Y=5x+17 Y=-2x+4 solve with substitution

The Fourier series for f(x) is f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...].

The square wave function can be defined as:

f(x) = {1 -π ≤ x < 0

-1 0 ≤ x < π

To find the Fourier series for this function, we first need to determine the coefficients a_n and b_n.

a_n = (1/π) ∫_0^π f(x) cos(nx) dx

= (1/π) ∫_0^π (-1) cos(nx) dx + (1/π) ∫_(-π)^0 cos(nx) dx

= (2/π) ∫_0^π cos(nx) dx

= (2/π) [sin(nπ) - sin(0)]

= 0

b_n = (1/π) ∫_0^π f(x) sin(nx) dx

= (1/π) ∫_0^π (-1) sin(nx) dx + (1/π) ∫_(-π)^0 sin(nx) dx

= -(2/π) ∫_0^π sin(nx) dx

= -(2/π) [cos(nπ) - cos(0)]

= (2/π) [1 - (-1)^n]

Therefore, the Fourier series for f(x) is:

f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...]

To find the first three Fourier approximations, we truncate this series at the third term.

F_1(x) = -(4/π) sin(x)

F_2(x) = (4/π) sin(x) + (4/3π) sin(3x)

F_3(x) = (4/π) sin(x) + (4/3π) sin(3x) - (4/5π) sin(5x)

These are the first three Fourier approximations of the square wave function f(x). The more terms we include in the Fourier series, the closer the approximations will be to the original function.

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The percentiles for the standard normal distribution

a. 0.93

b. -0.88

c. 0.67

d. -0.65

e. -1.28

To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.

The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.

Step 1: Write down the given percentiles as a decimal and round to two decimal places.

For example, for the 81st percentile, 0.81 will be used.

Step 2: Use the standard normal distribution table to find the corresponding z-score.

Step 3: Round off the obtained answer to two decimal places.

a) 81st percentile:

The area to the left of the z-score is 0.81.

The corresponding z-score is 0.93.

Hence, the 81st percentile for the standard normal distribution is 0.93.

b) 19th percentile:

The area to the left of the z-score is 0.19.

The corresponding z-score is -0.88.

Hence, the 19th percentile for the standard normal distribution is -0.88.

c) 76th percentile:

The area to the left of the z-score is 0.76.

The corresponding z-score is 0.67.

Hence, the 76th percentile for the standard normal distribution is 0.67.

d) 24th percentile:

The area to the left of the z-score is 0.24.

The corresponding z-score is -0.65.

Hence, the 24th percentile for the standard normal distribution is -0.65.

e) 10th percentile:

The area to the left of the z-score is 0.10.

The corresponding z-score is -1.28.

Hence, the 10th percentile for the standard normal distribution is -1.28.

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Answer: 1.2 miles

Step-by-step explanation:

1 hour = 60 min

60 x 0.02 = 1.2         1 minute and 20 seconds has elapsed

60 miles/ every 60 minutes or 1 mile a minute

1 x 1.2 = 1.2

she has traveled 1.2 miles

Answer: The answer is 120 mph (miles per hour)

Step-by-step explanation:

The one thing you need to do is to figure out how many mph did Ella drive for 2 hours.

So, you need to do 60 x 2, and you will get the answer 120.

And there's your answer!

The equations of straight lines are \hat{y} = 2h, \hat{y} = 23r + 4 and \hat{y}= 2s + 3t. Option(A),(B) and (F) are correct.

A line in the coordinate plane can be described with the help of a linear equation, that is, an equation that has a first-degree expression, like y = 2x – 3.

There are many ways to put the equation of a line in the form y = mx + b,

where m is the slope and

b is the y-intercept,

but they all require the use of algebraic properties of equations, such as addition, subtraction, multiplication, division, and substitution.

The equations of straight lines among the following are:  \hat{y} = 2h,  \hat{y} = 23r + 4 and \hat{y}= 2s + 3t

Hence, the correct options are:Option A: \hat{y} = 2h , Option B: \hat{y} = 23r + 4  and Option F: \hat{y}= 2s + 3t.

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The logarithmic expression given as log(15) -log(3) when simplified is log(5).

