Find the Fourier series for the periodic function: f(x)={0x2 if if −1≤x<00≤x<1f(x+2)=f(x)
Answers
The Fourier series for the given periodic function f(x) = {0 for −1 ≤ x < 0, x² for 0 ≤ x < 1} is: f(x) = 1/12 + ∑[n=1 to ∞] [(4/n²π²) cos(nπx)],
To find the Fourier series for the given periodic function f(x), we need to determine the coefficients of the trigonometric terms in the series.
First, let's determine the constant term (a₀) in the Fourier series. Since f(x) is an even function, the sine terms will have zero coefficients, and only the cosine terms will contribute.
The constant term is given by:
a₀ = (1/2L) ∫[−L,L] f(x) dx
In this case, L = 1 since the function has a period of 2.
a₀ = (1/2) ∫[−1,1] f(x) dx
To calculate the integral, we split the interval into two parts: [−1,0] and [0,1].
For the interval [−1,0], f(x) = 0, so the integral over this interval is 0.
For the interval [0,1], f(x) = x², so the integral over this interval is:
a₀ = (1/2) ∫[0,1] x² dx
= (1/2) [x³/3] from 0 to 1
= (1/2) (1/3)
= 1/6
Therefore, the constant term a₀ in the Fourier series is 1/6.
Next, let's determine the coefficients of the cosine terms (aₙ) in the Fourier series. These coefficients are given by:
aₙ = (1/L) ∫[−L,L] f(x) cos(nπx/L) dx
Since f(x) is an even function, the sine terms will have zero coefficients. So, we only need to calculate the cosine coefficients.
The coefficients can be calculated using the formula:
aₙ = (2/L) ∫[0,L] f(x) cos(nπx/L) dx
In this case, L = 1, so the coefficients become:
aₙ = (2/1) ∫[0,1] f(x) cos(nπx) dx
Again, we split the integral into two parts: [0,1/2] and [1/2,1].
For the interval [0,1/2], f(x) = x², so the integral over this interval is:
aₙ = (2/1) ∫[0,1/2] x² cos(nπx) dx
For the interval [1/2,1], f(x) = 0, so the integral over this interval is 0.
To calculate the integral over [0,1/2], we use integration by parts:
aₙ = (2/1) [x² sin(nπx)/(nπ) - 2 ∫[0,1/2] x sin(nπx)/(nπ) dx]
The second term in the integral can be simplified as follows:
∫[0,1/2] x sin(nπx)/(nπ) dx
= (1/(nπ)) [∫[0,1/2] x d(-cos(nπx)/(nπx)) - ∫[0,1/2] (d/dx)(x) (-cos(nπx)/(nπx)) dx]
= (1/(nπ)) [x (-cos(nπx)/(nπx)) from 0 to 1/2 - ∫[0,1/2] (1/(nπx)) (-cos(nπx)) dx]
= (1/(nπ)) [1/(2nπ) + ∫[0,1/2] (1/(nπx)) cos(nπx) dx]
= (1/(nπ)) [1/(2nπ) + 1/(nπ) ∫[0,1/2] cos(nπx)/x dx]
We can evaluate the remaining integral using techniques such as Taylor series expansion.
After evaluating the integrals, the coefficients aₙ can be determined.
Once the coefficients a₀ and aₙ are found, the Fourier series for the given function f(x) can be written as:
f(x) = a₀/2 + ∑[n=1 to ∞] (aₙ cos(nπx))
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Related Questions
Five countries enter a race. The first three racers in order, Jamaica finished before Barbados, but behind Trinidad. Haiti finished before Guyana, but behind Barbados. Who won the Bronze (finished in 3rd place)?
Answers
Answer:
Barbados won the Bronze.
Step-by-step explanation:
The information indicates that Jamaica finished before Barbados, but behind Trinidad which means that Trinidad was the first one, then Jamaica and the third one was Barbados:
1. Trinidad
2. Jamaica
3. Barbados
Then, it indicates that Haiti finished before Guyana, but behind Barbados which indicates that Haiti was in 4th place after Barbados and the last one was Guyana:
1. Trinidad
2. Jamaica
3. Barbados
4. Haiti
5.Guyana
According to this, the answer is that Barbados won the Bronze.
