Find the value of sin 20.Hence,state the value of sin 340

Answer:

x= 3

y = 0

Step-by-step explanation:

•Add the two equations to cancel out +6x and -6x

•Find the value of y

•Substitute the value of y into equation 1 to find the value of x.

Hope I was able to help you:)

To find the Fourier Series expansion of the given function f(x), we need to determine the coefficients of the series. The Fourier Series representation of f(x) is given by:

f(x) = a₀/2 + Σ(aₙcos(nπx/2) + bₙsin(nπx/2))

To find the coefficients a₀, aₙ, and bₙ, we can use the formulas:

a₀ = (1/2)∫[0,2] f(x) dx

aₙ = ∫[0,2] f(x)cos(nπx/2) dx

bₙ = ∫[0,2] f(x)sin(nπx/2) dx

Let's calculate these coefficients step by step.

1. Calculation of a₀:

a₀ = (1/2)∫[0,2] f(x) dx

Since f(x) is defined differently for different intervals, we need to split the integral into two parts:

a₀ = (1/2)∫[0,1] x dx + (1/2)∫[1,2] 1 dx

  = (1/2) * [(1/2)x²]₀¹ + (1/2) * [x]₁²

  = (1/2) * [(1/2) - 0] + (1/2) * [2 - 1]

  = (1/2) * (1/2) + (1/2) * 1

  = 1/4 + 1/2

  = 3/4

So, a₀ = 3/4.

2. Calculation of aₙ:

aₙ = ∫[0,2] f(x)cos(nπx/2) dx

Again, we need to split the integral into two parts:

For the interval [0,1]:

aₙ₁ = ∫[0,1] xcos(nπx/2) dx

Integrating by parts, we have:

aₙ₁ = [x(2/nπ)sin(nπx/2)]₀¹ - ∫[0,1] (2/nπ)sin(nπx/2) dx

    = [(2/nπ)sin(nπ/2) - 0] - (2/nπ)∫[0,1] sin(nπx/2) dx

    = (2/nπ)sin(nπ/2) - (2/nπ)(-2/π)cos(nπx/2)]₀¹

    = (2/nπ)sin(nπ/2) + (4/n²π²)cos(nπ/2) - (2/n²π²)cos(nπ)

    = (2/nπ)sin(nπ/2) + (4/n²π²)cos(nπ/2) - (2/n²π²)(-1)^n

For the interval [1,2]:

aₙ₂ = ∫[1,2] 1cos(nπx/2) dx

    = ∫[1,2] cos(nπx/2) dx

    = [(2/nπ)sin(nπx/2)]₁²

    = (2/nπ)(sin(nπ) - sin(nπ/2))

    = (2/nπ)(0 - 1)

    = -2/nπ

Therefore, aₙ = aₙ₁ + aₙ₂

    = (2/nπ)sin(nπ/2)

+ (4/n²π²)cos(nπ/2) - (2/n²π²)(-1)^n - 2/nπ

3. Calculation of bₙ:

bₙ = ∫[0,2] f(x)sin(nπx/2) dx

For the interval [0,1]:

bₙ₁ = ∫[0,1] xsin(nπx/2) dx

Using integration by parts, we have:

bₙ₁ = [-x(2/nπ)cos(nπx/2)]₀¹ + ∫[0,1] (2/nπ)cos(nπx/2) dx

    = [-x(2/nπ)cos(nπ/2) + 0] + (2/nπ)∫[0,1] cos(nπx/2) dx

    = -(2/nπ)cos(nπ/2) + (2/nπ)(2/π)sin(nπx/2)]₀¹

    = -(2/nπ)cos(nπ/2) + (4/n²π²)sin(nπ/2)

For the interval [1,2]:

bₙ₂ = ∫[1,2] sin(nπx/2) dx

    = [-2/(nπ)cos(nπx/2)]₁²

    = -(2/nπ)(cos(nπ) - cos(nπ/2))

    = 0

Therefore, bₙ = bₙ₁ + bₙ₂

    = -(2/nπ)cos(nπ/2) + (4/n²π²)sin(nπ/2)

Now we have obtained the coefficients of the Fourier Series expansion for the given function f(x). We can plot the points and draw the graph.

