A Histogram would be best
0.05% written as a decimal
Answer:
0.05% means 0.05 per every 100.
Step-by-step explanation:
We find it useful to convert 0.05% to decimal, because if you need to find 0.05% of any number, you can simply multiply that number with 0.0005.
hope this helps!!!!!
The value of 0.05% written as a decimal is 0.0005.
To write 0.05% as a decimal, you need to divide the percentage value by 100.
A decimal number is a number that uses the base-10 numbering system. It is a way of representing numbers using the digits 0-9 and a decimal point. Each digit in a decimal number represents a specific place value, which is a power of 10.
The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts or decimal fractions.
0.05% divided by 100 is equal to 0.0005.
Therefore, 0.05% written as a decimal is 0.0005.
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Find linearly independent functions that are annihilated by the given differential operator. (give as many functions as possible. use x as the independent variable. enter your answers as a comma-separated list.) d2 − 12d − 45
We want to find all [tex]f(x)[/tex] such that
[tex](D^2-12D-45)[f(x)]=0[/tex]
We have
[tex](D^2-12D-45)[f]=(D-15)(D+3)[f]=0[/tex]
so that either
[tex](D-15)[f]=0\implies f'-15f=0\implies f(x)=e^{15x}[/tex]
or
[tex](D+3)[f]=0\implies f'+3f=0\implies f(x)=e^{-3x}[/tex]
These solutions are linearly independent; we confirm this by computing the Wronskian:
[tex]W=\begin{vmatrix}e^{15x}&e^{-3x}\\15e^{15x}&-3e^{-3x}\end{vmatrix}=-3e^{12x}-15e^{12x}=-18e^{12x}\neq0[/tex]
We can also confirm that these solutions are correct by substituting the solutions for [tex]f(x)[/tex] in the differential equation:
[tex](D^2-12D-45)[e^{15x}]=225e^{15x}-12(15e^{15x})-45e^{15x}=0[/tex]
[tex](D^2-12D-45)[e^{-3x}]=9e^{-3x}-12(-3e^{-3x})-45e^{-3x}=0[/tex]
The linearly independent functions that are annihilated by the differential operator d2 − 12d - 45 are e^{15x} and e^{-3x}, found by solving the quadratic equation associated with the differential equation.
Explanation:The differential operator given is d2 − 12d - 45. To find out the linearly independent functions that are annihilated by this operator, we have to solve the homogeneous differential equation d2 − 12d - 45 = 0. This is a second order equation, so we expect two linearly independent solutions.
To find the solutions, we seek the roots of the associated quadratic equation m^2 - 12m -45 = 0. This can be factored into (m-15)(m+3), thus giving roots m = 15 and m = -3.
The general forms of the solutions for these roots are e^{15x} and e^{-3x} respectively. Therefore, the functions e^{15x} and e^{-3x} are linearly independent functions that are annihilated by the given differential operator d2 − 12d - 45.
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How many faces does a pyramid with a square base have? A. Five B. Eight C. Six D. Seven
Answer:
The answer is five.
Step-by-step explanation:
A pyramid with a square base has one square face and there are four triangle faces, so there are five in total.
I hope this helped! :-)
Number of faces of pyramid with a square base is 5.
Hence option A is correct.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Since we know that
A pyramid having square base have,
Number of square face = 1
Number of triangular face = 4
Hence total face in this triangle is,
= 1+4
= 5
Hence total faces = 5.
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Which polynomial represents a sum of cubes?
x^3 - 64
8x^3 + 125
16x^3 + 1
27x^3 + 4
Answer:
8x³ + 125
Step-by-step explanation:
Cubes: look for the exponent 3 and for perfect cubes such as 1, 8, 27, ...
8x^3 + 125 is a sum, and 8 is a perfect cube (the cube of 2), and x^3 is a cube, and 125 is a cube.
Thus, the correct answer is 8x^3 + 125 (which is equivalent to
(2x)³ + 5³).
What scale factor is shown by this graph?
