Solve for X anything can help

The given differential equation is

y" -y'+y=2 sin 3x------(1)

Let, y'=z

y"=z'

Substituting the value of , y, y' and y" in equation (1)

z'-z+zx=2 sin 3 x

z'+z(x-1)=2 sin 3 x-----------(1)

This is a type of linear differential equation.

Integrating factor

A function is selected as an integrating factor to make it easier to solve a particular differential equation. It is frequently used to resolve ordinary differential equations, but it is also employed in multivariable calculus when an inexact differential can be converted into an exact differential by multiplying through by an integrating factor. (which can then be integrated to give a scalar field).

Multiplying both sides of equation (1) by integrating factor and integrating we get

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The length of the hypotenuse AB is equal to the sum of the square of other two sides AC and BC. The measure of the curve DE is 10.5 units

The theorem states that the length of the hypotenuse AB is equal to the sum of the square of other two sides AC and BC.

According to the theorem;

AB^2 = AC^2 + BC^2

AB^2 = 6^2 + 8^2

AB^2 = 36 + 64

AB = 10

If the curve DE is 5% longer than line segment АВ, the measure of curve DE is given as;

DE = 1.05 * 10
DE = 10.5

Hence the measure of the curve DE is 10.5 units

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Answer:

5 and 4

Step-by-step explanation:

Answer:

f(6) = 35 × 6 - 175 = 35

Answer:

$ 7800

Step-by-step explanation:

P'(t) = 3t² + 10t + 6

\(P(t) = \int\limits^a_b {P'(t)} \, dt\)

For the 4th year, the limits are [3,4]

\(P(t) = \int\limits^4_3 {3t^2 + 10t + 6} \, dt\\\\= [\frac{3t^3}{3} + \frac{10t^2}{2} + 6t]^{^4}__{3}\\\\\)

\(=[\frac{3(4)^3}{3} + \frac{10(4)^2}{2} + 6(4)]-[\frac{3(3)^3}{3} + \frac{10(3)^2}{2} + 6(3)]\\\\=[\frac{3(64)}{3} + \frac{10(16)}{2} + 24]-[\frac{3(27)}{3} + \frac{10(9)}{2} + 18]\\\\= [64 + 5(16) + 24]-[27+5(9) + 18]\\\\= 168-90\\\\= 78\)

= $ 7800

Answer:

-29, -34, -39

Step-by-step explanation:

the numbers are going down by five each time.

-24-5=-29

-29-5=-34

-34-5=-39

Hope this helps!

Answer:

-29

Step-by-step explanation:

because -14 and -19 is minus 5

2x - 5y = 1

We need to group all the variable terms on one side and all the constant terms on the other side of the equation. Therefore move the term -5y to the other side of equation.

\(\rm{2x - 5y = 1 }\\ \)

\( \rm{2x - 5y + 5y = 1 + 5y}\\\)

Subtract -5y from both sides of the equation

Simplify 2x - 5y + 5y = 1 + 5y

Cancel -5y with 5y

Reorder 1 + 5y so highest order terms are first

\( \rm{x = \frac{5y + 1}{2} } \\ \)

Move factors not having X from the left side of equation 2x = 5y + 1

\( \rm{ \frac{2x}{2} = \frac{5y + 1}{2} } \\ \)

Divide both sides of equation 2x = 5y + 1 by 2

Cancel 2 with 2

\( \rm{ \frac{\cancel{2}x}{\cancel{2}} = \frac{5y + 1}{2} } \\ \)

\( \rm{x = \frac{5y + 1}{2} } \\ \)

Therefore, the x of 2x - 5y = 1 is \( \rm{ \frac{5y + 1}{2} } \)

2x - 5y = 1

\(\rm{-5y + 2x = 1}\\ \)

Reorder 2x -5y so highest order terms are first

-5y = -2x + 1

We need to group all the variable terms on one side and all the constant terms on the other side of the equation. Therefore move the term 2x to the other side of equation -5y + 2x = 1

\(\rm{-5y + 2x - 2x = 1 - 2x}\\\)

Subtract 2x from both sides of the equation

Simply - 5y + 2x -2x = 1 - 2x

Cancel 2x with -2x

Reorder 1 - 2x so highest order terms are first

\( \rm{y = - \frac{2x + 1}{5} }\\\)

Move factors not having y from the left side of equation -5y = -2x + 1

\(\rm{ \frac{ - 5y}{ - 5} = \frac{ - 2x + 1}{ - 5} }\\ \)