Using the provided data:

Dogs Stride length (meters): 1.5, 1.7, 2.0, 2.4, 2.7, 3.0, 3.2, 3.5, 2, 3.5

Speed (meters per second): 3.7, 4.4, 4.8, 7.1, 7.7, 9.1, 8.8, 9.9

learn more about integral here: brainly.com/question/31059545

#SPJ11

f and g are inverse functions algebraically and graphically .

f and g are inverse functions algebraically, we need to show that f(g(x)) = x and g(f(x)) = x for all values in their respective domains.

Let's start by evaluating f(g(x)):

f(g(x)) = f(x² - 2)

Substitute f(x) = √(x + 2):

f(g(x)) = √(x² - 2 + 2)

= √(x²)

= x

Since f(g(x)) = x, we have shown that f and g are inverses algebraically.

Now let's evaluate g(f(x)):

g(f(x)) = g(√(x + 2))

Substitute g(x) = x² - 2:

g(f(x)) = (√(x + 2))² - 2

= (x + 2) - 2

= x

Again, we have g(f(x)) = x, confirming that g and f are inverses algebraically.

To verify their inverse relationship graphically, we can plot the graphs of f(x) and g(x) on the same coordinate system and observe if they are reflections of each other across the line y = x.

Here is a graph showing the functions f(x) = √(x + 2) and g(x) = x² - 2

As we can see, the graphs of f(x) and g(x) are indeed reflections of each other across the line y = x, confirming that they are inverse functions.

To know more about inverse function click here :

https://brainly.com/question/29141206

#SPJ4

Answer:

567.06 in.²

Step-by-step explanation:

The mat is a semicircle.

The straight side is a diameter.

d = 38 in.

r = d/2 = 19 in.

Area of circle = πr²

Area of semicircle = πr²/2

A = 3.14159 × (19 in.)² / 2

A = 567.06 in.²

Answer:

0.85(x - 350)

Step-by-step explanation:

x - This is the employees salary before tax exempts

$350 - This is the amount of tax exempted from the employers salary

Income left after tax exempt expenses have been deducted = (x - 350)

If 15% of taxed income is collected, the remaining income would be - 100% - 15% = 85%

85% / 100 = 0.85

Therefore, the remaining salary that the employees take home is 0.85(x - 350)

Answer:

20 + x = 28

Step-by-step explanation:

let x = the # of dvds bought

28 is the total

20 is what he started of with so...

20 + x = 28

and x = 8

Hope this helped! Have a nice day, and feel free to follow me on insta (leo_g_rios)

-XxDeathshotxX

The rate of change of y with respect to x is given by dy/dx = xy - (3/2)x²y.

To find the rate of change of y with respect to x, we need to differentiate the given equation. The rate of change can be determined by taking the derivative of both sides of the equation with respect to x.

First, let's differentiate each term separately using the rules of differentiation.

Differentiating x²y with respect to x gives us 2xy using the product rule.

To differentiate 5, we know that a constant has a derivative of 0.

Differentiating 2ln(y) with respect to x requires the chain rule. The derivative of ln(y) with respect to y is 1/y, and then we multiply by dy/dx. So, the derivative of 2ln(y) is 2/y * dy/dx.

Differentiating x³ gives us 3x² using the power rule.

Now, we can rewrite the equation with its derivatives:

2xy - 2/y * dy/dx = 3x²

To solve for dy/dx, we can isolate it on one side of the equation. Rearranging the equation, we get:

2xy = 2/y * dy/dx + 3x²

To isolate dy/dx, we move the term 2/y * dy/dx to the other side:

2xy - 2/y * dy/dx = 3x²

2xy = 2/y * dy/dx + 3x²

2/y * dy/dx = 2xy - 3x²

Now, we can solve for dy/dx by multiplying both sides by y/2:

dy/dx = (2xy - 3x²) * (y/2)

Simplifying further, we have:

dy/dx = xy - (3/2)x²y

To know more about rate of change, refer here:

https://brainly.com/question/29181688#

#SPJ11

Answer:

Negative

Step-by-step explanation:

When an even number of negatives are multiplied together, the product will be positive (because two negatives cancel out). When an odd number of negatives are multiplied together, the product will be negative.