1/2
2
4
1
SEE ATTACHED image!
the scale factor is 2.
because
if you look at the length AL in the smaller shape, it is 2 squares.
now if you look at the length AL in the enlarged shape, it is 4 squares.
to find the scale factor, do 4 ÷ 2 which is 2.
therefore the scale factor is 2
Answer:
The correct option is 2. The scale factor is 2.
Step-by-step explanation:
The coordinates of preimage are A(1,2), T(0,0), K(4,1) and L(3,2).
The coordinates of image are A'(2,4), T'(0,0), K'(8,2) and L'(6,4).
If a figure dilated by scale factor k with center at origin then the rule of dilation is
[tex](x,y)\rightarrow (kx,ky)[/tex]
[tex]A(1,2)\rightarrow A'(2,4)[/tex]
[tex]k=\frac{\text{x coordinate of image}}{\text{x coordinate of preimage}}[/tex]
[tex]k=\frac{2}{1}[/tex]
[tex]k=2[/tex]
Therefore the scale factor is 2 and the correct option is 2.
A rectangular fish pond is 21 ft2 in area. If the owner can surround the pond with a 20-foot fence, what are the dimensions of the pond?
3.5 ft by 6 ft
4 ft by 6 ft
3 ft by 7 ft
3.5 ft by 7 ft
Answer:
3 ft by 7 ft
Step-by-step explanation:
Try the solutions and find the one that works.
3.5 × 6 — area OK, perimeter = 19 ft
4 × 6 — area = 24 ft², perimeter OK
3 × 7 — area OK, perimeter OK
3.5 × 7 — area 24.5 ft², perimeter 21 ft
___
The perimeter is the sum of the four side lengths; the area is the product of two adjacent side lengths.
The scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. Select the linear equation that fits the data for tree 1, where x is the year and y is the trunk diameter, in inches
Answer:
Step-by-step explanation:
0.3. x + 18.3
The data for tree 1 is an illustration of a linear equation.
The linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]
From the complete question, we have the following points
[tex]\mathbf{(x_1,y_1) = (1,18.6)}[/tex]
[tex]\mathbf{(x_2,y_2) = (3,19.2)}[/tex]
First, we calculate the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{19.2 - 18.6}{3 -1}}[/tex]
[tex]\mathbf{m = \frac{0.6}{2}}[/tex]
[tex]\mathbf{m = 0.3}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
So, we have:
[tex]\mathbf{y = 0.3(x - 1) + 18.6}[/tex]
[tex]\mathbf{y = 0.3x - 0.3+ 18.6}[/tex]
[tex]\mathbf{y = 0.3x + 18.3}[/tex]
Hence, the linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]
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Isabell is thinking of a even number between 234 and 250 the sum of the digits is double the digit in the ones place what is Isabell's number
Answer:
246.
Step-by-step explanation:
Let the number be 2xy, then
2 + x + y = 2y and y must be even because the whole number is even.
y = 2 + x .
Now x must be even because y is even.
The only 2 numbers which fit are x = 4 and y = 6 so the number is 246.
Checking: 2+4+6 = 12 and 12 = 2*6.
Assume that x is a variable that has been declared as a double and been given a value. Write an expression to compute the quartic root of x. The quartic root of a number is the square root of its square root. EXAMPLES: For example, the quartic root of 16.0 is 2.0 because: the square root of 16.0 is 4.0 and the square root of 4.0 is 2.0. Another example: the quartic root of 81.0 is 3.0 because the square root of 81.0 is 9.0 and the square root of 9.0 is 3.0. Thus, to find the quartic root of a number you take the square root of the number and then take the square root of that. In this exercise you must find the quartic root of x in a single expression-- you must not write any statements. Also, you may only use the sqrt() static method defined in the Math class-- no other methods. (HINT: you will need to call the Math.sqrt() method twice-- and you will need to pass the return value of one of those calls as argument to the other call. AND REMEMBER: write an expression, not a statement.)
Answer:
sqrt(sqrt(x))
Step-by-step explanation:
A quartic root of is written mathematically as . THe quartic root of 16 is 2 since 2*2*2*2 = 16. However, a quartic root can also be defined as the square root of a square root. For example the √16 = 4 and the √4 = 2. This is the same response as taking the quartic root. This means you can write it as the sqrt(sqrt(x)). In the example, it would be sqrt(sqrt(16)) = sqrt(4) = 2.
