give the number to which the fourier series converges at a point of discontinuity of f. (if f is continuous on the given interval, enter continuous.)

The time period required is 31.91 months(Approx)

The monthly payments based on the given information would be $129.88

Putting into a financial calculator;

PV=-1245

PMT=50

I/Y=(19/12)=1.58333333%

Solving for N;we get N=31.91

Hence time period required=31.91 months(Approx)

b.Putting into a financial calculator;

PV=-2456.80

N=(2*12)=24

I/Y=(23.99/12)=1.99916667%

Solving for PMT;we get PMT=129.88

Hence monthly payments=$129.88(Approx)

Read more about interest rates here:

https://brainly.com/question/2294792

#SPJ1

Answer:

The exchange rate at the post office is £1= 1.17 euros

How many euros will you get for £280?

Step-by-step explanation:

280 * 1.17 = 327.6

Answer:

Let x be the first unknown angle, and y be the second unknown angle.

We know that the sum of the three angles in a triangle is 180 degrees, so:

85 + 9kx + 10kx = 180

where k is a constant representing the ratio of the other two angles.

Simplifying the equation, we get:

19kx = 95

Dividing both sides by 19k, we get:

x = 5/k

Since the ratio of the other two angles is 9:10, we know that:

y = 9kx = 9k(5/k) = 45

So the measures of the two unknown angles are:

x = 5/k and y = 45

We cannot find the exact measures of x and y without more information, but we know that x and y are in a ratio of 9:10 and their sum is 180 - 85 = 95 degrees. We can set up the following equation to solve for k:

5/k + 45/k = 95

50/k = 95

k = 50/95

Using this value of k, we can find the measures of x and y:

x = 5/k = 5/(50/95) = 9.5

y = 9kx = 9(50/95)(9.5) = 47.37

Therefore, the measures of the two unknown angles are x = 9.5 degrees and y = 47.37 degrees (rounded to two decimal places).

Step-by-step explanation:

If f ( x ) = f ( g ( x ) ) , where f ( 5 ) = 7 , f ' ( 5 ) = 5 , f ' ( 0 ) = 3 , g ( 0 ) = 5 , and g ' ( 0 ) = 3 ,f'(0) = 15

We start by using the chain rule to find the derivative of f(x) with respect to x:

f'(x) = f'(g(x)) * g'(x)

Next, we evaluate this equation at x = 0, and use the given values to solve for f'(0):

f'(0) = f'(g(0)) * g'(0)

f'(0) = f'(5) * 3 (since g(0) = 5 and g'(0) = 3)

Now, we need to find f'(5) using the given information. We can start by using the definition of the derivative:

f'(5) = lim h->0 [f(5+h) - f(5)] / h

We know that f(5) = 7, so we can simplify this expression:

f'(5) = lim h->0 [f(5+h) - 7] / h

Using the fact that f(x) = f(g(x)), we can substitute g(x) for x:

f'(5) = lim h->0 [f(g(5+h)) - 7] / h

Now, we can use the mean value theorem to approximate f(g(5+h)):

f'(5) = lim h->0 [f'(g(c)) * g'(5+h)] / 1

where 5 < c < 5 + h. Since f'(5) = 5 and g'(5) = 3, we can simplify this expression:

f'(5) = lim h->0 [5 * 3] / 1 = 15

Therefore, we have found that f'(0) = f'(5) * 3 = 5 * 3 = 15.

For more questions like Equation click the link below:

https://brainly.com/question/29657983

#SPJ11

Answer:

The equation of the ellipse is:

(x^2)/16 + (y^2)/4 = 1

Step-by-step explanation:

An ellipse is a set of points on a plane, the sum of whose distances from two fixed points (called foci) is constant. The distance between the foci of an ellipse is denoted by 2c, and the distance between the center of the ellipse and one of its vertices is denoted by a.

In this problem, the foci are located at (2,0) and (-2,0), so the distance between the foci is 2c = 4, which means that c = 2. The major vertices of the ellipse are located at (4,0) and (-4,0), so the distance between the center and one of the vertices is a = 4.

