Find the arc length of the partial circle.
Either enter an exact answer in terms of pi or use 3.14, point, 14 for pi and enter your answer as a decimal.

The general solution of the given differential equation are:  [tex]e^{\frac{-x}{3}}[/tex] [A cos(x√ 2/3) + B sin(x√ 2/3) i ]

Now,

Given: 3y'' + 2y' + y = 0

To find: General solution of the given differential equation.

Finding:

=> [tex]3\frac{d^{2}y}{dx^{2}} + 2 \frac{dy}{dx} + y = 0[/tex]

The characteristic equation of this equation is:

=> 3m² + 2m + 1 = 0

=> m = [tex]\frac{(-2)± \sqrt{4 - 4(3)(1)}}{2(3)}[/tex]

=> m = [tex]\frac{(-2)±\sqrt{4-12}}{6}[/tex]

=> m = [tex]\frac{(-2)±2\sqrt{2}i}{6}[/tex]

=> m = [tex]\frac{(-1)±\sqrt{2}i}{3}[/tex] = [tex]\frac{-1}{3}[/tex] ± [tex]\frac{\sqrt{2}}{3}[/tex]

Thus, For a = -1/3 and b = (√2)/3,

General solution of the differential equation => [tex]e^{\frac{-x}{3}}[/tex] [A cos(x√ 2/3) + B sin(x√ 2/3) i ]

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No these lengths does not form a right triangle

There is a property of triangles which says that some of two sides of the triangle should be more than the third side of the triangle

So first case 6,30,5

30+6 =36 which is  more than 5

second case 5,30,6

5+30 =35 which is more than 6

third case 5,6,30

5+6 =11 which is not more than 30

as in third case the property is breached because sum of two sides of triangle is not more than third side so the figure cannot be a triangle .

And hence we cannot check whether it is a right angle triangle or not.

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Answer:

4 and 3

Step-by-step explanation:

You can create an equation with this. If your first number is y and your second is x, then we know that y is 5 less than 2x. This leads to your equation - y = 2x - 5.

With your equation, you can then figure out your numbers; we know there's a limited number of possibilities - anything 7 or less added to a number can equal 7 so:

7+0=7

6+1=7

5+2=7

4+3=7

3+4=7

2+5=7

1+6=7

0+7=7

From there, plug in one number for x and see if y matches the expected number. For example:

2(7)-5=9, so we know the 7,0 combination cannot be correct. As we go through the list, we find that 4,3 works:

2(4)-5=3

Based on the explanation below, the conclusion that Elan is tired because Elan stayed up late is invalid.

In the question, it is stated that if Elan stays up late, he will be tired the next day.

However, staying up late is not the only thing that could make Elan get tired.

This implies that there are so many other things than can make Elan get tired such as working for long hours.

It is possible that Elan was tired because Elans worked long hours.

By implication, the conclusion is invalid.

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Answer:

6

Step-by-step explanation:

Answer:

6(x+6y)

Step-by-step explanation:

The greatest common factor is 6.

6x+36y=

=6(x+6y)

The expression with the GCF factored out is 6(x+6y)

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Answer:

x=1

Step-by-step explanation:

-2(2x-4)=4x

Distributive property.

-4x+8=4x

+4x      +4x

8x=8

/8  /8

x=1

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the region of space between the parallel planes x = 0

and x = 5

0 < x < 5

A direction or plane traveling past a specific place is considered to be vertical in astronomy, geography, and other relevant fields and settings if it contains the local gravity direction at that location. On the other hand, if a direction or plane is perpendicular to the vertical direction, it is said to be horizontal. The y-axis in the Cartesian coordinate system is an example of something that can generally be drawn from up to down (or down to up). The word vertical is derived from the late Latin verticalis, which is from the same root as vertex and means "highest point" or more literally the "turning point" such as in a whirlpool.

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Answer:

a. zy = yz

Step-by-step explanation:

Commutative property of multiplication rule:

(a)(b) = (b)(a)

[tex]r = \frac{u_{4}}{u_{3}} = \frac{ - 56}{28} = - 2[/tex]

[tex]u_{n} = u_{1} \times r {}^{n - 1} \\ ie \colon \: u_{4} = u_{1} \times r {}^{4 - 1} \\ \: \: \: - 56 = u_{1} \times ( - 2) {}^{3} \\ u_{1} = \frac{ - 56}{ - 8} = 7[/tex]

[tex]S_{n} = ( \frac{1 - r {}^{n} }{1 - r} ) \: (u_{1}) \\ S_{6}=( \frac{1 - ( - 2) {}^{6} }{1 - ( - 2)} ) \: (7) \\ S_{6}= - 147[/tex]

a. The common ratio is -2.

b. The first term is 7

c. The sum of the GP is -147

(a) To find the common ratio (r), we can use the formula for the nth term of a geometric progression (G.P):

[tex]A_n = A_1 * r^(^n^-^1^)[/tex],

where Aₙ is the nth term, A₁ is the first term, r is the common ratio, and n is the term number.

