Find the first three nonzero terms in the Taylor polynomial approximation to the DE V" +9y + 5y3 = cos(10t), y(0) = 0, y' (0) = 1.

Answers

Answer 1

The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .

In the question ,

it is given that ,

the differential equation is

y'' + 9y + 5y³ = Cos(10t)   ...equation(1)

y(0) = 0, y'(0) = 1

for y = 0 , the differential equation is

y''(0) + 9y(0) + 5{y(0)}³ = Cos90)

y''(0) + 9 + 5 = 1 ;

y''(0) = 1.

differentiating equation(1) with respect to "t" , we have

y''' + 9y' + 15y²y' = -10Sin(10t)

y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)

y'''(0) + 9 + 0 = 0

y'''(0) = -9

The Taylor series is given by

y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....

Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have

y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....

= t + t²/2 - 3/2.t³ + ...

Therefore , the first three terms are t , t²/2 , -3/2.t³   .

Learn more about Taylor Series here

https://brainly.com/question/13163878

#SPJ4


Related Questions

4 is multiplied by the difference of 5 and a number.

Answers

Answer:

The difference is multiplied by 4 can be represented as 4 (x - 1/2) According to the question, 4 (x - 1/2) = 5 x - 1/2 = 5/4 x = 5/4 + 1/2 x = (5 + 2)/4 x = 7/4 Therefore, the number is 7/4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Im assuming the question is to write this into actual numbers,

answer: 4(5-x)

what is the value of x in the equation 2/3(1/2x+12)=1/2(1/3x+14)-3; k 0.03 1.01 k 2.45 1.81 k; which table represents a direct variation function 3 1 2 5 10; what is the solution (a, c) to this system of linear equations?; which is the graph of linear inequality 6x + 2y > โ10?; which input value produces the same output value for the two functions x=-12; which is the graph of y-3=-2/3(x+6); which graph shows the solution to the system of linear inequalities? 2x โ 3y <12 y < โ3

Answers

The value for x in the given equation is -24.

Combine.  1/2 and x.

2x/6 + 24/3 = (x/6 + 14/2) -3

2x/6 + 48/6 = (x+42)/6 - 18/6

2x = 42 - 18 - 48

2x = -48

x = -24

A direct variation is a proportionality relationship in which two quantities follow a direct relationship.

An INEQUALITY is a statement which shows that two quantities are not equal or may not be equal. If two quantities are not equal, then one is greater than the other.

≥ (greater than or equal to) means at least that amount or more.

≤ (less than or equal to) means at most that amount or less.

To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Please click the image to view the graph

6x + 2y > 10

Replace the input variable in the formula with the value provided.

Calculate the result.

To learn more about equation here

https://brainly.com/question/29769033

#SPJ4

Suppose a math class contains 40 students, 23 females (five of whom speak French) and 17 males (six of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.

Answers

6/11 is the probability that a randomly selected student speaks French, given that the student is male

What is Probability?      

It is a branch of mathematics that deals with the occurrence of a random event.

There are 11 members who speak french and 5 are females in 11 members

5/11

p(a given b) = p(a and b) / p(b).

6 of the people in the group are men that speak french, then the probability of (a and b) becomes 6/40

probability that a person speaks french is 11/40

p(a given b)=6/40/11/40

=6/40×40/11=6/11

Hence, 6/11 is the probability that a randomly selected student speaks French, given that the student is male.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

A drawer contains 24 spoons and forks. There are three times as many spoons and than forks.
A. Write a system of linear equations that represent the situation.
B. How many spoons are in the drawer?
C. How many forks are in the drawer?