The formula for the equation of an ellipse centered at the origin is:

(x^2)/(a^2) + (y^2)/(b^2) = 1

where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex. Since the center of this ellipse is at the origin and the major axis lies on the x-axis, we know that b = a, so we can substitute a for b in the equation:

(x^2)/(a^2) + (y^2)/(a^2) = 1

To find a, we use the fact that c^2 = a^2 - b^2:

a^2 - b^2 = c^2

a^2 - a^2 = 4

b^2 = 4

b = 2

Now we can substitute a = 4 and b = 2 into the equation:

(x^2)/(16) + (y^2)/(4) = 1

This is the equation of the ellipse.

Answer:

26.4

Step-by-step explanation:

You can add Y together because they have the same variable making it 10y

The equation is now 10y - 84 = 180

Add 84 to 180 since on the left side it was -84 (Imagine it crossed a magic bridge and become the opposite of what it is)

The equation is now 10y = 264

Divide the equation by 10 because 10 crossed a "magic bridge" to the other side and became division instead of multiplication

The equation is now solved = 26.4

We can cross check this by adding it to the first equation

3(26.4) + 7(26.4) - 84

which gives us 180

Hope this helps

Answer: y=26.4

Step-by-step explanation:

First we need to simplify 3y+7y .... that would be 10y.

Now we have 10y-84=180. We can add 84 to both sides of the equation

So now we have 10y= 180+84 = 10y= 264

Divide both sides by 10= y= 26.4

Now we can check this answer by inputting 26.4 to all the y values in the equation.

(3*26.4) +(7*26.4) - 84=180

79.2 + 184.8 -84=180

180=180    so we know 26.4 is the correct answer

Answer:

238.64

Step-by-step explanation:

center to edge is a radius

2pi(radius) = circumference, so 6.28(38) = circumference = 238.64

Thomas can fill 35 of these 1/4 gallon containers with the light-blue mixture.

To find out how many 1/4 gallon containers Thomas can fill with the light-blue mixture, we need to divide the total volume of the mixture by the volume of one container.

The total volume of the mixture can be found by adding the volumes of blue and white paint that Thomas mixed

Total volume = 4 3/8 gallons + 6 5/8 gallons

To add these mixed numbers, we need to find a common denominator, which is 8

Total volume = (4 x 8 + 3) / 8 gallons + (6 x 8 + 5) / 8 gallons

Total volume = 35/8 gallons

Now we can set up the two equations

Total volume = number of containers x volume per container

We know the total volume is 35/8 gallons, and the volume per container is 1/4 gallon, so we can write

35/8 = (1/4) x number of containers

Number of containers = total volume / volume per container

We can rearrange the above equation to solve for the number of containers

Number of containers = total volume / volume per container

Number of containers = 35/8 / 1/4

Number of containers = 35/8 x 4

Number of containers = 35

Learn more about total volume here

brainly.com/question/13436458

#SPJ4

The given question is incomplete, the complete question is:

Thomas has some leftover paint that he would like to sell. he mixes 4 3/8 gallons of blue paint with 6 5/8 gallons of white paint. then, he pours this light-blue mixture into 1/4 gallon containers. find out how many of these 1/4 gallon containers he can fill?

Answer:

= 75 cubic units

Step-by-step explanation:

Volume = height * width * length

Then:

volume = 4 1/2 * 3 1/3 * 5

4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2

3 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3

Then:

volume = 9/2 * 10/3 * 5/1

volume = (9*10*5) / (2*3*1)

volume = 450 / 6

Volume = 75 cubic units

Step-by-step explanation:

Example 1:

Given pair: (3;2)

{2x + 3y = 12,

{x - 4y = -5;

Make x the subject from the 2nd equation:

x = -5 + 4y

Replace x in the 1st equation:

2 × (-5 + 4y) + 3y = 12

-10 + 8y + 3y = 12

11 y = 12 + 10

11y = 22 / : 11

y = 2

y = 2x = -5 + 4 × 2 = -5 + 8 = 3

The answer: (3;2)

The given pair is the solution of the system of equations

.