Given that the 3rd term (A₃) is 28 and the 4th term (A₄) is -56, we can set up two equations using the formula above:

[tex]28 = A_1 * r^(^3^-^1^)[/tex],     (Equation 1)

[tex]-56 = A_1 * r^(^4^-^1^)[/tex].     (Equation 2)

Dividing Equation 2 by Equation 1, we get:

[tex]-56/28 = (A_1 * r^(^4^-^1^)^) / (A_1 * r^(^3^-^1^))\\-2 = r.[/tex]

Therefore, the common ratio (r) is -2.

(b) To find the first term (A1), we can substitute the known values into one of the equations. Let's use Equation 1:

[tex]28 = A_1 * (-2)^(^3^-^1^)\\28 = A_1 * (-2)^2\\28 = A_1 * 4\\A_1 = 7[/tex]

Therefore, the first term (A₁) is 7.

(c) To find the sum of the geometric progression, we can use the formula for the sum of the first n terms of a geometric progression:

[tex]S_n = (A_1 * (1 - r^n)) / (1 - r)[/tex],

where Sₙ is the sum of the first n terms.

Given that there are 6 terms (n = 6), A₁ = 7, and r = -2, we can calculate the sum (S₆):

[tex]S_6 = (7 * (1 - (-2)^6)) / (1 - (-2)).[/tex]

Simplifying:

S₆= (7 * (1 - 64)) / (1 + 2),

S₆ = (7 * (-63)) / 3,

S₆ = -147.

Therefore, the sum of the geometric progression is -147.

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Answer:

73.39

Step-by-step explanation:

Answer:

73.705

Step-by-step explanation:

73.700

73.705

73.710

Divide 0.01 by 2 and u would get 0.005

The type of question is GCF .

The factor of a number is a number that can divide another number perfectly without leaving any remainder.  Highest common factor is the highest factor that is common to two or more numbers

Factors of 8, 16 and 24 = 1, 2, 4, 8,

Highest common factor = 8

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Answer:

42

Step-by-step explanation:

45 divided by 5 is 9.

210 divided by 5 is 42.

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Sorry If I'm Wrong

Paula shovels 3 square feet more than Melinda in 1 minute.

We are given two equations relating the distance covered by each while they shovel. Assuming the x to be representative of Melinda's speed and y to be representative of Paula's speed. Making at least one coefficient same for both the equation.

Equation 1 : 30x + 30y = 450

Equation 2 : 20x + 25y = 345

Dividing equation 1 and equation 2 by 5.

Equation 3 : 6x + 6y = 90

Equation 4 : 4x + 5y = 69

Multiplying equation 3 with 4 and equation 4 with 6.

Equation 5 : 24x + 24y = 360

Equation 6 : 24x + 30y = 414

Subtracting Equation 5 from Equation 6.

  24x + 30y = 414

- 24x + 24y = 360

6y = 54

y = 9

Keep the value of y in equation 3

6x + 6×9 = 90

6x + 54 = 90

6x = 90 - 54

6x = 36

x = 6

So, Melinda's speed is 6 square feet per minute and Paula's speed is 9 square feet per minute.

Difference between speed = 9 - 6

Difference = 3 square feet per minute

Hence, Paula's speed is 3 square feet per minute more than Melinda.

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The complete question is -

Melinda and Paula shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paula shoveled for 25 minutes to complete 345 square feet of driveway.

30x + 30y = 45020x + 25y = 345

How much more can Paula shovel in 1 minute than Melinda?

3 square feet per minute

6 square feet per minute

9 square feet per minute

15 square feet per minute

Answer:

A: 3 square feet per minute

Step-by-step explanation:

The expressions that are equivalent to the given expression are 4 - 6 and -6 + 4

The expression is given as:

(4 * 1) - 6

Evaluate the product of 4 and 1

So, we have:

(4 * 1) - 6 = 4 - 6

By the subtractive property of and equation, we have:

(4 * 1) - 6 = -6 + 4

Hence, the expressions that are equivalent to the given expression are 4 - 6 and -6 + 4

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11/12 - 3/4 = 1/6

1/2 + 4/9 = 17/18

11/12 - 3/4

= 11-9/12

= 2/12

= 1/6

1/2 + 4/9

= 9+8/18

= 17/18

Hence the solution to the expression in it's simplest form is 1/6 and 17/18

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Answer:

1/6and 17/18

Step-by-step explanation:

11/12-3/4

find the l.c.m

11/12-3/4=11-9/12=2/12=1/6

1/2+4/9=9+8/18=17/18

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Answer:

18.7 units (3 s.f.)

Step-by-step explanation:

The distance between two points is given by the formula below, where [tex](x_1, y_1)[/tex] is the first coordinate and [tex](x_2, y_2)[/tex] is the second coordinate.

[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]

Substitute the given points into the formula:

Distance between (0, -5) and (18, -10)

= [tex]\sqrt{[-10 -(-5)]^{2} + (18-0)^{2} }[/tex]

= [tex]\sqrt{(-10+5)^2+18^2}[/tex]

= [tex]\sqrt{(-5)^2+18^2}[/tex]

= [tex]\sqrt{349}[/tex]

= 18.7 units (3 s.f.)