Answers

s+f=24 and s=3f are system of equations to represent the situation and there are 18 spoons and 6 folks in the drawer.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Let s=number of spoon

Let f=number of forks

Since there are 3 times as many spoons as forks, s=3f

s+f=24

3f+f=24

4f=24

Divide both sides by 4

f=6

Now put f value in s=3f

s=3(6)

s=18

Hence, s+f=24 and s=3f are system of equations to represent the situation and there are 18 spoons and 6 folks in the drawer.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 y2/3

Answers

The equation of the tangent line to the curve at the given point (−3, 3, 1) (asteroid) is y-[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}(x+3)[/tex]

Applying implicit differentiation, the equation of the tangent line is given by:

y - [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex] (x+3)

The equation of a line tangent to a function f(x) at a point (x0, y0) is given by:

y-y0 = f'(x0,y0)(x-x0)

In this problem, point (-3, [tex]\sqrt{3}[/tex]), thus x0 = -3, y0 = [tex]\sqrt{3}[/tex]

The function is:

[tex]x^{2} /3+ y^{2}/3 = 4\\[/tex]

To find the derivative, we have to apply implicit differentiation, thus:

[tex]2x/3* dx/dx + 2y/3*dy/dx = 0[/tex]

[tex]2y/3*dy/dx = -2x/3[/tex]

[tex]dy/dx = -x/y[/tex]

Thus:

[tex]f(-3, \sqrt{3)} = -(-3/\sqrt{3} * \sqrt{3}/\sqrt{3})[/tex] = [tex]\sqrt{3}[/tex]

Then, the equation to the line tangent is:

y-y0 = f'(x0,y0)(x-x0)

y-[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}(x+3)[/tex]

Refer to this complete question:

Use implicit differentiation to find an equation of the tangent line to the curve at the given point x2/3 + y2/3 = 4 (−3, 3, 1) (asteroid).

To know more about the tangent line visit: https://brainly.com/question/22426360

#SPJ4

Find the midpoint of PQ. SEE17. P(3, 5), Q(-2, 13) 18. P(-2, 2.5), Q(1.4, 4) 19. P(4 1/3, 3 1/6), 0(-2 1/5, 3 2/3)

Answers

Therefore, The necessary midpoints are Mz(1 1/5, 3 1/4), My (-0.3, 3.25), and Mx(1/2, 9).

Where does the middle point lie?

Sometimes you have to locate the precise midpoint between two other plane point. You might, for instance, wish to locate a line that divides a given line segment into two equal halves. The "halfway" is the name given to this midpoint.

Here,

M can be used to indicate where two coordinates (x, y) and (a, b) meet in the middle (s, t)

s = x +a/2; t = y +b/2

Mid points

For P(3, 5), Q (-2, 13)

s = 3 - 2 / 2 ; t = 5 + 13 /2

1 / 2 =s ;

t= 9

Mx(1/2, 9) is a midpoint.

For P(-2, 2.5), Q (1.4, 4)

s = -2 + 1.4 / 2 ; t = 2.5 + 4 / 2

s = -0.3 ; t = 3.25

My middle (-0.3, 3.25)

For P(4 1/3, 3 1/6), Q (-2 1/5, 3 2/3)

s = (4 1 / 3 - 2 1/5 ) / 2 ; t = (3 1/6 + 3 2/3) / 2

s = 1 1/15        : t = 3 1/4

Midpoints Mz(1 1/5, 3 1/4)

Thus, the required midpoints are  Mx(1/2, 9), My (-0.3, 3.25) and  Mz(1 1/5, 3 1/4).

To know more about mid point, visit

https://brainly.com/question/11302835

#SPJ4

My age this year is multiple of 8. My age next year is a multiple of 7. How old am I?

Answers

Solution

8x + 1 = 7

y - x = 1

y = 1 + x

sub 1 + x in eqtn i

8x + 1 = 7 { 1 + x }

8x + 1 = 7 + 7x

8x - 7 = 7 - 1

x = 6

y - 6 = 1

y = 1 + 6

y = 7

So,

8x = 8 x 6 = 48

7y = 7 x 7 = 49

My present years is 48

Next year i will be 49

What is multiple?

Multiple can be defined as a number that is the product of a given number and some other natural number. For example when we multiply 7 × 3=21 or 8×3 =24

Therefore my present age is 48 and next year will be 49

Learn more about multiple here: brainly.com/question/25821700

#SPJ1

multiply the polynomial (x 2y)(4x - 3). write your answer in descending order of x. please use the palette below to enter your answer.