Example 2:

Given pair: (0; -4)

{x + y = -4,

{x - 5y = 20;

x = -4 - y

(-4 - y) - 5y = 20

-4 - y - 5y = 20

-6y = 20 + 4

-6y = 24 / : (-6)

y = -4

y = -4x = -4 - (-4) = -4 + 4 = 0

The answer: (0; -4)

The given pair is the solution

.

Example 3:

Given pair: (3;3)

{x + 2y = 9,

{4x - y = 15;

x = 9 - 2y

4(9 - 2y) - y = 15

36 - 8y - y = 15

-9y = 15 - 36

-9y = -21 / : (-9)

[tex]y = 2 \frac{1}{3} [/tex]

[tex]x = 9 - 2 \times 2 \frac{1}{3} = 9 - 2 \times \frac{7}{3} = 9 - \frac{14}{3} = \frac{13}{3} = 4 \frac{1}{3} [/tex]

The given pair is not the solution

.

Example 4:

Given pair: (1; -2)

{2x - 3y = 8,

{3x + 2y = -1;

2x = 8 + 3y / : 2

x = 4 + 1,5y

3(4+1,5y) + 2y = -1

12 + 4,5y + 2y = -1

6,5y = -1 - 12

6,5y = -13 / : 6,5

y = -2

y = -2x = 4 + 1,5 × (-2) = 4 - 3 = 1

The given pair is the solution

.

Example 5:

Given pair: (1;5)

{5x - 2y = -5,

{3x - 7y = -32;

-2y = -5 - 5x / : (-2)

y = 2,5 + 2,5x

3x - 7(2,5 + 2,5x) = -32

3x - 17,5 - 17,5x = -32

-14,5x = -32 + 17,5

-14,5x = -14,5 / : (-14,5)

x = 1

x = 1y = 2,5 + 2,5 × 1 = 5

The given pair is the solution

.

Example 6:

Given pair: (-1; -3)

{3x + y = -6,

{2x = 1 + y;

y = -6 - 3x

2x = 1 + (-6 - 3x)

2x = 1 - 6 - 3x

2x + 3x = 1 - 6

5x = -5 / : 5

x = -1

x = -1y = -6 - 3 × (-1) = -6 + 3 = -3

The given pair is the solution

The measure of angle m∠KSP is 14⁰.

A special property of a parallelogram is that opposite angles are equal in measure. This means that if you take any two angles of a parallelogram that are opposite each other, they will have the same degree measure.

The measure of angle m∠KSP is calculated as follows;

The measure of angle P and R = ¹/₂[ 360 - (76 x 2)] (sum of angles in quadrilateral )

The measure of angle P and R = 104

The measure of QPK = 180 - (76 x 2) (sum of angles in a triangle )

The measure of QPK =  28⁰

Angle P consists of QPK plus KPS

KPS = 104 - QPK

KPS = 104 - 28

KPS = 76

The measure of angle m∠KSP is calculated as;

KSP = 180 - (90 + 76) ( sum of angles in a triangle)

KSP = 14⁰

Learn more about angle of parallelogram here: https://brainly.com/question/20526916

#SPJ1

Answer:

38

Step-by-step explanation:

We know that Q and P are supplementary because they are parallelograms.

So,

180 - < Q = < P                               Use substitution

180 - 76 = < P                                 Solve

180 - 76 = 104

104 = < P

Since we know that < QPK and < KPS are congruent and are apart of < P we can multiply < P by 1/2 to find either < QPK or < KPS.

So,

1/2(104)                                           Simplify using distributive property

52

If a shape is a triangle, then it’s interior angles all add up to 180.

< KPS + < PKS + < KSP = 180        Use substitutions

52 + 90 + < KSP = 180                  Move variables to one side

< KSP = 180 - 52 - 90                    Simplify  
< KSP = 38

And there’s your answer: 38

Answer:

  k = 2/5

Step-by-step explanation:

Given a diagram with triangles ONM and OAB such that M is the midpoint of OB, A lies on AN with AN = 2·OA, and P is the point of intersection of NM and AB, you want the ratio AP/AB.