Which expression could NOT be changed to have a denominator of 24 in order to solve?
1218 – 14
1220 – 28
816 – 16
616 – 26
Answers
Answer:
I think C. Not exactly sure though
The expression could NOT be changed to have a denominator of 24 in order to solve is 12/20 - 2/8.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.1. 12/ 18- 1/4
= 6 x 2 / 6 x 3- 1/4
= 2/3 - 1/4
= 32/24 - 6/24
2. 12/20 - 2/8
= 3/5 - 1/4
= 12/20 - 5/20
3. 8/16 - 1/6
= 1/2 - 1/6
= 12/24 - 4/24
4. 6/16 - 2/6
= 3/8 - 1/3
= 9/24 - 8/34
Thus, the fraction cannot a denominator of 24 in order to solve is 12/20- 2/8.
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what makes 3+7+2= +2true?
Answers
The equation 3+7+2=+2 is actually not true, but false.
Is the 3+7+2= +2true?The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.
In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.
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Use the product notation to rewrite the following expression. (t − 6) · (t2 − 6) · (t3 − 6) · (t4 − 6) · (t5 − 6) · (t6 − 6) · (t7 − 6) = π7k = 1
Answers
The expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).
As per the question, we can write the expression as:
(t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9)
Using product notation, we can write this as:
Π⁷k =1 \((t^k - 9)\)
where Π represents the product of terms, k is the index of the product, and the subscript 7 indicates that the product runs from k = 1 to k = 7.
Therefore, the expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).
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What is the value of z?
N
11
z+25°
Z-27°
Z-11°
Answers
Check the picture below.
\(z+25=(z-27) + (z-11)\implies z+25=2z-38 \\\\\\ 25=z-38\implies \boxed{63=z}\)
Jon's summer baseball league has 64
thirteen-year-olds and 40
fourteen-year-olds. Write the ratio of
thirteen-year-oldsto
fourteen-year-olds in all three forms.
HELP ASAP PLEASE
Answers
Answer:
64 - 40 because there are 64 thirteen year olds and 40 fourteen year olds.
Step-by-step explanation:
Which of the following is true about the
Pythagorean Theorem?
A: The Pythagorean Theorem can be used
to determine the side lengths of any right
triangle
B: The Pythagorean Theorem can be used to
determine the side lengths of any triangle.
C: The Pythagorean Theorem can be used
to determine the angle measures of any
right triangle.
D: The Pythagorean Theorem can be used
to determine the angle measures of any
triangle.
—
If you got a good answer, ima give you brainliest.
Answers
Answer:
A. The Pythagorean Theorem can be used to determine the side lengths of any right triangle
Step-by-step explanation:
The Pythagorean Theorem is supposed to be used to identify the SIDE lengths of ANY RIGHT TRIANGLE.
I also had this question today as well, and I got it correct :)
The statement i.e. true about the Pythagorean Theorem is option A.
A. The Pythagorean Theorem can be used to determine the side lengths of any right triangle
The following information should be considered;
It is to be used for identifying the side length for any kind of right triangle. The right triangle should be of 90 degree. Therefore, all the other options are wrong.
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What is the slope and the y-intercept? y=-8x + 89
Answers
y=-8x + 89
Slope m= 8
y- intercept = +89. For x= 0
A 20-ounce soft drink costs $1.80. A 12-ounce soft drink costs $1.32.
Answers
Answer:
Where do you get this soft drink?
F(x) = 3 x 2 − 3 x − 6 The domain of a the function f(x) is { -10, -1, 1, 5 }. What is the range of the relation?
Answers
Answer:
{324, 0, -6, 54}
Step-by-step explanation:
Given that F(x) = 3x² − 3 x − 6 If the domain of a the function f(x) is { -10, -1, 1, 5 }.