In the given expression, there is also a singular (1) at the end, which we can ignore since anything multiplied by 1 is itself. The other numbers are all negative and there are 3 of them, and since 3 is an odd number, the product will be negative.

I hope this helps!

Answer:

The third choice

Step-by-step explanation:

Negative, because the product (–7)(–2) is positive, and the product (–5)(1) is negative and the product of a positive and a negative number is negative,

pls mark as brainliest hope you have a nice day!

The area of the circle on the paper is 4.5 cm when traced around the edge of the quarter on a sheet of paper.

The area of the circle is equal to the product of the square of the radius of the circle and pi.

A = πr²

where 'r' is the radius of the circle

The diameter of a quarter is 2.4 cm. You trace around the edge of the quarter on a sheet of paper.

The area of the circle on the paper = πr²

Here r = (diameter of a quarter)/2 = 2.4/2 = 1.2 cm

The area of the circle on the paper = π(1.2)²

The area of the circle on the paper = π × 1.44

The area of the circle on the paper = 4.5238

Round the answer to the nearest tenth.

The area of the circle on the paper = 4.5 cm

Thus, the area of the circle on the paper is 4.5 cm

Learn more about the Circumference and area of the circle here:

brainly.com/question/19794723

#SPJ1

Answer:its 4.5

Step-by-step explanation:

Answer:

r = - 3.25, p = -1.5

Step-by-step explanation:

→ Rearrange p - 2r = 5

p = 5 + 2r

→ Substitute into 6p - 4r = 4

6 ( 5 + 2r ) - 4r = 4

→ Expand

30 + 12r - 4r = 4

→ Simplify and solve

r = - 3.25

→ Substitute into p - 2r = 5

p + 6.5 = 5

→ Minus 6.5 from both sides

p = -1.5

Answer: B

Step-by-step explanation:

You need to show what you have problem with and then I could help you.

Answer:

I did the best I could graphing it but it's weird. It's all I got. So here you go. I hope it helps! have a nice day!

Step-by-step explanation:

The transformation for which the equation f(x) = g(x) will have two solutions is given as follows:

B. g(x) = -f(x).

The zeros of a function are the values of the input x for which the output y of the function assumes a value of y.

Hence, on the graph of a function, the zeros of a function are the values of x for which the graph either touches or crosses the x-axis.

For the transformation g(x) = -f(x), the zeros of the function remain constant, as the numeric values have the signal exchanged, however zero has no sign, hence the zeros remain the same, giving two solutions to the system of equations f(x) = g(x).

More can be learned about the zeros of a function at brainly.com/question/16550963

#SPJ1

Answer:

17

Step-by-step explanation:

85/5=17

Answer:

\(2z^3\sqrt{14z}\)

Step-by-step explanation:

\(\sqrt{56z^7}\\ \sqrt{4*14*z^6*z}\\2 z^3\sqrt{14z}\)

Answer:

\(\sqrt{4}\)\(\sqrt{z^2}\)\(\sqrt{z^2}\)\(\sqrt{z^2}\)

Step-by-step explanation:

\(\sqrt{56z^7}\) = \(\sqrt{4}\)\(\sqrt{14}\)\(\sqrt{z^2}\)\(\sqrt{z^2}\)\(\sqrt{z^2}\)\(\sqrt{z}\)

the perfect squares are:

\(\sqrt{4}\)\(\sqrt{z^2}\)\(\sqrt{z^2}\)\(\sqrt{z^2}\) = 2z³

Given:

The length of the top diagram is 60 units.

Required:

The length of the bottom diagram.

Explanation:

Now the first diagram has two parts 80% and 20%, and the 20% further gives us the second diagram.

So to know the length of second diagram we need to find the 20% of first diagram.

so we need to calculate 20% of 60, that is

So the length of second diagram is 12 units.