Please refer to the attached diagram.

Point C is located at the midpoint of AN, which makes OA≅AC≅CN, or AN is 2/3 of ON. Segments AD and CE are parallel to AN, so divide OM into thirds. The length DM is 2 of those thirds, and the length MB is equal to OM, so is 3 of those thirds. That is, the ratio DM/DB is (2/3)/(2/3+3/3) = 2/5.

Triangle BAD is similar to triangle BPM, so the ratio AP/AB is also 2/5.

Answer:

4%

Step-by-step explanation:

The formula for simple interest is I = Prt, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.

In this case, we know that:

P = £500 (the principal amount)

I = £40 (the interest earned)

t = 2 years (the time the money was invested)

We can rearrange the formula to solve for r:

r = I / Pt

Substituting the given values, we get:

r = 40 / (500 x 2)

r = 0.04 or 4%

Therefore, the simple interest rate per annum is 4%.

The standard deviation of demand over the lead time is 23.72.

The demand over lead time is normally distributed with a mean of 80. The reorder point for a 95% service level is 119. To calculate the standard deviation of demand over the lead time, we need to use the following formula:

z = (x - μ) / σ, where z is the number of standard deviations from the mean, x is the reorder point for a 95% service level, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

To solve for σ, we need to first find the z-score for a 95% service level, which can be obtained from the standard normal distribution table.

The z-score for a 95% service level is 1.645.

Substituting the given values in the formula, we get:

1.645 = (119 - 80) / σ

Solving for σ, we get:σ = (119 - 80) / 1.645

σ = 23.72

Therefore, the standard deviation of demand over the lead time is 23.72.

To learn more about standard deviation visit : https://brainly.com/question/475676

#SPJ11

You should invite at least 23 guests to your party to have at least a 2/3 chance of having a guest with the same birthday as yours.

For your party, you need to invite at least 23 randomly chosen guests in order to have a probability of 2/3 or higher of having a guest with the same birthday as yours. This is known as the birthday paradox and it is based on the probability of two people having the same birthday. To calculate the number of guests needed for the probability of having at least one match, you can use the following formula:

P(at least one match) = 1 - (365/365)^n

where n is the number of guests you invite.
So, to solve for n, you would rearrange the equation to:

n = ln(1-P) / ln(365/365)

When P = 2/3, this equation gives us n = 23.

To learn more about probability visit : https://brainly.com/question/13604758

#SPJ11

Answer:

  x = 10

Step-by-step explanation:

You want to find the value of x, where a chord of segment lengths 9 and x crosses a chord of segment lengths 6 and 15.

The product of the segment lengths is the same for intersecting chords:

  9x = 6·15

  x = 90/9 . . . . divide by 9

  x = 10

Answer: A. (x,y)----->(x,-y)

because their x coordinates are all -6. But their y coordinates are 6 and -6.

We don't have enough information to determine the exact side length of either square A or square C, so we cannot directly calculate their areas. However, we can use the relationship between the areas of the squares to make some conclusions.

Since the area of square B is 64 square units, we know that its side length is √64 = 8 units.

Similarly, since the area of square C is 100 square units, we know that its side length is √100 = 10 units.

Square A is composed of square B and four identical triangles. We know the area of square B is 64 square units, so we need to determine the area of the four triangles to find the area of square A.

Each triangle has a base of 8 units (which is also the length of one side of square B) and a height of half the length of one side of square A. Let's call this length x.

The area of one triangle is (1/2) * 8 * x = 4x square units.

The total area of the four triangles is 4 times the area of one triangle, which is 16x square units.

Therefore, the area of square A is 64 + 16x square units.

We still don't know the exact value of x, but we can make some observations. Since square A is larger than square B, we know that x > 4. And since the triangles make up exactly half of square A (the other half being square B), we know that the area of square A is twice the area of the four triangles. Therefore:

64 + 16x = 2(16x)

64 + 16x = 32x

64 = 16x

x = 4

So the length of each side of square A is 8 + 2x = 16 units, and its area is 64 + 16x = 128 square units.

The length of CA is just the length of one side of square C, which is 10 units.