To get the range, we will find f(x) for all the domains
at x = -10
f(-10) = 3(-10)²-3(-10) - 6
f(-10) = 3(100)-3(-10) - 6
f(-10) = 300+30-6
f(-10) = 330-6
f(-10) = 324
at x = -1
f(-1) = 3(-1)²-3(-1) - 6
f(-1) = 3(1)-3(-1) - 6
f(-1) = 3+3-6
f(-1) = 6-6
f(-1) = 0
at x = 1
f(1) = 3(1)²-3(1) - 6
f(1) = 3(1)-3(1) - 6
f(1) = 3-3-6
f(1) = 0-6
f(1) = -6
at x = 5
f(5) = 3(5)²-3(5) - 6
f(5) = 3(25)-3(5) - 6
f(5) = 75-15-6
f(5) = 60-6
f(5) = 54
Hence the range of the relation are {324, 0, -6, 54}
I need some help with this, please. The output of a function is 9 less than 10 times the input. Find the input when the output is 11.
Answers
Answer:
2
Step-by-step explanation:
10i -9 = 11
10i = 20
I = 2
2 is the answer
So the equation is
y=10x-9Put y=11
10x-9=1110x=11+910x=20x=2Matt starts swimming lessons on 5 day . He goes every 10 days . How many lessons will Matt go to in 30 days?
Answers
Answer: 3 lessons
Step-by-step explanation:
Matt starts swimming lessons on Day 5.
He then goes to swimming lessons every 10 days. The dates he went on lessons are therefore:
First lesson = Day 5
Second lesson = Day 5 + 10 days = Day 15
Third lesson = Day 15 + 10 days = Day 25
Fourth lesson = Day 25 + 10 days= Day 35
He therefore only went for 3 lessons because the 4th lesson was after Day 30.
in 2012, gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. suppose that random samples of 100 respondents were selected from both vermont and hawaii. from the survey, vermont had 65.3% who said yes and hawaii had 62.2% who said yes. what is the value of the sample proportion of people from vermont who exercised for at least 30 minutes a day 3 days a week? group of answer choices unknown 0.6375 0.653 0.622
Answers
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.
We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.
To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.
Step 1:
Convert the percentage to a decimal.
65.3 / 100 = 0.653
Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.
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use the criterion developed in mathchapter d to prove that δqrev in equation 6.1 is not an exact differential (see also problem d-11).
Answers
To prove that δqrev in equation 6.1 is not an exact differential, we can use the criterion developed in math chapter d. The criterion states that if a differential equation is exact, then its partial derivatives must satisfy the condition ∂M/∂y = ∂N/∂x.
In equation 6.1, δqrev is defined as δqrev = TdS. If we express δqrev in terms of its partial derivatives, we get:
∂(δqrev)/∂S = T
∂(δqrev)/∂T = S
Now, let's calculate the partial derivatives of ∂(∂(δqrev)/∂S)/∂T and ∂(∂(δqrev)/∂T)/∂S:
∂(∂(δqrev)/∂S)/∂T = ∂T/∂S = 0 (since T does not depend on S)
∂(∂(δqrev)/∂T)/∂S = ∂S/∂T = 0 (since S does not depend on T)
Since these partial derivatives are equal to zero, we can conclude that δqrev is not an exact differential, as it does not satisfy the condition ∂M/∂y = ∂N/∂x.
Therefore, we have proven that δqrev in equation 6.1 is not an exact differential.
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find an equation of the tangent line to the curve at the given point. y = ln(x2 โ 5x + 1), (5, 0)
Answers
The equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0) is y = 0.
To find the equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0), we need to find the slope of the tangent line at that point.
The derivative of y = ln(x^2 - 5x + 1) is:
y' = (2x - 5)/(x^2 - 5x + 1)
At the point (5,0), we have:
y' = (2(5) - 5)/(5^2 - 5(5) + 1) = 0
So the slope of the tangent line at (5,0) is 0.
