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.

Answer:

2-3=4-5

Step-by-step explanation:

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.

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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.

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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.

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

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.

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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.

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

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).

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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).

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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.

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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.

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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.

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.

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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).

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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.

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The complete question is as shown in the following image

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

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.

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

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

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.

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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.

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

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.

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

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.

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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.

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.

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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

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Full question:

is in the image uploaded

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

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

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

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.

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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.

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The right question is given below:

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)

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

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.

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.

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

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.

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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.

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.

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