The quartic root of a variable x can be calculated using the expression Math.sqrt(Math.sqrt(x)), which calls the square root function twice. This computes the square root of x, then computes the square root of the result, yielding the quartic root.
Explanation:In order to compute the quartic root of a variable x, we call the Math.sqrt() method twice in a nested manner. The quartic root is essentially the square root of a square root, hence the need for the double call. The appropriate expression in this case would be:
Math.sqrt(Math.sqrt(x))
This expression first computes the square root of x and then computes the square root of the result, which gives us the quartic root of x. As a result, if x is 16.0, the result of this expression would be 2.0, and if x is 81.0, the result would be 3.0.
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Enter an inequality that represents the phrase the sum of 1 and y is greater than or equal to 6.
1+y (greater than or equal to symbol) 6
Which of the following equations represents a line that is paraellel to Y=5x-4 and passes through the point (3, 4)?
A. Y=5x-7
B. Y=5x+19
C. Y=-1/5x-4
D. Y=5x-11
choice D is the correct solution
PARALLEL slopes always have the same slope no matter what because they are parallel
The equation of the line that is parallel to y = 5x-4 and passes through the point (3, 4) is y = 5x - 11 because it has the same slope, 5, as the given line depicting parallelism and it passes through the specified point.
Explanation:In Mathematics, two lines are parallel if their slopes are equal. In this case, the given line is y = 5x - 4, and its slope is 5. To find an equation of a line that is parallel to this line and passes through a specific point, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes.
Replace m with 5 (the slope of the given line), and (x1, y1) with (3, 4) (the point through which the line passes), and we have y - 4 = 5(x - 3). Distributing and simplifying, we get y = 5x - 15 + 4 = 5x -11. Therefore, the equation of the line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.
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You ask a friend to think of a number from 5 to 12. What is the probability that his number will be 8?
1/8 chance since there are 8 numbers from 5 to 12 and 1 is only one number so 1/8
If a board game was originally $25 and it is on sale for $18 what is the percent of discount?
Arnold can read 3 pages in 7 minutes. Brenda can read 8 pages in 14 minutes. Who is the faster reader? Justify your answer.
Answer:
Brenda
Step-by-step explanation:
You can divide the number of pages by the number of minutes to find the amount of minutes it takes to read 1 page. For Arnold, 3 pages / 7 minutes = 1 page per approximately 0.43 minutes. For Brenda, 8 pages / 14 minutes = 1 page per approximately 0.57 minutes. Brenda reads slightly faster since 0.57 > 0.43
(Q4) Which values of a and b in the exponential function y = a (bx) would result in the following graph?
Answer: second option.
Step-by-step explanation:
By definition, you know that:
[tex]b^0=1[/tex]
You can see in the graph that the interception with the y-axis is at -1.
Therefore, in that point: x=0 and y=-2
Substitute into the function and solve for a:
[tex]-1=a(b)^0\\-1=a(1)\\a=-1[/tex]
Now, choose any point of the function and substitute this point and the value of a into the function and solve for b. Then you obtain:
Point (2,-4)
[tex]-4=-1(b)^2\\\frac{-4}{-1}=b^2\\b=\sqrt{4}\\b=2[/tex]
Answer:
Its B
Step-by-step explanation:
Because it is
On edge
Write the augmented matrix corresponding to the system of equations. 3x + 4y − 5z = 8 x + 2z = −3 4x − 3y = 6 Incorrect: Your answer is incorrect.
3x+4y-5z=8
1x+0y+2z=-3
4x-3y+0z=6
|`3 4 (-5)`||`x`| |`8`|
| 1 0 2 | |y |=|-3 |
|.4 (-3) 0 .||.z.| |.6.|
30 points!!!
To convert measurements in the metric system, you can move the decimal point left or right. Why does this work? The metric system only uses decimal numbers. Converting in the metric system does not involve multiplication or division. The metric system is based on powers of 10. The metric system does not have conversion factors.