The equation of the tangent line can be written as:
y - y1 = m(x - x1)
where (x1, y1) is the point of tangency and m is the slope.
Since the slope is 0, we have:
y - 0 = 0(x - 5)
which simplifies to:
y = 0
Therefore, the equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0) is y = 0.
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The distance between City A and City B is 200 miles. A length of 1.5 feet represents this distance on a certain wall map. City C and City D are 3.5 feet apart on this map. What is the actual distance between City C and City D?
Answers
The actual distance between City C and City D is 466.67 miles.Therefore, the actual distance between City C and City D is 466.67 miles.
To find the actual distance between City C and City D, we can use the scale on the map. We know that 1.5 feet represents 200 miles, so we can set up a proportion:
1.5 feet : 200 miles = 3.5 feet : x miles
Cross-multiplying, we get:
1.5 feet * x miles = 3.5 feet * 200 miles
Simplifying, we get:
x miles = (3.5 feet * 200 miles) / 1.5 feet
x miles = 466.67 miles
Therefore, the actual distance between City C and City D is 466.67 miles.
Using the given information, we can set up a proportion to find the actual distance between City C and City D.
On the map:
1.5 feet represents 200 miles (between City A and City B)
Let x be the actual distance between City C and City D:
3.5 feet represents x miles
Now we can set up a proportion:
1.5 feet / 200 miles = 3.5 feet / x miles
Cross-multiply and solve for x:
1.5 * x = 3.5 * 200
1.5x = 700
Now divide by 1.5:
x = 700 / 1.5
x = 466.67 miles (approximately)
The actual distance between City C and City D is approximately 466.67 miles.
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(−4x
2
+x)−(−8x
2
−2x+6)
Answers
Answer:
4x^2 + 3x - 6
Answer:
4x^2+3x-6
Step-by-step explanation:
Help MY LAST LAST QUESTION
Answers
Answer: 1/6>x
Step-by-step explanation:
4x+6>10x+5
subtract 4x from both sides
then you have
6>6x+5
subtract 5 from both sides
1>6x
then divide by 6
1/6>x
Answer:
x < 1/6
Step-by-step explanation:
4x + 6 > 10x + 5
-6x + 6 > 5
-6x > -1
x < 1/6
So, the answer is x < 1/6
HELP! I WILL NAME YOU THE BRAINLIEST. Solve the system by graphing.
y = x + 4
-x + y = -3
Answers
Step-by-step explanation:
Not sure if this is meant to be a trick question, but there is no solution to this system of linear equations. Just by analyzing them in slope intercept form y=mx+b, it is evident that slope, m, of both is 1.
This is even easier to see by graphing the equations as straight lines. Rearranging the second to solve for y, we get y = x - 3. Graphing, we place a point at the y-intercept at (0,-3), and then plug in an arbitrary value for x, say x=4. According to the equation, y would be 1 when x is 4 - and we get the point (4,1). Likewise, for the equation y = x + 4, we plot the y-intercept at the point (0,4) and pick another arbitrary value for x. Say x=4 here as well. According to the equation, y would be 8 when x is 4 - and we get the point (4,8). We then draw a straight line between these two points for both equations.
The lines we drew are parallel and, by the definition of parallel, will never intersect. Geometrically, the intersection of a system of two equations provides the solution to the equation. In 2D this is a point with x and y coordinates. Here, there is no intersection and thus no solution to the system.
In other words, there are no real number x values where the difference of x and 3 is the same as the sum of x and 4. This should make intuitive sense, and the graph of the equations provides a visual proof for this intuition.
Hope this helps!
Jessie thinks that the first step in solving the equation shown below could be to use the addition property of his equality. His friend robin thinks that yhe multiplication property of equality could be used first. Who is correct and why? 2/5 x - 3/2 = 5/2 x + 6
Answers
Answer:
jessie
Step-by-step explanation:
because math is math
The solution for the given equation is -15/7.