Hence, the interest rate is 0.03 percent, or 3%. it is expressed as a percentage .

The amount of money earned or charged on a principal sum of money over time is referred to as interest in mathematics. In financial transactions like loans, investments, and savings accounts, it is frequently utilized.  Simple interest is calculated for the full time period as a fixed percentage of the principal amount. For instance, after a year, you would owe $50 in interest if you borrowed $1,000 at a simple interest rate of 5% per year.

given

We can use the following formula for simple interest to determine the interest rate given the principal, period, and simple interest:

I = P * r * t

where r is the interest rate expressed as a decimal, P is the principal, I is the simple interest, and t is the amount of time in years.

This formula can be changed to account for the interest rate:

r = I / (P * t)

In this instance, the principal, period, and simple interest are all provided. These values can be plugged in to find the interest rate:

r = I / (P * t)

r = 600 / (4000 * 5)

r = 0.03

Hence, the interest rate is 0.03 percent, or 3%. it is expressed as a percentage .

To know more about interest visit:

https://brainly.com/question/28792777

#SPJ1

By answering the presented question, we may conclude that If the two graphs are identical, F(x) may polynomials be a valid factorization of G(x), but more study is required to establish this.

A polynomial is a mathematical statement composed of variables and coefficients that be combined using only addition, subtraction, multiplication, and non-negative integer exponents. The phrase 2x3 + 5x2 - 3x + 1 is a polynomial, for example, where x is the variable and the coefficients of the various components are 2, 5, -3, and 1. Polynomials may include one or more variables, but each term must have the same variable (s). The degree of a polynomial is the highest exponent of its variable (s). In the above example, the degree of the polynomial is 3. Polynomials are used in many areas of mathematics, including algebra, calculus, and numerical analysis.

If you believe that one polynomial function is not the right factorization of another, you may use your graphing calculator to confirm this by graphing both functions and comparing their graphs.

Then, in your calculator, insert the polynomial function that you believe is the right factorization. Let us refer to this function as G. (x).

Graph the function G(x) on your calculator by hitting the "graph" button or the equivalent button.

Examine the two graphs. If the two graphs disagree, F(x) does not represent the right factorization of G. (x). If the two graphs are identical, F(x) may still be a valid factorization of G(x), but more study is required to establish this.

To know more about polynomials visit:

https://brainly.com/question/11536910

#SPJ1

Number of people = number of cups of coffee + 1 = 5 + 1 = 6

Therefore, there were 5 friends with Dylan at the cafe.

Let's start by subtracting the change Dylan received from the amount he paid to find out the total cost of everything he bought:

Total cost =

We know that Dylan bought himself a cup of tea, which costs less than a cup of coffee. So, the £5.39 must have been spent on buying coffee for his friends.

Let's assume that each cup of coffee costs £1. We can use this assumption to find out how many cups of coffee Dylan bought for his friends:

Number of cups of coffee = total cost ÷ cost per cup of coffee = £5.39 ÷ £1 = 5.39

Since we can't buy a fraction of a cup of coffee, we can round this number down to the nearest whole number. Therefore, Dylan bought 5 cups of coffee for his friends.

However, we need to remember that Dylan himself also bought a drink, which wasn't a cup of coffee. So, the total number of people at the cafe was:

Number of people =[tex]number of cups of coffee + 1 = 5 + 1 = 6[/tex]

Therefore, there were 5 friends with Dylan at the cafe.

To know more about the order of subtraction visit:

https://brainly.com/question/30143384

#SPJ1

The visitor should run 1.2 miles to minimize the time it takes to reach the island.

Consider the following figure.

Let us assume that x (CD) represents the distance covered when visitor runs at a rate of 5 mph

So, the time taken by visitor would be:

t₁ = x/5

Let the distance covered 10 - x when visitor swims at a rate of 3 mph

From figure consider right triangle ABC.