Divide both sides of equation -5y = -2x +1 by -5

Simplify \(\rm{ \frac{ - 5y}{ - 5} = \frac{ - 2x + 1}{ - 5} } \)

Cancel 5 with -5

Resolve sign on fraction \( \rm{\frac{ - 2x + 1}{ - 5} }\)

Therefore, the y of 2x-5y = 1 is \(\rm{\frac{ - 2x + 1}{ - 5} } \)

3x + 2y = 11

We need to group all the variable terms on one side and all the constant terms on the other side of the equation. Therefore move the term 2:y to the other side of equation 3 x + 2y - 2y = 11 - 2y

Subtract 2y from the both sides of the equation

Simplify 3x + 2y - 2y = 11 - 2y

Cancel 2y with 2y

Reorder 11 - 2y so highest order terms are first

\( \rm{x = \frac{2y + 11}{3} } \\ \)

Move the factors not having x from the left side of equation 3x = -2y +11

\( \rm{ \frac{3x}{3} = \frac{-2y + 11}{3} } \\ \)

Divide both sides of equation 3x = 2y + 11 by 3

Cancel 3 with 3

\( \rm{ \frac{\cancel{3}x}{\cancel{3}} = \frac{-2y + 11}{3} } \\ \)

\( \rm{x = \frac{2y + 11}{3} } \\ \)

Therefore, the x for 3x + 2y = 11 is \( \rm{ \frac{2y + 11}{3} } \)

2y + 3x = 11

Reorder 3x + 2y so highest order terms are first

\(\rm{2y + 3x = 11}\\\)

We need to group all the variable terms on one side and all the constant terms on the other side of the equation. Therefore move the term 2:y to the other side of equation 2y + 3x = 11

\(\rm{2y + 3x - 3x = 11 - 3x}\)

Subtract 3y from the both sides of the equation

Simplify 2y + 3x - 3x = 11 - 3x

Cancel 3x with - 3x

Reorder 11 - 3x so highest order terms are first

\( \rm{y= - \frac{3x + 11}{3} } \\ \)

Move factors not having y from the left side of equation 2y = -3x + 11

\( \rm{ \frac{2y}{2} = \frac{-3x + 11}{3} } \\ \)

Divide both sides of equation 2y = -3x + 11 by 2

Cancel 2 with 2

\( \rm{ \frac{\cancel{2}y}{\cancel{2}} = \frac{-3x + 11}{3} } \\ \)

\( \rm{y = \frac{-3x + 11}{3} } \\ \)

Therefore, the y for 2y + 3x = 11 is \( \rm{ \frac{-3x + 11}{3} } \)

Answer:

600 m

Step-by-step explanation:

Given that :

Mina's constant pace = 1.6m/s

Time taken = 20 minutes

Abeni's pace = 1.4 m/s

Time taken = 30 minutes

Difference in the distances covered :

Recall :

Distance covered = Speed * time

Mina's distance = 1.6 * (20 * 60 seconds) = 1920m

Abeni's distance = 1.4 * (30 * 60 seconds) = 2520 m

Difference :

2520 m - 1920 m

= 600 m

Answer:

x = 6

Step-by-step explanation:

The 2 angles are vertical angles and are congruent , so

11x - 14 = 7x + 10 ( subtract 7x from both sides )

4x - 14 = 10 ( add 14 to both sides )

4x = 24 ( divide both sides by 4 )

x = 6

Given the following number:

Let's write it in a fraction or mixed number in the lowest terms.

Since the decimal is 0.14, putting it into fraction will be:

Simplifying,

258 is a whole number, thus, it will become a mixed number, we just add 258 and 7/50.

The answer is, therefore:

The measure of ∠4, ∠3 and ∠7 are 115°, 65° and 65° respectively.

An equation is an expression used to show the relationship between two or more numbers and variables.

From the diagram:

∠2 + ∠4 = 180° (sum of angles in a straight line)

∠4 + 65 = 180

∠4 = 115°

b) ∠2 = ∠3 (vertically opposite angles)

∠3 = 65°

c) ∠3 = ∠7 (corresponding angles)

∠7 = 65°

The measure of ∠4, ∠3 and ∠7 are 115°, 65° and 65° respectively.

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Answer:

j = 2

Step-by-step explanation:

Combine like terms

6j-11j-11j+10=-13

-16j+19=-13

Subtract 19 from both sides of the equation

-16j+19=-13

-16+19-19=-13-19

Simplify

-16j=-32

Divide both sides of the equation by the same term

Simplify again

Which gives you j=2

let p (t) = 600(0.974)^t be the population of a good place in the year 1900. a) rewrite this equation in the form p(t) = ae^(kt)

The final form of the given exponential function p(t) = 600(0.974)^t is p(t) = 600e^(-0.0264t).