Answers

The descending order of the multiplied polynomial is 4x² - 3x + 8xy - 6y

The word polynomial in math refers the algebraic expression in which the exponents of all variables should be a whole number.

Here we have given the polynomial l (x + 2y)(4x - 3).

And we need to do the multiplication operation on it and then write your answer in descending order of x.

AS per the following formula, the multiplication of the polynomial is calculated as,

=> (a + b) ( c + d) = (ac + ad + bc + bd)

Here let us consider a = x and b = 2y, c = 4x and then d = -3

Then the resulting value after the multiplication, it can be written as,

=> (x(4x) + x(-3) + 2y(4x) + 2y(-3))

When we simplify this one then we get

=> 4x² - 3x + 8xy - 6y

To know more about polynomial here.

https://brainly.com/question/11536910

#SPJ4

Writing equations of lines
Write the equation of each line with the given information

Answers

Answer:

y = [tex]\frac{-3}{2}[/tex] x + 2

Step-by-step explanation:

I can see the slight tracings of the slope triangle.  I can see that you went down 3 and right 2.  That would be a slope of [tex]\frac{-3}{2}[/tex] and the y intercept is 2.  That is where the line is crossing the y axis.

y=mx+b

if b is your “b”egin number, you placed +2

you’re mx is your slope. you went down 3 so that’s -3 and over 2 so that’s -3over2

answer: y=-3/2+2

quadratic function shifted 4 left units, stretched vertically by a factor of 2, reflected over the x-axis, and shifted down 3 units_ a. Write the equation for the transformed function: (3 points) b. Sketch the graph: (2 points)

Answers

a. The equation for the transformed function is y = -2(x + 4)^2 - 3.

b. The graph of the transformed function will be a parabola with a vertex located at (x,y)=(-4,-3). The parabola will open downwards, have a maximum at -3, and have a line of symmetry along the x-axis. The parabola will have an x-intercept at x=-4, and will stretch outwards to the right and left infinitely. The graph will look like a U-shaped curve that is shifted down 3 units and has a maximum at -3.

To begin, we can start with the equation of a standard parabola, y=x^2. To shift the parabola 4 units to the left, we can add a -4 to the x term in the equation, giving us y=x^2-4. To stretch the parabola vertically by a factor of 2, we can multiply the equation by -2, giving us y=-2(x^2-4). To reflect the parabola over the x-axis, we can multiply the equation by -1, giving us y=-2(x^2-4) -3. This gives us the equation y=-2(x+4)^2 - 3, which is the equation of the transformed function.

Learn more about parabola here :

https://brainly.com/question/4074088

#SPJ4

Joe Jan wants to receive $22,000 each year for the next 22 years. Assume a 6% interest rate compounded annually. How much must Joe invest today? (Round your answer to the nearest cent.)

Answers

9482.7 must Joe invest today to receive $22,000 each year for the next 22 years.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Joe Jan wants to receive $22,000 each year for the next 22 years.

6% interest rate compounded annually.

Convert 6% to decimal value

6/100=0.06

A=P(1+rt)

22000=P(1+0.06(22))

22000=P(1+1.32)

22000=P(2.32)

Divide both sides by 2.32

P=9482.7

Hence, 9482.7 must Joe invest today to receive $22,000 each year for the next 22 years.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

find the absolute maximum and absolute minimum of f (x, y) among points in the triangle with vertices (0, 0), (1, 0), and (1, 1).

Answers

The absolute maximum and absolute minimum of f(x,y) = 3 + xy -x - 2y is f(0,0) and f(1,1) respectively.

The absolute maximum point is a point where the function obtains its greatest possible value.

And Absolute minimum is a point where the function obtains its least possible value. This is the smallest value that a mathematical function can have over its entire curve.

Given equation is, f(x,y) = 3 + xy - x - 2y

we will check absolute maximum and absolute minimum of f(x,y) at the points (0,0), (1,0), (1,1).  

f(0,0) = 3 + (0)(0) - 0 - 2(0) = 3

f(1,0) = 3 + (1)(0) - 1 - 2 (0) = 2

f(1,1) = 3 + (1)(1) - 1 - 2(1) = 1

Therefore we get absolute maximum at f(0,0) and absolute minimum at f(1,1).