Using Pythagoras theorem,

BC² = 7² + (10 - x)²

BC = [tex]\sqrt{49 + (10-x)^2}[/tex]

Now the times taken by visitor when he swims at a rate of 3 mph,

t₂ =  [tex]\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]

so, the total time would be:

t = t₁ + t₂  

[tex]t=\frac{x}{6}+\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]

Differentiating with respect to x we get,

[tex]\frac{dt}{dx}=\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}[/tex]

consider dt/dx = 0

[tex]\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}=0[/tex]

If we solve above equation for x we get, x = 11.2 and x = 8.8

The distance the visitor should run to minimize the time would be:

10 - 8.8 = 1.2 miles

Therefore, the required distance is 1.2 miles

Learn more about the Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ4

In the percentage , the total number of students in sixth grade is 250.

What is percentage?

Percentage is Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Here we know that total number of students is 100%.

Students purchased their  lunch = 24%

Students brought their lunch from home = 190

Then percentage of students brought their lunch from home is

=> (100%-24%) = 190

=> 76% = 190

Then Total number of students in sixth grade is,

76%   = 190

100% = x

=> x = [tex]\frac{190\times100\%}{76\%}[/tex] =  250.

Hence the total number of students in sixth grade is 250.

To learn more about percentage refer the below link

https://brainly.com/question/24877689

#SPJ1

Answer:

Step-by-step explanation:

The mean is found by adding the numbers and dividing by how many numbers there are.

              [tex]Mean=\frac{-2+3+0-15+5-20-4}{7} =\frac{-33}{7} =-4\frac{5}{7}[/tex]

you know that i have gave wrong Ans  

explanation: because i need points

Answer:

Step-by-step explanation:

where’s the figure ?

A.

by simply putting the suggested solution into the equation and see if it stays true. if yes, it is a solution.

(5 + 2i)² - 10(5 + 2i) = -29

25 + 20i - 4 - 50 - 20i = -29

21 - 50 = -29

-29 = -29 true

yes, it is a solution.

B. for a parabola the 2 solutions are usually symmetrical around the center line.

so, I suspect 5 - 2i to be a solution too.

(5 - 2i)² - 10(5 - 2i) = -29

25 - 20i - 4 - 50 + 20i = -29

21 - 50 = -29

-29 = -29 true

yes, it is a solution too.

C.

nowhere.

with 2 complex solutions there are no real number solutions left. and that means there is no intersection with the x-axis.

every quadratic equation must have 2 and only 2 solutions. a solution is normally an intersection with the x-axis (the x- value when y = 0).

The equation for the cost of ticket 13.50 = 1.5m is and the price for a matinee movie ticket is $9.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's use "m" to represent the price of a ticket to a matinee movie.

From the given information, we know that the cost of a ticket to an evening movie is 1.5 times more than a ticket for a matinee movie.

This means that -

Cost of an evening movie ticket = 1.5 × Cost of a matinee movie ticket

We also know that the cost of a ticket to an evening movie is $13.50.

Substituting this value into the equation above, we get -

$13.50 = 1.5m

To solve for "m", we can divide both sides of the equation by 1.5 -

$13.50 / 1.5 = m

m = $9

Therefore, the price of a ticket to a matinee movie is $9.

To learn more about equation from the given link

https://brainly.com/question/28871326

#SPJ1

The inequality in the expression [tex]41-x < 17[/tex] is the less than inequality

The solution to the inequality is [tex]x > 24[/tex]

The inequality is given as:

[tex]41-x < 17[/tex]

Subtract 41 from both sides of the inequality

[tex]41 - 41 -x < 17 - 41[/tex]

Evaluate the difference

[tex]-x < -24[/tex]

Multiply both sides by -1

[tex]-1 \times -x < -24 \times -1[/tex]

Evaluate the product

[tex]x > 24[/tex]

Answer:

Median: 19

Mean: 18

Step-by-step explanation:

Numbers: 19, 20, 40, 3, 17, 5, 22

Number in order from least to greatest: 3, 5, 17, 19, 20, 22, 40

The median is the number in the middle of a data set.

The median is: 19

The mean is the average of a set of data.

The mean is: [tex]\frac{3 + 5 + 17 + 19 + 20 + 22 + 40}{7}[/tex] = 18

So, Median is 19

      Mean is 18