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The average acceleration during the time interval 0 seconds to 10 seconds is [tex]\frac{V_{1}-V_{2} }{10}[/tex] unit per second per second.

As per the question statement, we are supposed to find out the average acceleration during the time interval 0 seconds to 10 seconds. But before solving this question we should be aware about what actually average acceleration is.

Average acceleration : [tex]\frac{change in velocity}{total time interval}[/tex]

Here in the question, we are not given information about velocity of the object hence we assume the initial and final velocities of the object to be [tex]V_{1}[/tex] and [tex]V_{2}[/tex] respectively, hence

Change in velocity = [tex]V_{1}-V_{2}[/tex]

Total time interval = [tex](10 - 0)sec=10sec[/tex]

Therefore by definition of average acceleration we get

[tex]A_{avg}[/tex][tex]= \frac{V_{1}-V_{2} }{10}[/tex] unit per sec per second

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Step-by-step explanation:

...........................

Answer: 37.98 (I assume you mean times)

Step-by-step explanation:

Calculator :)

The radians will the hour hand on a clock rotation for 23hr and 6hr is 23/6π and π.

We have to find the radians will the hour hand on a clock rotation for 23hr and 6hr.

One revolution is done by fully around the circle with the radius. After one full rotation, the radius subtends an angle of 2π radians at the circle's center. To illustrate the conversion of 1 radian to degrees, we will use the knowledge that 2π radians = 360 degrees.

2π radians = 360°

Divide the above equation by 2,

⇒ π radians = 180°

Divide the above equation by π,

⇒ 1 radian = 180°/π

⇒ 1 radian = 57.296°

Only 12 hours are represented by one full rotation of the hour hand. A whole rotation equals 360°, or two radians.

11 hours rotation equals to 330°, or 11π/6 radians.

23 hours=12+11

=360°+330° (or) 2π+11π/6

=690° (or) 23π/6

Now, 6 hours=12/2

=360°/2 (or) 2π/2

=180° (or) π.

Therefore, the radians will the hour hand on a clock rotation for 23hr and 6hr is 23/6π and π.

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Answer:

660%

Step-by-step explanation:

6 x 100= 600%

3/5 = 0.6 × 100 = 60%

600% + 60% = 660%

we get that the expression ( 2 x + 3 ) / 3 + ( x - 4 ) / 4 can be written as an equation as 11 x / 12.

We are given an expression:

( 2 x + 3 ) / 3 + ( x - 4 )/ 4

We need to simplify it and write it as an equation.

Taking the LCM, we get that:

4( 2 x + 3) + 3 (x - 4) / 12

simplifying brackets, we get that,

8 x + 12 + 3 x - 12 / 12

Combining the like terms, we get that:

8 x + 3 x / 12

11 x / 12

Therefore, we get that the expression ( 2 x + 3 ) / 3 + ( x - 4 ) / 4 can be written as an equation as 11 x / 12.

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Answer:

the answer is becareful

The multiplication of [tex](2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )[/tex]in scientific notation is [tex]9.6 \times {10}^{21} [/tex]

Multiply the decimal numbers to multiply the integers in scientific notation. Add the 10 power exponents after that. In scientific notation, place the new power of 10 with the decimal.

given that [tex](2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )[/tex]

Now, find the answer in scientific notation

[tex](2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )[/tex]

combine the all the like terms

[tex](2.4 \times 4)( {10}^{14} \times {10}^{7} )[/tex]

According to the exponent same base rule, an exponent will be added if the bases of two exponents are the same.

[tex](9.6) \times ( {10}^{14 + 7)} ) \\ 9.6 \times {10}^{21} [/tex]

Hence,the multiplication of[tex](2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )[/tex] in scientific notation is [tex]9.6 \times {10}^{21} [/tex]

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The correct answer is 9x-18.

The ability to reverse other functions makes a function an inverse function. It is somewhat similar to undoing another function, which returns you to your starting point. Driving from home to the shop is a function, and driving from the shop back to home is a function.

The inverse of a trigonometric function, the inverse of a rational function, the inverse of a hyperbolic function, and the inverse of a log function are just a few examples of the various types of inverse functions.

Substituting f(x) with y

f(x)=1/9x+2

y=1/9x+2

x=1/9y+2

x-2=1/9y

y=9x-18

Thus inverse is f^-1(x)=9x-18

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Answer:

Step-by-step explanation:

Not sure..

The total cost of the books will be €3276.

It should be noted the school bought 234 books at €14 each.

Therefore, the total cost of the books will be:

= Price × Total books

= €14 × 234

= €3276

Therefore, the total cost of the books will be €3276.

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Based on the information given, the value of x is 4

A line segment can be defined as the part of a straight line bounded by two distinct end points, and also contains every point on the line that is between its endpoints.

From the information given, we have PQ and RS are on the the same line with points Q and R as the line segments

We have that;

9x - 7 = 29

collect  like terms

9x = 29 + 7

9x = 36

Make 'x' the subject

x = 36/ 9

x  = 4

Thus, the value of x is 4

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