Given that

log(15) -log(3)

The form is

log(c)

Using the logarithmic identity that states log(a) - log(b) = log(a/b), we can rewrite the given expression as:

log(15) - log(3) = log(15/3)

And simplifying the expression inside the logarithm, we get:

log(15) - log(3) = log(5)

So the given expression, log(15) - log(3), can be written in the form log(c) as log(5).

This means that the logarithm of 5 is equivalent to the difference between the logarithms of 15 and 3.

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The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.

We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:

x_1 = y

x_2 = y'

x_3 = y''

with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.

The resulting system of equations is:

x_1' = x_2

x_2' = x_3

x_3' = (2t^2 - t)x_2 - 4x_3 + 2t

This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.

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Answer:

A is correct

Step-by-step explanation:

Whatever value you put in for "y" will keep both of the equations equal

Answer:

We are given two similar triangles, triangle ABC and triangle DEF, and some measurements of triangle ABC. We are also given that DF, one of the sides of triangle DEF, is equal to 15 units. Using this information, we are asked to find the difference between the lengths of sides AB and EF.

To solve the problem, we can first use the angle-angle similarity theorem to determine that the corresponding angles of the two triangles are equal. Therefore, angle DEF is equal to angle BCA, and angle ABE is equal to angle DFE.

Next, we can use the law of sines to find the length of side AB. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides and angles in the triangle. Applying this to triangle ABC, we have:

AB/sin(73) = BC/sin(48)

Substituting the value of BC as 19 units, we can solve for AB to get:

AB = 22.78 units

Similarly, we can use the law of sines to find the length of side EF. Since angle DFE is equal to angle ABE, we can use the same ratio as above to get:

EF/sin(73) = DF/sin(48)

Substituting the value of DF as 15 units, we can solve for EF to get:

EF = 18.20 units

Finally, we can subtract EF from AB to get:

AB - EF = 22.78 - 18.20 = 4.58 units

Therefore, the difference between the lengths of sides AB and EF is 4.58 units.

If g(x) is the transformed function, then

   [tex]g(x) = - f\big( ~2 (x-3)~ \big) + 5[/tex]

or

   [tex]g(x) = - \big( ~2 (x-3)~ \big)^2 + 5[/tex]

The domain is still all real numbers, (-infty, infty).

The range is (-infty, 5], since it was reflected vertically and then translated up by 5 units.

Answer:

18 times bigger

Step-by-step explanation:

Step-by-step explanation:

There are 8 fluid ounces in a cup....

   divide the number of ounces by 8 to find the number of cups

# ounces /  8 ounces/cup    =    cups

As the demand for tobacco is inelastic so the consumers are the group who are less responsive to a higher price as an outcome of it the consumers will have to bear the largest share of the tobacco tax.

This inelasticity of demand will lead to only a small decline in the quantity demanded after the tax have been leived , therefore the deadloss weight will be in really small degree. the percentage increase in price of any amount will overcome a smaller decline in the quantity which eventually would lead to a rise in the tax revenue collection.

Inelasticity of demand refers to the degree to which the quantity demanded of a particular good or service changes in response to a change in its price. When demand is inelastic, a change in price will result in a proportionally smaller change in quantity demanded. This is typically the case for goods or services that are considered necessities or have few substitutes available.

For example, if the price of insulin, a life-saving medication for diabetics, increases by 10%, it is unlikely that the quantity demanded will decrease by 10%. People with diabetes require insulin to manage their condition, and there are few substitutes available, so they are willing to pay a higher price to maintain their health.

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Complete Question: -

Suppose the supply of tobacco is elastic and the demand for tobacco is inelastic. If an excise tax is levied on the suppliers of tobacco, will the incidence fall mostly on consumers or mostly on producers? Will there be a large amount or small amount of deadweight loss? Will tax revenue from the tobacco tax fall or rise?

The resultant value of the given expression 4(x²+3)-2y is 157 respectively.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra.

Here, we refer to these letters as variables.

An expression is a group of words with operators between them.

The equation is the union of two expressions joined by the symbol "equal to" (=).

For instance, 3x-8. Ex: 3x-8 = 16.