Now the second diagram has two parts 60% and 40%, and the 60% further gives us the third diagram.

So to know the length of third diagram we need to find the 60% of second diagram.

so we need to calculate 60% of 12, that is

So the length of third diagram is 7.2 units.

Now the third diagram has two parts 30% and 70%, and the 70% further gives us the fourth diagram.

So to know the length of the fourth diagram we need to find the 70% of the third diagram.

So we need to calculate 70% of 7.2, that is

So the length of fourth diagram is 5.04 units

Final Answer:

The length of the bottom diagram, that is the fourth diagram, is 5.04 units.

Answer:

Step-by-step explanation:

sin(x) = opposite over hypotenuse

= 3/(3sqrt(2))

= 1/sqrt(2)

= sqrt(2)/2

x = arcsin( sqrt(2)/2 )

= arcsin( sqrt(2)/2 )

= 45°

To say that two variables are negatively correlatted means that when one variable increases, the other variable decreases.

Negative correlation refers to a relationship between two variables where they tend to move in opposite directions. When one variable increases, the other variable tends to decrease, and vice versa. This negative relationship indicates an inverse association between the two variables.

Option A, "When one variable increases, the other decreases," accurately describes negative correlation. As one variable increases, the other variable decreases, reflecting the negative relationship between them.

Negative correlation does not imply that both variables change at the same rate (Option D). In negative correlation, the relationship is characterized by the opposite direction of change, not necessarily the same magnitude or rate of change.

Option B, "When variable increases, the other also," suggests a positive correlation, where both variables move in the same direction. This is not the case in negative correlation.

Option C, "When one variable decreases, the other also decreases," is a misinterpretation of negative correlation. In negative correlation, when one variable decreases, the other variable tends to increase, not decrease.

To know more about variable click here

brainly.com/question/2466865

#SPJ11

Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

2.5(cos 5π/6  + i sin 5π/6) is the polar form  of the complex number

Complex numbers are numbers that are expressed in the form of a+ib, where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1)

Given: the complex number (5√3)/4 - 5/4 i

In polar form:

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

θ  = tan⁻¹( (-5/4) / (5√3 /4) )

θ = -30°

θ = -30+180 = 150°

θ = 5π/6

r = √( (5√3)/4)² +(- 5/4)²) = 2.5

Thus,

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

r(cosθ + isinθ) = 2.5(cos 5π/6  + i sin 5π/6 )

Therefore, the polar form  of the complex number is 2.5(cos 5π/6  + i sin 5π/6)

Learn more about complex number on:

https://brainly.com/question/27844433

#SPJ1

The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

Answer:

4 +(3.5*h)=r

Step-by-step explanation:

4 plus 3.5 times hour equals total

Answer:

the answer would be 12 apples pies andbakr

The option that illustrates the changing composition of the american family is that D) an increase in the number of non-family households.

A family is any two or more people who live together and are related by blood, marriage, or adoption; all of these people are regarded as belonging to the same family. Family supports us during both the best and worst of times, which makes these ties crucial.

Family is crucial because they can provide unwavering love, support, and security; they constantly strive to bring out the best in you even when you are unable to see it for yourself. In this case, the option that illustrates the changing composition of the american family is an increase in the number of non-family households. Therefore, the correct option is D.

Learn more about family on:

https://brainly.com/question/12397063

#SPJ1

Answer:

-5(7a+ 6)

Explanation:

Given the expression:

-35a - 30

-35a = -5 * 7 * a

-30 = -5 * 6

You can see from the factors that -5 is common to both

Hence -5 is the GCF

Factoring out -5 from the expression will give;

-5(7a+ 6)

This gives the correct factor

Answer:

r = 8/5

Step-by-step explanation:

Step 1: Simplify

10/25 = r/4

10/25 simplifies to 2/5

5/25 = r/4

Step 2: Multiply all terms by the same value to eliminate fraction denominators

2/5 = r/4

4 × 2/5 = 4 × r/4

r/4 cancels out and becomes r

4 × 2/5 = r

4 × 2/5 = 8/5
8/5 = r

or

r = 8/5