The exponential function is a mathematical function where an independent variable is raised to a constant, and it is always found in the form y = ab^x. Here, we need to rewrite the given equation p(t) = 600(0.974)^t in the form p(t) = ae^(kt)Round k to at least 4 decimal places.

We know that exponential function is in the form p(t) = ae^(kt)

Here, the given equation p(t) = 600(0.974)^t ... equation (1)

The given equation can be written as:

p(t) = ae^(kt) ... equation (2)

Where,p(t) is the population of a good place in the year 1900

ae^(kt) is the form of the exponential function

600(0.974)^t can be written as 600(e^(ln 0.974))^t

p(t) = 600(e^(ln 0.974))^t

p(t) = 600(e^(ln0.974t) ... equation (3)

Comparing equations (2) and (3), we get: a = 600

k = ln 0.974

Rounding k to at least 4 decimal places, we get k = -0.0264

Therefore, the final form of the given exponential function p(t) = 600(0.974)^t is p(t) = 600e^(-0.0264t)

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EXPLANATION:

The cube of the sum of 6 is equal to 18 and any number can form any mathematical expression, but that does not mean that it is a line, because both the value of 18 and that other number must maintain a constant pattern that allows obtaining a straight line.

Something linear is means a trend or pattern that is involved with that other value in a process.

Answer:

B. Rectangle T, Rectangle P, Rectangle S.

Step-by-step explanation:

To determine which list shows the correct order of the length of the diagonals of the rectangles from shortest to longest, let all the lengths be in decimal form:

Rectangle P = 6.7 cm

Rectangle S = \( \frac{34}{5} cm \) = 6.8 cm

Rectangle T = \( \sqrt{36.5} cm \) ≈ 6.04

Thus:

6.04 cm < 6.7 cm < 6.8 cm

Therefore, from the shortest to the longest, we have:

Rectangle T < Rectangle P < Rectangle S.

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The number of hours to work to pay for the new computer is 111 hours

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The cost difference between the new and refurbished computer is $800.00 - $640.00 = $160.00. This means that you would save $160.00 by buying the refurbished computer instead of the new one.

Let's say you work for "x" hours, then your gross pay will be:

A = 10x dollars

Your FICA deduction will be 7.65% of your gross pay:

0.0765 ( 10x ) = 0.765x dollars

Your federal tax withholding will be 12% of your gross pay:

0.12 ( 10x ) = 1.2x dollars

Your state tax withholding will be 8% of your gross pay:

0.08 ( 10x ) = 0.8x dollars

The total amount of taxes that will be deducted from your paycheck is the sum of these three amounts:

0.765x + 1.2x + 0.8x = 2.765x dollars

So your net pay will be:

10x - 2.765x = 7.235x dollars

On simplifying the equation , we get

Now, we can calculate the number of hours you would need to work to pay for the new computer:

800 = 7.235x

x ≈ 110.5 hours

Hence , the number of hours is x = 111 hours

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Answer:

2 positive unit tiles is needed

Step-by-step explanation:

Given the expression x^2 – 3x – 10, the partial factorization is as shown;

x^2 – 3x – 10

=  x^2 +2x – 5x – 10

= x(x+2)-5(x+2)

= (x-5)(x+2)

Note that negative values are represented as tiles labelled below (negative tiles) while positive values are tiles labelled above (positive tiles)

From the second line we can see that first term 1 is labeled + x squared, second is labelled +2x (two positive tiles above), then the 5 tiles below + x squared are labeled negative x, and the 10 tiles below the + x tiles are labeled negative.

Hence base on the partial factorization and the underlined statement, we can see that 2 positive unit tiles is needed to complete the factorization

Answer:

B i think

Step-by-step explanation:

The value of y is given as follows:

y = 23.

Hence the angle measures are given as follows:

69º, 23º and 88º.

The sum of the measures of the internal angles of a triangle is of 180º.

The internal angles for the triangle in this problem have the measures given as follows:

Hence the value of y is obtained as follows:

3y + y + 4y - 4 = 180

8y = 184

y = 184/8

y = 23.

Hence the angle measures are given as follows:

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Answer:  BC = 10

======================================================

Work Shown:

The term "collinear" means all points fall on the same straight line.

Point B is on segment AC.