Moving the decimal point left or right works in the metric systems because; The metric system is based on powers of 10.
Why does moving decimal point left or right work for metric system conversions?It follows from the task content that the reason for moving the decimal point left or right in metric system conversions be identified.
It follows from metric system conversions that;
centi- indicates 10-² = 0.01milli- indicates 10-³ = 0.001kilo- indicates 10³ = 1000deci- indicates 10-¹ = 0.1Based on the aforementioned, it can be concluded that the measurements conversion in the metric system is such that the decimal point is moved left or right.
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To the nearest hundredth, what is the value of x?
Use a trigonometric ratio to compute a distance
Question 3 options:
62.25
100.25
101.12
128.32
➷ cos38 = 79/x
x = 79/cos38
x = 100.2524
The correct option would be 100.25
✽➶ Hope This Helps You!
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➶ Have A Great Day ^-^
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Answer:
100.25
Step-by-step explanation:
Using the cosine ration in the right triangle, then
cos38° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{79}{x}[/tex]
Multiply both sides by x
x × cos38° = 79 ( divide both sides by cos38° )
x = [tex]\frac{79}{cos38}[/tex] ≈ 100.25
Graph the following equation
[tex]f(x) = \frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex]
If you can. Also, what is the Oblique Asymptote.
Answer:
Graphic attached
Step-by-step explanation:
The oblique asymptote of the function has the shape of a line of the form
[tex]y = mx + b[/tex]
We need to find the slope m and the intercept b.
The oblique asymptote is found by these two limits:
[tex]m = \lim_{x \to \infty}\frac{f(x)}{x}\\\\b = \lim_{x \to \infty}[f(x) - mx][/tex]
If [tex]f(x) = \frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex] then:
[tex]m = \lim_{x \to \infty} \frac{\frac{(2x+3)(x-6)}{(x+2)(x-1)}}{x}\\\\m = \lim_{x \to \infty} \frac{2x^2-9x-18}{x^3 +x^2 -2x}\\\\m = 0[/tex]
The slope is 0. Therefore the function has no oblique asymptote.
Horizontal asymptote:
[tex]y = 2[/tex]
Vertical asymptote
[tex]x = -2\\x = 1[/tex]
To get to your school, 25 of the students walk, 13 of the students ride the bus, and the rest come in cars. How many students come to school in cars?
Answer:
12
Step-by-step explanation:
subtract 25 minus 13 and you get 12 which means 12 students come in cars
2+(x+y)=(2+x)+y is and example of which algebraic property?
A)Distributive property
B)Associative property of addition
C)Commutative property of addition
D)Symmetric property
distributive property because u need to mulptiply the number outside with the parentheses
Answer:
A)Distributive property
Step-by-step explanation:
This is because you need to multiply
There are 11 more goats than sheep in the farm. Together there are 137 animals in the farm. How many goats and how many sheep are there?
Answer:
The number of goats in the farm is [tex]74[/tex]
The number of sheep in the farm is [tex]63[/tex]
Step-by-step explanation:
Let
x----> the number of goats in the farm
y----> the number of sheep
we know that
[tex]x+y=137[/tex] ----> equation A
[tex]x=y+11[/tex] -----> equation B
substitute the equation B in equation A and solve for y
[tex](y+11)+y=137[/tex]
[tex]2y=137-11[/tex]
[tex]2y=126[/tex]
[tex]y=126/2=63[/tex]
Find the value of x
[tex]x=63+11=74[/tex]
therefore
The number of goats in the farm is [tex]74[/tex]
The number of sheep in the farm is [tex]63[/tex]
The sum of four numbers is 20 and their average is 5. When a fifth is added, the new average is 6. What is the fifth number?
Answer:
10
Step-by-step explanation:
We'll note the numbers as [tex]x_{n}, x_{n+1} ...[/tex]
[tex]x_1 + x_2 + x_3 + x_4 = 20\\Avg = 5\\\frac{x_1 + x_2 + x_3 + x_4 + x_5 }{5} = 6 = \frac{20 + x_5}{5}\\ 4 + \frac{x_5}{5} = 6\\\\frac{x_5}{5} = 2\\\x_5 = 10[/tex]
Answer:
10.