So, the value would be:

4(x²+3)-2y

Insert values as follows:

=4((-6)²+3)-2(-1/2)

=4(36+3)+1=157

Therefore, the resultant value of the given expression 4(x²+3)-2y is 157 respectively.

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Complete question:

What is the value of this expression when x= -6 and y= -1/2? 4(x2+3)-2y

It will take approximately 27.7 minutes for the coffee to cool from 54.8°C to 44.9°C when following exponential decay model.

A quantity declines over time proportionate to its existing value through a process known as exponential decay. An exponential function of the form f(t) = ab raised to t, where an is the beginning value, b is the decay factor (a number between 0 and 1), and t represents time, mathematically describes this.

Several real-world circumstances, like population increase, radioactive decay, and the loss of electrical charge in a capacitor, exhibit exponential decay.

Given that the situation follows a exponential decay model.

The exponential decay is given as:

[tex]T(t) = T0 * e^{(-rt)}[/tex]

Substituting the values T0 = 54.8, r = 0.02, and T(t) = 44.9.

[tex]44.9 = 54.8 * e^{(-0.02t)}\\0..8208 = e^{(-0.02t)}\\ln(0.8208) = -0.02t\\t = ln(0.8208)/(-0.02) = 27.7 minutes[/tex]

Hence, it will take approximately 27.7 minutes for the coffee to cool from 54.8°C to 44.9°C.

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Answer:

(2x - y)(3b + c + 2d)

Step-by-step explanation:

Factorize:

From the first two terms 6bx and (-3by) take out the common factor 3b.

From the third and fourth term 2cx and (-cy) take out the common factor c.

From the fifth and sixth term 4dx and (-2dy) take out the common factor 2d.

6bx - 3by  + 2cx - cy + 4dx - 2dy = 3b(2x - y) + c(2x - y) + 2d(2x - y)

                                                      = (2x - y)(3b + c + 2d)

Answer:

2

Step-by-step explanation:

literally just 2 it's quite simple

The profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.

a) Find the profit-maximizing level of output (Q)To determine the profit-maximizing level of output, we must calculate the marginal cost and marginal revenue of the firm.MC= dTC/dQ= -6Q^2-100+68Q=2(17Q^2-34Q-50)So, the marginal cost of the firm is MC= 2(17Q^2-34Q-50)To find the marginal revenue (MR) we must differentiate the revenue function with respect to Q.MR= dTR/dQ= P + Q(dP/dQ)= 20-4QHence, the marginal revenue is MR= 20-4QAt the point of maximum profit, marginal cost (MC) equals marginal revenue (MR).Therefore, 2(17Q^2-34Q-50)=20-4Q34Q^2-68Q-100=0Solving the above equation gives Q=1.91Therefore, the profit-maximizing output is 1.91 units.b) What price should you charge for your product?The price the firm should charge for its product is given by the demand function, P=20-2Q.Substituting Q=1.91 into the demand function,P= 20-2(1.91) = $16.18c) Based on your answers in the previous two questions, how much profit is this firm making at the profit-maximizing level of output?The total profit of the firm is given by the difference between the revenue and the total cost.TR= P x Q = 16.18 x 1.91 = $30.92TC= 100-2(1.91)^3-100(1.91)+34(1.91)^2 = $60.34Profit = TR- TC= $30.92-$60.34= -$29.42At the profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.

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Answer:

Step-by-step explanation:

To find the product

Its gonna be

12g^4h^5

Assuming that a corporation has cumulative voting and two directors are up for election. The maximum number of votes a shareholder who owns 100 shares can cast for candidate Jones is 40.

Cumulative voting is a voting method used by shareholders in a company to elect a board of directors.

In this type of voting, each shareholder is given the number of votes equal to the number of shares they own, multiplied by the number of candidates. This means that if there are two candidates and a shareholder has 100 shares, then they can cast up to 200 votes for each candidate.

In this case, there are 5 candidates, and two directors are to be elected. Therefore, the total number of votes will be the sum of the votes required for each director, which will be 100.

The maximum number of votes that a shareholder with 100 shares can cast for each candidate will be equal to the total number of votes multiplied by the percentage of the vote that each candidate is allocated.