An absolute minimum also called a global minimum, occurs when a point of the function is lower any other point on the function within the function's domain. A local minimum also called relative minimum occurs when a point is lower than the points surrounding it.

Given question is incomplete. Complete question is:

find the absolute maximum and absolute minimum of f (x, y) = 3 + xy - x -2y  among points in the triangle with vertices (0, 0), (1, 0), and (1, 1).

To know more about maximum here

https://brainly.com/question/13176730

#SPJ4

Please help witht this ones. I need help

Answers

28. The pair of angles is classified as: alternate exterior angles.

29. The pair of angles is classified as: alternate interior angles.

30. The measure of the larger angle is of: 160º.

How to classify the pair of angles?

In both items 28 and 29, we have that two parallel lines are cut by a transversal, hence the angles are classified as follows:

3 and 6: alternate exterior angles, as they are on the opposite side of the transversal line, and both are outside the region between the two parallel lines.2 and 7: alternate interior angles, as they are between the two parallel lines, on the opposite side of the transversal.

What are linear pairs?

Two angles are called linear pairs if they are supplementary, that is, if the sum of their measures is of 180º.

In this problem, we have that two angles form a linear pair, hence:

x + y = 180º.

The measure of the greater angle is eight times the measure of the smaller angle, hence:

x = 8y.

Thus:

8y + y = 180

9y = 180

y = 20º.

Then the measure of the larger angle is of:

x = 8y = 8 x 20 = 160º.

More can be learned about angle measures at https://brainly.com/question/25716982

#SPJ1

the statistical method used to predict values of one numerical variable based on the values of another is___

Answers

The statistical method used to predict the values of one numerical variable based on the values of another is regression analysis.

Regression analysis:

Regression analysis is a statistical method that shows the relationship between two or more variables. Usually expressed in a graph, the method tests the relationship between a dependent variable against independent variables.

Regression analysis is used to estimate the relationship between a dependent variable and one or more independent variables.

The common form of regression analysis is linear regression. Regression analysis allows us to infer that there is a relationship between two or more variables.

Therefore regression method is used to predict values of one numerical on another.

To know more about the regression analysis refer to the link given below:

https://brainly.com/question/7781679

#SPJ4

a rectangle's length is 3 inches greater than its width. if the perimeter of the rectangle is 30 inches, find the length. (all answers are given in inches.)

Answers

The length of the rectangle is calculated to be 9 inches if the length of the rectangle is 3 inches greater than its width

The formula for the perimeter of a rectangle can be given as follows;

perimeter = 2 ( x + y )

Here x represents length and y represents width;

Since the length of a rectangle is 3 Inches more than its width, therefore;

x = y + 3

Since the perimeter of the rectangle is 30 inches, therefore;

2 ( x + y ) = 30

Simplifying by dividing both sides by 2 as follows;

2 ( x + y ) / 2 = 30 / 2

x + y = 15

As x = y + 3; substituting this value in x + y = 15 as follows;

y + 3 + y = 15

Rearranging;

y + y + 3 = 15

2y + 3 = 15

2y = 15 - 3

2y = 12

y = 12 / 2

y = 6

As x = y + 3

x = 6 + 3

x = 9 inches

Hence the width of this rectangle is 6 inches and the length is 9 inches.

To learn more about length; click here:

https://brainly.com/question/26759758

#SPJ4

How do you regroup 4 digit numbers?

Answers

We take carry 1 if there is more then 9 when we are adding or subtracting in the regrouping 4 digit number.

Given that,

We have to find how do we regroup 4 digit numbers.

We know that,

When performing operations like subtraction and addition, regrouping is accomplished by creating groups of tens. Regrouping refers to rearranging integers into place value-based groupings to facilitate operations. Because you must rearrange the numbers into place value to complete the procedure, it is known as regrouping.

Addition with regrouping or addition with carryover refers to additions where the addends' digit sums exceed 9 in any of the columns. Finding the digit sum of two integers requires regrouping. Only the units place digit of the total is then written in the appropriate column.