Step-by-step explanation:
The average of the 5 numbers =
(20 + x) / 5 = 6 where x is the 5th number.
20 + x = 30
x = 10
The fifth number is 10.
What are the values of x and y?
Answer:
b: [tex] x= 8 \sqrt7 y= 4 \sqrt{21} [/tex]
Step-by-step explanation:
Euclid 1st theorem:
[tex] x^2 = 16 * (16+12); y^2 = 12*(12+16) [/tex]
Calculation is trivial
FIND THE DEGREE MEASURE OF ANGLE DPR.
[tex]\widehat{DPR}=\frac{1}{2}(\stackrel\frown{ET}-\stackrel\frown{DR}) = \frac{1}{2} (118 - 26) = \frac{92}{2} = 46°[/tex]
Which is 5logx - 6log(x-8) written as a single logarithm?
Answer:
option a
[tex]log\frac{x^{5} }{(x-8)^{6} }[/tex]
Step-by-step explanation:
Given in the question an expression
5logx - 6log(x-6)
To solve this question we will apply two of the logarithm property
1) power rule
alogx = log[tex]x^{n}[/tex]
log[tex]x^{5}[/tex] - log[tex](x-8)^{6}[/tex]
2) substraction rule
The log of a quotient is the difference of the logs
loga (x/y) = loga x - loga y
[tex]logx^{5}- log(x-8)^{6}[/tex]
log[tex]\frac{x^{5} }{(x-8)^{6} }[/tex]
Answer:
a edge
Step-by-step explanation:
If the volume of a cone is 593.46 cubic inches and the radius is 9 inches what is the height
PLEASE HELP!!!! 50 POINTS
Find an equation of the line. Write the equation using function notation. through (8,-4) perpendicular to 2y=x-4
First you need to rewrite the equation in the form y = mx +b:
2y = x-4
Divide all terms by 2:
2y / 2 = x/2 - 4/2
Simplify:
y = 1/2x - 2
The slope of the line is 1/2.
A perpendicular line has a slope of the negative reciprocal, which would be -2.
Now using the point slope method:
y - y1 = m(x-x1)
Using the given point of (8,-4) and m = -2
you get:
y +4 = -2(x-8)
Simplify:
y +4 = -2x +16
Now subtract 4 from both sides to get the final equation:
y = -2x +12
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A cylinder has diameter 34 m and height 27 m. A label at bottom states drawing not to scale.
Find the volume of the cylinder. Use 3.14 for
π
PLEASE WRITE YOUR ANSWER IN STEPS CLEAR, I WILL GVE 100 POINTS ASAP AND BRAINLIEST
The volume of the cylinder is 25295.26 cubic meters.
Explanation:To find the volume of a cylinder, we can use the formula V = π * r^2 * h, where r is the radius and h is the height. Given that the diameter is 34 m, the radius is half of that, which is 17 m. The height is given as 27 m.
Plugging in the values into the formula, we get V = 3.14 * (17^2) * 27. Evaluating this expression, we find that the volume of the cylinder is 25295.26 cubic meters.
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The volume of a cylinder is 25295.26 cubic meters.
Explanation:To find the volume of a cylinder, use the formula V = πr^2h, where V represents the volume, π is a constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
In this case, the diameter of the cylinder is given as 34 m, so the radius is half of the diameter, or 17 m.
The height of the cylinder is given as 27 m. Substitute these values into the formula to calculate the volume.
V = 3.14 × (17^2) × 27
= 25295.26 cubic meters.
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116. use what you know about the area and circumference of circles to answer the questions below. show all work. leave answers in terms of π. homework help ✎ if the radius of a circle is 14 units, what is its circumference? what is its area? if a circle has diameter 10 units, what is its circumference? what is its area? if a circle has circumference 100π units, what is its area? if a circle has circumference c, what is its area in terms of c?
Answer:
28π and 196π
10π and 25π
2500π
A = C/4π
Step-by-step explanation:
The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and area.
if the radius of a circle is 14 units, what is its circumference? what is its area?