The given equation is \(\frac{2}{5}x-\frac{3}{2} =\frac{5}{2}x+6\).
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved as follows:
\(\frac{2}{5}x-\frac{3}{2} =\frac{5}{2}x+6\)
⇒ \(\frac{2}{5}x-\frac{5}{2}x=6-\frac{3}{2}\)
⇒ \(\frac{4}{10}x-\frac{25}{10}x=\frac{12}{2} -\frac{3}{2}\)
⇒ (-21/10) x =9/2
⇒ x = 9/2 × (-10/21)
⇒ x = 3/1 × (-5/7)
⇒ x = -15/7
Therefore, the solution for the given equation is -15/7.
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Can someone help me with this pleaseee…….
Answers
The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.
We have,
To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:
Distance Formula:
If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:
AB = √((4 - (-5))² + (5 - 5)²) = 9
BC = √((2 - 4)² + (0 - 5)²) = √(29)
CD = √((-5 - 2)² + (-2 - 0)²) = √(74)
DA = √((-5 - (-5))² + (5 - (-2))²) = 7
Therefore,
The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.
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Prove or disprove. a) If two undirected graphs have the same number of vertices, the same number of edges, the same number of cycles of each length and the same chromatic number, THEN they are isomorphic! b) A relation R on a set A is transitive iff R² CR. c) If a relation R on a set A is symmetric, then so is R². d) If R is an equivalence relation and [a]r ^ [b]r ‡ Ø, then [a]r = [b]r.
Answers
All the four statements are true.
a) The statement is false. Two graphs can satisfy all the mentioned conditions and still not be isomorphic. Isomorphism requires a one-to-one correspondence between the vertices of the graphs that preserves adjacency and non-adjacency relationships.
b) The statement is true. If a relation R on a set A is transitive, then for any elements a, b, and c in A, if (a, b) and (b, c) are in R, then (a, c) must also be in R. The composition of relations, denoted by R², represents the composition of all possible pairs of elements in R. If R² CR, it means that for any (a, b) in R², if (a, b) is in R, then (a, b) is in R² as well, satisfying the definition of transitivity.
c) The statement is true. If a relation R on a set A is symmetric, it means that for any elements a and b in A, if (a, b) is in R, then (b, a) must also be in R. When taking the composition of R with itself (R²), the symmetry property is preserved since for any (a, b) in R², (b, a) will also be in R².
d) The statement is true. If R is an equivalence relation and [a]r ^ [b]r ‡ Ø, it means that [a]r and [b]r are non-empty and intersect. Since R is an equivalence relation, it implies that the equivalence classes form a partition of the set A. If two equivalence classes intersect, it means they are the same equivalence class. Therefore, [a]r = [b]r, as they both belong to the same equivalence class.
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Select the value that make the inequality w≥6 true
Answers
Answer:
Every number that is greater than 6
g A vat with 500 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 5 gal/min and the mixture is pumped out at the same rate. What is the percentage of alcohol after an hour
Answers
After an hour, the percentage of alcohol in the vat is approximately 4.92%.
After an hour of pumping beer with 6% alcohol into the vat at a rate of 5 gallons per minute and simultaneously pumping the mixture out at the same rate, the percentage of alcohol in the vat can be calculated as follows:
Initially, the vat has 500 gallons of beer with 4% alcohol content. This means there are 20 gallons of alcohol in the vat (500 * 0.04).
Now, let's consider the beer being pumped in at a rate of 5 gallons per minute with a 6% alcohol content. Over the course of an hour (60 minutes), this amounts to 300 gallons of beer, containing 18 gallons of alcohol (300 * 0.06).
As the mixture is being pumped out at the same rate, only 500 gallons of beer remain in the vat after an hour. The total alcohol in the vat is the sum of the alcohol from the initial beer and the pumped-in beer, minus the amount of alcohol pumped out. The mixture pumped out contains the same proportion of alcohol as the mixture in the vat, so it amounts to (5 gallons/minute * 60 minutes) * X%, where X% is the percentage of alcohol in the mixture at the end of an hour.