        (1)  (1)

   3   1    9   5

+  6   2   3    7

--------------------

   9    4    3   2
Therefore, We take carry 1 if there is more then 9 when we are adding or subtracting in the regrouping 4 digit number.

To learn more about regrouping visit: https://brainly.com/question/11556652

#SPJ4

estimate the area under the curve given the following fuction, interval, and number of subintervals using the right endpoint method.

Answers

The area under the given curve is 77/60. SO the option B is correct.

In the given question we have to estimate the area under the curve given the following fuction, interval, and number of subintervals using the right endpoint method.

The given function is

F(x) = 1/x; [1,5]; n=4

The given options are:

A≈77/240

A≈77/60

A≈77/15

A≈25/3

A≈25/12

Since, f(x) =1/x

∆x = (b-a)/n

∆x = (5-1)/4

∆x =4/4

∆x = 1

Now the table is

x               1            2            3            4            5

f(x)            1            1/2          1/3         1/4          1/5

R(4) = [f(2)+f(3)+f(4)+f(5)]∆x

R(4) = [1/2+1/3+1/4+1/5]1

R(4) = (30+20+15+12)/60

R(4) = 77/60

Hence, the area under the given curve is 77/60. SO the option B is correct.

To learn more about area of the curve link is here

brainly.com/question/21563214

#SPJ4

The right question is given below:

which of the following numbers does not have 8 as a factor? A. 25424, B. 15000, C. 36502, D. 10008​

Answers

By dividing, we find The number that does not have 8 as a factor is C. 36502.

what is factor?

A factor of a number is a positive integer that divides evenly into the number. For example, the factors of 6 are 1, 2, 3, and 6.

what is division?

Division is a mathematical operation that involves dividing one number (the dividend) by another number (the divisor) to determine the quotient, which is the result of the division.

to check whether 8 is a factor of 25424, you can divide 25424 by 8:

25424 / 8 = 3178

Since the result is an integer, 8 is a factor of 25424.

To check whether 8 is a factor of 15000, you can divide 15000 by 8:

15000 / 8 = 1875

Since the result is an integer, 8 is a factor of 15000.

To check whether 8 is a factor of 36502, you can divide 36502 by 8:

36502 / 8 = 4562.75

Since the result is not an integer, 8 is not a factor of 36502.

To check whether 8 is a factor of 10008, you can divide 10008 by 8:

10008 / 8 = 1251

Since the result is an integer, 8 is a factor of 10008.

Therefore, the number that does not have 8 as a factor is C. 36502.

To learn more about division visit:

https://brainly.com/question/1575906

#SPJ4

The probability that Callista drives faster than
the speed limit (event A) is 0.34, and the
probability that she gets to a wedding on time
(event B) is 0.45. The probability that she gets to
the wedding on time given that she drives faster
than the speed limit is 0.85. Are events A and B
dependent or independent?

Answers

Events A and B dependent as the occurrence of one event affect the chances of the occurrence of the other event.

What is Probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

To understand this branch, it is extremely important to know its most basic definitions, such as the formula for calculating probabilities in equiprobable sample spaces, probability of the union of two events, probability of the complementary event, etc.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

Since we have given that

A be the event that Callista drives faster than the speed limit.

P(A)=0.34

B be the event that she gets to a wedding on time.

P(B)=0.45

The probability that she gets to the wedding on time given that she drives faster than the speed limit is 0.85 i.e.

P(A|B)=0.85

but for A and B to be independent ,

P(A).P(B)= P(A and B)

0.34×0.45=0.153

but,

[tex]P(A|B) = \frac{P(AnB)}{P(B)}[/tex]

P(AnB) = 0.85 x 0.45

P(AnB) = 0.3825

So, P(A∩B) does not satisfy the condition.

Hence, A and B are not independent events.

Learn more about probability here: https://brainly.com/question/13604758

#SPJ1

a hungry statistician analyzed nutritional information from 77 food items available for purchase at a popular coffee shop (seattle's worst). the statistician produces a multiple regression model with response variable calories, and three predictors.