For example, if candidate Jones is allocated 20% of the votes, then the maximum number of votes that a shareholder with 100 shares can cast for candidate Jones will be:

Total number of votes = 2 x 100 = 200

Percentage of votes allocated to candidate Jones = 20%

Maximum number of votes for candidate Jones = 200 x 20/100 = 40.

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The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.

Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.

Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.

Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.

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Answer:

$63 more in tax

Step-by-step explanation:

Takis is 5.25 in tax  

PlayStation is 68.25

well, we know the tax is 10.5% so let's get them for both.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]

[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]

The value of m∠B is 212 - 24x.

The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.

As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.

To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.

Thus,

m∠A + m∠B + m∠C + m∠D = 360

Substituting the given values, we get:

(16x)° + m∠B + (8x+20)° + 128° = 360

Simplifying and solving for m∠B, we get:

m∠B = 360 - (16x)° - (8x+20)° - 128°

m∠B = 212 - 24x

Therefore, the value of m∠B is 212 - 24x.

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Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.

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The perimeter of the non-shaded region in the figure can be calculated to be 14 inches.

Given a figure.

The middle portion of the figure is not shaded.

It is required to find the perimeter of the non-shaded region.

It is given that:

The whole area of the shaded region = 78 inches²

The area of the small square which is situated at the bottom is:

Area of small square = 2 × 4

                                  = 8 inches²

So, the area of the rest of the shaded area = 78 - 8

                                                                       = 70 inches²

Now, the area of the whole region without the small square is:

Area = 10 × (10 - 2)

        = 80 inches²

So, the area of the non-shaded region = 80 - 70

                                                                = 10 inches²

The width of the non-shaded rectangle is 2 inches.

So, length = 5 inches.

So, the perimeter is:

P = 2(5 + 2)

  = 14 inches

Hence, the perimeter is 14 inches.

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The figure is given below.

New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

The area of the tennis court is given by:

A = lw

where l is the length of the court and w is the width of the court.

Substituting the given values, we have:

[tex]$$260.7569 = l \cdot 10.97$$[/tex]

Solving for l, we get:

[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]

To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:

w' = w - 0.25w = 0.75w

Substituting the given values, we have:

[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]

where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:

[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]

Therefore, the new area of the court is reduced by 25%.

To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:

[tex]$w' = 0.75w$$[/tex]

Dividing both sides by w, we get:

[tex]$\frac{w'}{w} = 0.75$$[/tex]

This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

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Answer:

2916 cm^2

Step-by-step explanation:

Area = side x side = 54 x 54 or 54^2 = 2916 cm^2

Answer:

The other guy is right, 2916 cm^2 is the answer

Step-by-step explanation:

Do you need help with any other questions, if so I'm available to help you.

The correlation coefficient may assume any value between -1 and 1. Correct answer option A.

This means that the coefficient might be negative, zero, or positive, with -1 being a perfect negative correlation, 0 representing no connection, and 1 representing a perfect positive correlation.

The correlation coefficient is a numerical measure of two variables' linear connection. It is a measure of the strength of the link between two variables. A correlation coefficient of 1 indicates that there is a perfect positive connection, a coefficient of -1 indicates that there is a perfect negative correlation, and a coefficient of 0 shows that there is no correlation between the two variables.

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from the given circle having tangents, the value of x is 130°.

A line that touches a curve at one point, y = f(x), is said to be the curve's tangent line. (x0, y0). The point at which it is drawn is substituted into the derivative f'(x) to find its slope (m), and y - y0 = m is used to find its equation. (x - x0).

In geometry, a tangent is a straight line that touches a curve or a surface at a single point, without intersecting it at that point. In the case of a curve, the tangent line at a point on the curve has the same slope as the curve at that point.

In trigonometry, the tangent is a mathematical function that relates the angles of a right triangle to the ratio of the length of the opposite side to the length of the adjacent side.

From the given figure,

We know that

50 + AB = 180

AB = 180 - 50

AB = 130

The value of x or arc AB is 130°.

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The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).

The fraction represents a portion or part of a whole.

There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.

The fractional distance traveled on day one = ²/₅

The remaining fractional distance = ³/₅ (1 - ²/₅)

The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)

The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)

Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.

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