Substitute r = 14.
C = 2πr = 2π(14) = 28π
A = πr² = π(14)² = 196π
if a circle has diameter 10 units, what is its circumference? what is its area?
Substitute r = 5.
C = 2πr = 2π(5) = 10π
A = πr² = π(5)² = 25π
if a circle has circumference 100π units, what is its area?
Substitute C = 100π to find the radius. Then substitute the radius into the are formula.
C = 2πr
100π=2πr
100 = 2r
50 = r
A = πr² = π(50)² = 2500π
if a circle has circumference c, what is its area in terms of c?
Cole the circumference formula for r. Then substitute the expression into the area formula.
C = 2πr
r = C / 2π
A = πr² = π(C/2π)² = πC/4π² = C/4π
1. Circumference: [tex]\(28\pi\)[/tex]units, Area: [tex]\(196\pi\)[/tex] square units.
2. Circumference: [tex]\(10\pi\)[/tex]units, Area: [tex]\(25\pi\)[/tex]square units.
3. Area: [tex]\(2500\pi\)[/tex]square units.
4. Area: [tex]\(\frac{C^2}{4\pi}\)[/tex] square units.
Let's go through each question one by one, using the formulas for the circumference and area of a circle.
1. If the radius of a circle is 14 units, what is its circumference? What is its area?
- The circumference [tex]\( C \)[/tex] of a circle is given by the formula:
[tex]\[ C = 2\pi r \][/tex]
where [tex]\( r \)[/tex] is the radius.
Given [tex]\( r = 14 \)[/tex] units, we have:
[tex]\[ C = 2\pi \times 14 = 28\pi \text{ units} \][/tex]
- The area [tex]\( A \)[/tex]of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
Given [tex]\( r = 14 \)[/tex] units, we have:
[tex]\[ A = \pi \times 14^2 = \pi \times 196 = 196\pi \text{ square units} \][/tex]
2. If a circle has diameter 10 units, what is its circumference? What is its area?
- The diameter [tex]\( d \)[/tex] is related to the radius by [tex]\( d = 2r \)[/tex]. Therefore, the radius [tex]\( r \)[/tex] is:
[tex]\[ r = \frac{d}{2} = \frac{10}{2} = 5 \text{ units} \][/tex]
- Using the circumference formula [tex]\( C = 2\pi r \):[/tex]
[tex]\[ C = 2\pi \times 5 = 10\pi \text{ units} \][/tex]
- Using the area formula [tex]\( A = \pi r^2 \):[/tex]
[tex]\[ A = \pi \times 5^2 = \pi \times 25 = 25\pi \text{ square units} \][/tex]
3. If a circle has circumference [tex]\( 100\pi \)[/tex] units, what is its area?
- Given the circumference [tex]\( C = 100\pi \),[/tex] we can find the radius [tex]\( r \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]
[tex]\[ 100\pi = 2\pi r \][/tex]
Dividing both sides by [tex]\( 2\pi \):[/tex]
[tex]\[ r = \frac{100\pi}{2\pi} = 50 \text{ units} \][/tex]
- Using the area formula [tex]\( A = \pi r^2 \):[/tex]
[tex]\[ A = \pi \times 50^2 = \pi \times 2500 = 2500\pi \text{ square units} \][/tex]
4. If a circle has circumference [tex]\( C \),[/tex] what is its area in terms of [tex]\( C \)[/tex]
- Given the circumference [tex]\( C \),[/tex] we can express the radius [tex]\( r \)[/tex] in terms of [tex]\( C \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]
[tex]\[ r = \frac{C}{2\pi} \][/tex]
- Using the area formula [tex]\( A = \pi r^2 \)[/tex] and substituting [tex]\( r = \frac{C}{2\pi} \):[/tex]
[tex]\[ A = \pi \left( \frac{C}{2\pi} \right)^2 = \pi \left( \frac{C^2}{4\pi^2} \right) = \frac{\pi C^2}{4\pi^2} = \frac{C^2}{4\pi} \][/tex]