Answers

For given  regression model, the number 59.89 in the table tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

In this question we have been given a summary of regression model.

We need to explain the meaning of the number 59.89 in the table.

For given regression model, to view the results of the model, we can use the summary() function in R programming.

In given summary consider the 'Coefficients' table.

The first row gives the estimates of the y-intercept, and the second row gives the regression coefficient of the model.

The 'Estimate' column is the estimated effect, also called the regression coefficient or r² value.

The number 59.89 in the table is coefficient for IsSandwich.

This number tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

Therefore, the meaning of the number 59.89 in the table: for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

Learn more about the regression model here:

https://brainly.com/question/14983410

#SPJ4

The complete question is as shown in the following image

compute the determinants in exercises 1-8 using a cofactor expansion across the first row. in exercises 1-4, also compute the determinant by a cofactor expansion down the second column.

Answers

The determinants using co - factor expansion across the first row is 1 .

Given :

compute the determinants in exercises 1-8 using a co - factor expansion across the first row.

[tex]\left[\begin{array}{ccc}3&0&4\\2&3&2\\0&5&-1\end{array}\right][/tex]

Determinant of a matrix :

The determinant of a matrix is the scalar value computed for a given square matrix. Linear algebra deals with the determinant, it is computed using the elements of a square matrix.

determinant = 3 ( 3 * -1 - ( 5 * 2 ) - 0 ( 2 * -1 - ( 0 * 3 ) + 4 ( 2 * 5 - 0 * 3 )

= 3 ( -3 - 10 ) - 0 ( -2 - 0 ) + 4 ( 10 - 0 )

= 3 * -13 - 0 + 4 * 10

= -39 + 40

= 1

Learn more about the matrix here:

https://brainly.com/question/28180105

#SPJ4

Full question:

is in the image uploaded

a well known social media company is looking to expand their online presence by creating another platform. they know that they current average 2,500,000 users each day, with a standard deviation of 625,000 users. if they randomly sample 50 days to analyze the use of their existing technology, identify each of the following, rounding to the nearest whole number if necessary: Provide your answer below: read M users Guides o= users Gallery Webex = users deric Support - Users urveys FEEDBACKM ORE INSTRUCTION URIME . Provous O Type here to search

Answers

The value of standard deviation is 88,389.

The Normal distribution id the contionuouse distribution with unimodal and symmetric shaped, it is widely used to approximated discrete distribution and sample mean and a total sum of the random variable, the approximation depends on the concept og the Central limit theorem.

The Central limit theorem states that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.

We have given that,

average = 2.500,000

standard deviation σ = 625,000

sample n = 50.

Therefore S = σ / √n

                    = 625000 / √50

                    = 625000 / 7.071

                 S = 88,389

Hence the standard deviation will be 88,389.

To know more about deviation here

https://brainly.com/question/16966492

#SPJ4

John started his employment with a salary of Sh. 120,000 per annum which was increased
by Sh. 10,000 every year up to the top of the scale of Sh. 1,500,000 per annum.
REQUIRED
i. In how many years’ time does he reach to the top scale? (3 marks)
ii. What is the total amount he would earn during this period

Answers

In 138 years time, john will reach to the top scale and the total amount he would earn during this period will be $1380000.

What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have John who started his employment with a salary of $120,000 per annum which was increased by $10,000 every year up to the top of the scale of $1,500,000 per annum.

We can write the equation governing the increase as -

y = 120000 + 10000x

For -

y = 1500000, we can write -

1500000 = 120000 + 10000x

10000(12 + x) = 1500000

x + 12 = 150

x = 138 years

The total amount he would earn during this period will be -

A = 10000 x 138 = $1380000

Therefore, in 138 years time, john will reach to the top scale and the total amount he would earn during this period will be $1380000.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ1

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 36 minutes of calls is
$24.24, and the remaining credit after 55 minutes of calls is $21.20. What is the remaining credit after 63 minutes of calls?

Answers

The remaining credit after 63 minutes of calls is $19.92.