To find X%, we can set up the following equation:
20 (initial alcohol) + 18 (alcohol pumped in) - 5 * 60 * X% = 500 * X%
Solving for X, we get:
38 - 300 * X% = 500 * X%
Rearranging and solving for X, we find that:
X% ≈ 4.92%
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A polygon has eight sides.
a. Name the polygon
b. If two sides of this polygon
are represented by the
expression (2x + 10) and (7x
+ 5), find x.
c. Find the length of each
side of this polygon.
Answers
Answer:
a. octagon
b. (9x + 15) = 24
c. 24 because all of the sides are equal
Step-by-step explanation:
You add the x values together and the other together to get (9x + 15) which is 24
Suppose f'(2) = 9 and g'(2) = 5. Find h'(2) where h(x) = 2f(x) + 3g(x) + 3. h' (2)=
Answers
To find h'(2), we need to differentiate the function h(x) = 2f(x) + 3g(x) + 3 with respect to x.
Using the linearity property of derivatives, the derivative of h(x) is the sum of the derivatives of each term:
h'(x) = 2f'(x) + 3g'(x)
Given that f'(2) = 9 and g'(2) = 5, we can substitute these values into the equation:
h'(2) = 2f'(2) + 3g'(2)
= 2(9) + 3(5)
= 18 + 15
= 33
Therefore, h'(2) = 33. This means that at x = 2, the rate of change of the function h(x) is 33.
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What is the multiplicative rate of change of the
function?
O 2/3. O 3/4. O 4/3. O 3/2
Answers
Answer:
3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
I did the test.
Item 15 Your math class is collecting canned food for a local food drive. The goal is to collect at least 130 cans but no more than 250 cans due to space limitations. There are 24 students in your math class and your teacher has promised to bring in 10 cans. Select which inequalities represent the possible numbers $n$ of cans that each student should bring in.
Answers
For this case, the first thing we must do is define variables.
We have then:
n: number of cans that each student must bring
We know that:
The teacher will bring 5 cans
There are 20 students in the class
At least 105 cans must be brought, but no more than 205 cans
Therefore the inequation of the problem is given by:
Answer:
105 < 20n + 5 < 205
the possible numbers n of cans that each student should bring in is:
105 < 20n + 5 < 205
A customer was so happy with your service that they wanted to give you a 15% tip on the price of the car. If their car costs $43,780, how much would they pay you in tip?
Answers
Answer:
$6,567
Step-by-step explanation:
Multiply $43,780 by .15
Which of the following methods can be used in solving quadratic equation of the form ax²+bx+c=0?
Answers
The two real solutions to this quadratic equation are -2 and 3/2.
The Quadratic Formula is the most popular method for solving quadratic equations of the form ax²+bx+c=0. It is derived from the quadratic equation which states that if a, b, and c are real numbers, and a is not equal to zero, then the roots of the quadratic equation ax²+bx+c=0 can be determined by the following equation:
x = (-b ± √(b² - 4ac))/(2a)
The quadratic formula can be used to solve for the two real solutions of any quadratic equation. It works by determining the discriminant, which is the number under the square root in the equation. The discriminant is calculated by subtracting 4ac from b². The ± symbol indicates that there are two solutions, one with the plus sign and one with the minus sign.
For example, if we have a quadratic equation 2x²+5x-3=0, the discriminant can be calculated as follows:
b² - 4ac = (5)² - 4(2)(-3) = 25 + 24 = 49
The two solutions can then be found using the formula:
x = (-5 ± √49)/(2(2))
x = (-5 ± 7)/(4)
x = -2 or 3/2
Therefore, the two real solutions to this quadratic equation are -2 and 3/2.
Learn more about quadratic equation here:
https://brainly.com/question/30098550
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Complete question:
Which of the following methods can be used in solving quadratic equation of the form ax²+bx+c=0?
A) Factoring
B) Completing the Square
C) Quadratic Formula
D) Graphing