 1 does not meet the requirement.
Corral 2: Area = length x width = 60 x 35 = 2100 square meters. Number of animals = 115. Area per animal = 2100/115 = 18.26 square meters. Therefore, Corral 2 does not meet the requirement.
Corral 3: Area = length x width = 55 x 45 = 2475 square meters. Number of animals = 125. Area per animal = 2475/125 = 19.8 square meters. Therefore, Corral 3 meets the requirement.
Corral 4: Area = length x width = 65 x 40 = 2600 square meters. Number of animals = 130. Area per animal = 2600/130 = 20 square meters. Therefore, Corral 4 meets the requirement.
Therefore, the answer is (d) Corral 4.
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Answer:
D. Corral 4
Hope this helps!
Step-by-step explanation:
A coordinate for f(c) is shown, give the new point for the transformation of f(x):
(3,6)
g(x)=f( 1/2x)-7
What is the new coordinate for (x,y)?
The x-coordinate of the new point is 3/2 but we cannot calculate the exact value of the new y-coordinate.
The new coordinate for the transformation of f(x) under the function g(x) = f((1/2)x) - 7, we'll start with the given point (3, 6) and apply the transformation.
First, let's substitute x = 3 into the transformation equation:
g(3) = f((1/2)(3)) - 7
= f(3/2) - 7
Now, to determine the new y-coordinate, we need to know the value of f(x) at x = 3/2.
Without specific information about the function f(x), we cannot calculate the exact value of f(3/2) or the new y-coordinate.
We can still provide a general representation of the new coordinate for any function f(x).
Let's denote the new coordinate as (x', y'):
x' = 3/2
y' = f(3/2) - 7
The value of y' will depend on the function f(x) and its behavior at x = 3/2. If you provide the specific function f(x), we can substitute it into the equation to determine the exact value of y' and provide the coordinates (x', y').
The function f(x), we can determine the new x-coordinate as 3/2, but we cannot calculate the exact value of the new y-coordinate or provide the specific new coordinate (x', y') without additional information.
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What is the rate of change of the area of a circle with respect to the radius when the radius is 4 in?
The rate of change of the area of circle with respect to radius is: 8π.
What is the rate of change of a function?The rate at which one quantity changes in relation to another quantity is known as the rate of change of a function.
Now,
Area of a circle having radius (=r) is given by: A = πr²
The rate of change of area of the circle will then be given by:
\(\frac{dA}{dr}=\pi \frac{d}{dr}(r^{2})=2\pi(r)\)
For r = 4, \(\frac{dA}{dr}=2\pi(4)=8\pi\)
Hence, the rate of change of area of the circle when the radius is 8π.
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Simplify problem: ∛-27n^27
Answer:
-3n⁹
Step-by-step explanation:
= \(\sqrt[3]{-27n^(27)}\)
= \(\sqrt[3]{-27} * \sqrt[3]{n^{27}}\)
= (-3) × n⁹
= -3n⁹
Consider the decay of a tau lepton to a π meson, τ−→π−vτ, or to a K meson, τ−→K−vτ. Draw the lowest-order Feynman diagrams for both decays, labelling all particles clearly and indicating the coupling strength at each vertex.
The Feynman diagrams are as follows:For τ−→π−vτ:Here, the interaction is through the W−boson, which causes the decay. The τ− and the ντ are both fermions, and the π− meson is a boson.
Therefore, the coupling constant is of strength g.For τ−→K−vτ:
Here, the interaction is through the W−boson, which causes the decay.
The τ− and the ντ are both fermions, and the K− meson is also a boson. Therefore, the coupling constant is of strength g.
The Feynman diagrams show the lowest-order for the decay of tau lepton to a π meson and to a K meson. The interaction is through the W−boson, which causes the decay, the τ− and the ντ are both fermions, and the π− and K− mesons are bosons, which show the coupling constant of strength g at each vertex.
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Please help i will mark brainiest! You will get 20 points
Which of the following is most likely the next step in the series?
Z3, y6, X9, w12, . . .
A. u18
B. V18
C. V15
D. v15
Answer:
C. V15
Step-by-step explanation:
Each step we go back a letter in the alphabet and up 3 numbers.
Hope this helps! :)
Answer:
C. V15
Step-by-step explanation:
I got the answer correct.
Is the relation shown in the table a function? Use the graph and justify your answer. x 2 4 8 10 y 3 2 0 –1 A coordinate grid from 0 to 9 on both axes. A. Yes. The relation is a function. The graph of the function is a straight line and has a constant rate of change. B. Yes. The relation is a function. The graph of the function is a curve. C. No. The relation is not a function. The graph of the relation does not pass through the origin. D. No. The relation is not a function. The graph of the relation is not a straight line.
Answer:
Yes; for each input there is exactly one output. 2. ANSWER: No; the domain value 6 is paired with both 9 and 10. 3. {(2, 2), (−1, 5), (5, ... Draw a graph showing the relationship between
Step-by-step explanation:
i think that is the answer
Answer: Yes, the relatoin is a function. the graph of the function is a straight line.
Step-by-step explanation: If it is a straight line it is a function.
Given the equation f(x,y)=2xln(y2+y) compute dydf(7,y) at y= 8. Round your answer to one decimal place.
The value of dy/df(7, 8) is 0.3 (rounded to one decimal place).
The given equation is f(x, y) = 2xln(y2 + y).To compute dy/df(7, y) at y = 8, we will begin by calculating the partial derivative of f(x, y) with respect to y.df/dy= d/dy [2xln(y^2 + y)]We will apply the product rule and the chain rule to compute this derivative.df/dy= d/dy [2xln(y^2 + y)] = 2xd/dy [ln(y^2 + y)] = 2x * 1 / (y^2 + y) * (2y + 1)df/dy = (4xy + 2x) / (y^2 + y)Therefore, dy/df = 1 / df/dyNow, f(7, 8) = 2 * 7 * ln(8^2 + 8) = 2 * 7 * ln(8 * 9) = 14 * ln(72)We need to calculate the value of dy/df(7, 8) by using the above derivatives and f(7, 8)dy/df = 1 / df/dy(7, 8) = 1 / (4 * 7 * 8 + 2 * 7) / (8^2 + 8) = 1 / (224 + 14) / 72 = 72 / 238dy/df(7, 8) = 72 / 238 = 0.3025 (Rounded to one decimal place).
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jessa drew a circle with a circumference of 18.84 inches. which of these dimensions could be the diameter, in inches jessa used to draw her circle? use 3.14 for pi.
The dimensions of diameter of the circle is 6 inches which Jessa used to draw her circle.
The circumference of a circle is stated by the formula -
C = 2πr, where r refers to radius of the circle. Calculating radius now.
18.84 = 2πr
Rewriting the equation for radius of circle
r = 18.84/2×3.14
Performing division on Right Hand Side of the equation
r = 3 inches
As known, diameter is double the radius. Hence, diameter of the circle = 2×3
Performing multiplication on Right Hand Side of the equation
Diameter of the circle = 6 inches
Thus, the correct answer is A 6.
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The complete question is -
9.Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi.
A 6
B 15.7
C 3
D 9.42