What is the remaining credit after 63 minutes of calls?

From the information illustrated, the remaining credit after 36 minutes of calls is $24.24, and the remaining credit after 55 minutes of calls is $21.20.

The rate will be:

= (24.24 - 21.20) / (55 - 36)

= 3.04 / 19

= 0.16

The remaining credit after 63 minutes of calls will be:

= $21.20 - ((63 - 55) × $0.16)

= $21.20 - $1.28

= $19.92

The credit is $19.92.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

An employee in the 12% tax bracket
invests $1000.00 in a Roth IRA. When the
employee retires, her salary is in the 22%
tax bracket. What tax will be assessed on
the initial investment at retirement?
A. Since the employee used a Roth IRA, she will pay no taxes on her
investment at retirement.
B. Not enough information to answer
C. $120.00
D. $220.00

Answers

A. Since the employee used a Roth IRA, she will pay no taxes on her investment at retirement.

The Roth IRA is a type of individual retirement account (IRA) that allows the investor to contribute after-tax money to the account. This means that the investor pays taxes on the contributions upfront, but the investment grows tax-free and can be withdrawn tax-free at retirement. Therefore, the employee in this scenario will not have to pay any taxes on her initial investment of $1000.00 at retirement, regardless of her tax bracket at that time.

Which of the following represents a one to one function?
A.Students to thier height
B.Students to their weight
C.Students to their LRN
D.Students to their age​

Answers

Students to their LRN represent a one-to-one function.

If there is exactly one y in the range for every x in the domain of a function f, then that function is a one-to-one function. The range has no y equivalent to more than one x in the domain.

To put it another way, a function is referred to as a "one-to-one" function if various elements of A have different images in B. That is, there are various outputs for various inputs.

Here, each student has a different LRN or Learner Reference Number. No two students will have the same LRN. Therefore, this function is a one-to-one function. The correct option is C.

Two or more students can have the same height, weight, or age. Therefore, the incorrect options are options A, B, and D.

To know more about one-to-one function:

https://brainly.com/question/18154364

#SPJ4

Determines if a number is prime or composite
12. Choose the words that make the sentence true.
17
prime
The number 7 is plies with
two factors.
composite
because it has
exactly
more than
to 10lbsts els alto alghia
iqhiur

Answers

Step-by-step explanation:

the 1 is 2 is 3 so what is 4?

Answer:

Step-by-step explanation:

17 is prime and the number 7 is also prime. Composite numbers are numbers have more than two factors other than 1 and itself. Like 12, 14, and 16.

you are using the plus sign more than once in the example of 2+3=4+5

Answers

Answer:

2-3=4-5

Step-by-step explanation:

develop a least squares estimated regression line. (round your numerical values to five decimal places.)

Answers

The least squares estimated regression line is  0.5x+1.667

If your data shows a linear relationship between the X and Y variables, you will want to find the line that best fits that relationship. That line is called a Regression Line and has the equation ŷ= a + b x. The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance (the sum of squares of the errors).

Data rarely fit a straight line exactly. Usually, it is satisfactory with rough predictions. Typically, you have a set of data whose scatter plot appears to “fit” a straight line. This is called a Line of Best Fit or Least-Squares Line.

To know more about Least-Squares Line visit: brainly.com/question/2141008

#SPJ4

Determine which letter best represents an equivalent fraction.
A.18/20
B.3/15
C.7/8

Answers

Answer: A

Step-by-step explanation: when 18/20 is turned into a decimal it comes out as even and is the best one you can choose from