Through the segment addition postulate, we can say

AB+BC = AC

This is the idea where we glue together smaller segments to form a larger segment, and we keep everything to be a straight line.

Apply substitution and solve for x

AB+BC = AC

2x-12+x+2 = 14

3x-10 = 14

3x = 14+10

3x = 24

x = 24/3

x = 8

Then we can find the length of BC

BC = x+2

BC = 8+2

BC = 10

--------

Note that AB = 2x-12 = 2*8-12 = 16-12 = 4

and how AB+BC = 4+10 = 14 which matches with AC = 14

Therefore we have shown AB+BC = AC is true to confirm the answer.

Collinear points are points on the same line.

The value of BC is 10

Since points A, B and C are on the same line, where B is between points A and C.

So, we have:

\(AC = AB + BC\)

Substitute values for AC, AB and BC

\(14 = 2x - 12 + x + 2\)

Collect like terms

\(2x +x =14 + 12 - 2\)

\(3x =24\)

Divide both sides of the equation by 3

\(x =8\)

Substitute 8 for x in BC = x + 2

\(BC =8 + 2\)

\(BC =10\)

Hence, the value of BC is 10

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Answer:

a) 28.34 m

Step-by-step explanation:

Finding ∠RQS :

Length of arc RS :

Answer:

90°

Step-by-step explanation:

follow the tangent rule.

The expression for the total amount deposited after M months is $100 + $50M.

From the above question, M is the number of months, the expression that shows the total amount deposited after M months can be calculated as follows:

Amount deposited = $100 + $50M

To calculate the total deposit amount after M months, we need to know the monthly deposit amount. Let us denote the monthly deposit amount by D (currency unit).

The formula for total deposits after M months can be written as:

Total Deposits = M * D

In this formula, M represents the number of months and D represents monthly deposits.

Multiply the number of months by the monthly deposit amount to get the total deposit amount after M months.

Total amount deposited after M months = $100 + $50M.So, the expression for the total amount deposited after M months is $100 + $50M.

Question:- Let m be the number of months. Write an expression to show the total amount deposited after m months. 25m Write an expression to show the total amount in Trey's savings account after m months.

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Answer:

The answer is 2.55

Step-by-step explanation:

As, the original price = $17

So, 85% of it have been reduced from it so

85% of 17

= 85/100 x 17 = 14.45

So it have reduced by $14.45

So, $17 - $14.45= $2.55

A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.

A probability distribution is a list of all of the possible outcomes of a random variable, along with its corresponding probability values.

A probability distribution links each outcome of a random variable or process with its probability of occurrence.

A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.

These models have a mathematical background, and can be very picky. For them to work properly, the random variable you are trying to fit in must meet different assumptions so that the outcomes of the model have the correct probabilities, and also so that you can test and validate the model against real data from the random variable.

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Answer:

x = -2 ; x = 6/5

Step-by-step explanation:

5x + 2 >=0

5x >= -2

5/5 x >= -2/5

x >= -2/5

if x >= -2/5

5x +2 = 8

5x = 8 -2

5x = 6

5/5 x = 6/5

x = 6/5

if x < -2/5

-5x -2 = 8

-5x = 8+2

-5x = 10

-5/-5 x = 10/-5

x = -2

Answer:

a) 160km

b) it will take 3.2 hours or 192 minutes or 3 hours and 12 minutes

Step-by-step explanation:

a) d=speedxtime

so, 64x2. 5=160km

b) time=d/s

so, 160/50

it will take 3.2 hours or 192 minutes or 3 hours and 12 minutes

Answer:

look down

Step-by-step explanation:

The normal probability plot is a graphical technique to identify substantive departures from normality. This includes identifying outliers, skewness, kurtosis, a need for transformations, and mixtures. Normal probability plots are made of raw data, residuals from model fits, and estimated parameters.

Answer:Point percentages

Step-by-step explanation:

Answer:

The answer is

The first one, the second one and the last one.

Hope this helps.

Answer:

The answer will be option no.1

Step-by-step explanation:

Angles:

Since,

Sum of angles in a right angle are equal to 180°

So,

90+x+x= 180

2x= 180-90

2x= 90

x= 90/2

x= 45°

There fore the other two angles will be of 45° and one angle will be of 90°

Sides:

(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2

(Hyp)^2 = (Base)^2 + (Per)^2

Since in option no.1, the given sides are 1, 1 and √2

So,

(√2)^2 = (1)^2 + (1)^2

2= 2

Hence 1, 1 and √2 are proved to be the correct sides

Hope you understand

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