Other Questions
why do i keep getting urinary tract infections?; what is the fastest way to get rid of a bladder infection?; what causes uti; what causes a uti in a woman; what are the symptoms of a bladder infection in females; water infection; uti treatment; uti symptoms What will happen when fragmentation occurs? in considering the four stages of identity development, james marcia theorized that an adolescent must undergo and to attain a mature identity. Explain why dehydration synthesis make sense as the name of the reaction of creating polymers from monomers. Imagine you are trying to explain the process of protein sorting to your friend who is also taking LS7A. You show them the figure to the right. Provide an explanation for what this figure represents. Be sure to define the term signal peptide and any other terms in the diagram you think your friend would not already know. a manufacturer planned to use $82.00 of materials per unit produced, but in the most recent period it actually used $80.00 of material per unit produced. during this same period, the company planned to produce 1,200 units, but actually produced only 1,000 units. the flexible-budget variance for materials is: keep the knees and hips at 90-degree angles and the wrists straight. elevate the knees, keep the hips at a 90-degree angle, and keep the shoulders back keep the monitor above the eyes and the keyboard slightly raised keep the monitor at eye level and the keyboard slightly raised. how many coulombs of positive charge are contained in the atomic nuclei of this gas? Clara (1) trabaja (trabajar) para una agencia matrimonial. Sus amigos (2) dicen (decir) que Clara es como Cupido y tambin que (3) tienen (tener) que trabajar menos y buscarse novio porque ltimamente se (4) encuentran (encontrar) un poco sola. Yo (5) reconzco (reconocer) que a veces (6) pienso (pensar) ms en los dems que en m misma y que (7) debo (deber) salir ms. Write a class named GasTank containing: An instance variable named amount of type double, initialized to 0. An instance variable named capacity of type double. A constructor that accepts a parameter of type double. The value of the parameter is used to initialize the value of capacity. A method named addGas that accepts a parameter of type double. The value of the amount instance variable is increased by the value of the parameter. However, if the value of amount is increased beyond the value of capacity, amount is set to capacity. A method named useGas that accepts a parameter of type double. The value of the amount instance variable is decreased by the value of the parameter. However, if the value of amount is decreased below 0, amount is set to 0. A method named isEmpty that accepts no parameters. isEmpty returns a boolean value: true if the value of amount is less than 0.1, and false otherwise. A method named isFull that accepts no parameters. isFull returns a boolean value: true if the value of amount is greater than capacity-0.1, and false otherwise. A method named getGasLevel that accepts no parameters. getGasLevel returns the value of the amount instance variable. A method named fillUp that accepts no parameters. fillUp increases amount to capacity and returns the difference between the value of capacity and the original value of amount (that is, the amount of gas that is needed to fill the tank to capacity). the royal era in addition to the unities of the rules of play construction, the unity of tone dictated that group of answer choices thin contractile protein involved in cross-bridge formation, comes in filamentous or globular forms. t/f robert capa and henri cartier-bresson felt that it was important to form the independent photo agency named magnum because: PLEASE HELP ASAP PROJECT: THE RESEARCH REPORTWrite a research report of at least 900 words on a topic of your choice. Be sure to appropriately narrow your topic and choose something that you can adequately research.Here is your goal for this assignment:Write a research report.Your research report should include the following:Document your sources properly, using MLA format (click here to review the MLA Style Guide).You must submit an outline with your report.Remember that a research report is a formal piece of writing.You must use at least two sources for your report; only one of which can be a website source. Journal articles found using an online database, such as EBSCOhost, are not considered to be website sources.You must cite at least one direct quotation in your report.Use what you've learned about well developed paragraphs and effective transitions.Be sure your report is free of conventional and grammatical errors, and is at least 900 words long.Include a works cited page. Why are larger populations generally more stable than smaller populations?; Which is better high genetic diversity or low genetic diversity Why?; Why do populations benefit from higher genetic diversity?; Why is a genetically diverse population more likely to survive? I need help with the 1st question please the php function that is executed is a connection to a database cannot be made is the____ function. die | isset| end | connect. plan recommendation: we need to perform an endoscopic retrograde cholangiopancreatogram or magnetic resonance cholangiopancreatogram. given the less invasive nature, i recommended ms. mendel have an mr cholangiogram, which is scheduled for later this week. if the results confirm primary sclerosing cholangitis, we will begin medical treatment and then schedule a percutaneous hepatic biopsy. which of the following statements is not true, given this health record information? in contrast to digital marketing, where customers receive clear and correct information about any product or service, there is little likelihood that customers will be misled by salespeople in traditional marketing. why are notochord more closely related to echinoderms than other invertebrates?