find x and y pls help

Sum of the series will be (19/30)

Partial differentiation is the method of determining a function's partial derivative. By holding the other variable constant, one may use this method to get the partial derivative of a function with respect to one variable.

An equation having an unknown function of two or more variables and its partial derivatives with respect to these variables is known as a partial differential equation. A partial differential equation has the highest-order derivatives as its order. is a partial differential equation of order 2, as an illustration.

Ordinary differential equations, often known as ODEs, are equations for which only one variable's derivatives are considered. Consequently, there is just one independent variable. PDEs are equations that rely on the partial derivatives of a number of distinct variables.

Using partial fractions, we have

[tex]\frac{6}{(n+8)(n+10)}=\frac{A}{n+8}+\frac{B}{n+10}\\\\=\frac{A(n+10)+B(n+8)}{(n+8)(n+10)} \\\\ 6=A(n+8)+B(n+10)[/tex]

Put n=-8,

we have 6=0+2B=>B=3

Put n=-10,

we have 6=-2A =>A=-3

[tex]$$\begin{aligned}& \sum_{n=1}^{\infty} \frac{6}{(n+8)(n+10)}=\sum_{n=1}^{\infty}\left(\frac{3}{n+8}-\frac{3}{n+10}\right) \\& =3 \sum_{n=1}^{\infty} \frac{1}{n+8}-\frac{1}{n+10} \\& =3\left[\left(\frac{1}{9}-\frac{1}{11}\right)+\left(\frac{1}{10}-\frac{1}{12}\right)+\left(\frac{1}{11}-\frac{1}{13}\right)+\left(\frac{1}{12}-\frac{1}{14}\right)+\ldots\right] \\& =3\left[\frac{1}{9}+\frac{1}{10}\right]=\frac{19}{30}\end{aligned}$$[/tex]

other terms will be cancelled out

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The correct question should be:

Find the sum of the convergent series: [tex]$$\sum_{n=1}^{\infty} 6 /(n+8)(n+10)$$[/tex]

Answer:

A mary go round I'm sorry I am middle school

The graph demonstrates the relationship, and it indicates that the machine can produce 1200 soda bottles every minute.

The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.

given

y=20x

The total number of bottles produced in the specified amount of time, expressed in seconds, is represented by y.

When x=1 and y=20, the machine can produce 20 soda bottles each second.

There are 60 seconds in a minute, thus when x=60, y=20*60 equals 1200 drink bottles.

The graph demonstrates the relationship, and it indicates that the machine can produce 1200 soda bottles every minute.

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Janice donated 20 pants and 80 t-shirts of clothing to the Salvation Army.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, Janice donates 100 items of clothing to the Salvation Army and the number of t-shirts were 4 times the number of pants.

Therefore, If the number of pants is 'x' then the number of t-shirts are '4x'.

So, x + 4x = 100.

5x = 100.

x = 20.

So, The number of pants are 20 and the number of t-shirts are 80.

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Answer: D

Step-by-step explanation:

MNOP is a rhombus then, the length of the segment MP = 49 unit.

One kind of parallelogram is the rhombus, which has four sides and four vertices.

The length of each side is the same as the length of the opposing angle.

Given:

A rhombus is given in the attached image.

In rhombus,

every side is equal in length.

That means,

the parallel sides are equal.

9x - 77 = 3x + 7

6x = 84

x = 14

So,  3(14) + 7 = 42 + 7 unit

That means, the side in rhombus = 49 unit.

Therefore, MP = 49 unit.

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The complete question is given in the attached image.

The limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined.

We can see that the denominator [tex]x^2[/tex][tex]y^2[/tex] goes to 0 as (x,y) approaches (0,0), and that can cause the function to go to infinity. However, the numerator (cos(xy) -1) does not have a specific value as (x,y) approaches (0,0) the cosine function oscillates between -1 and 1 as xy approaches zero, and therefore it does not approach a specific value.

The term (x,y) → (0,0) means that x and y are approaching 0 independently. There are different paths in which x and y can approach zero. Hence, by the squeeze theorem, we can see that if we approach (x,y) to (0,0) along the path y = mx, where m is a nonzero constant, the function goes to infinity, but if we approach (x,y) to (0,0) along the path x = 0 or y = 0, the function goes to -1.

Therefore, the limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined, as the function does not approach a specific value along all paths.

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Answer:

Step-by-step explanation:

m

2

+

2

m

+

1

2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

2

m

=

2

⋅

m

⋅

1

Rewrite the polynomial.

m

2

+

2

⋅

m

⋅

1

+

1

2

Factor using the perfect square trinomial rule

a

2

+

2

a

b

+

b

2

=

(

a

+

b

)

2

, where

a

=

m

and

b

=

1

.

(

m

+

1

)

2

An inequality to determine at what times the car will be ahead of the truck is; 63x > 55x + 30

The graph of the inequality is attached and the solution is (3.75, 236.25).

We are told that;

x represent the number of hours that the car and truck travel

The truck is traveling at an average rate of 55 mph. Thus, the expression 55x represents the distance the truck travels in x hours.

The car is traveling at a rate of 63 mph. Thus, the expression 63x represents the distance the car travels in x hours.

In the beginning, the truck was 30 miles ahead of the car. So, we need to solve the inequality:

63x > 55x + 30

Use technology to graph y = 63x and y = 55x + 30 gives us;

The intersection point is (3.75, 236.25)

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Answer:

x=2

Step-by-step explanation:

x+11=6x+1

10=5x

x=2

The perimeter of a rectangle is given by the formula P = 2(L + W), where P is the perimeter, L is the length, and W is the width.

We know that the perimeter of the parking lot is 354 m, and the width of the parking lot is 83 m. We can use this information to find the length of the parking lot.

Substituting the known values into the formula, we get:

354 = 2(L + 83)

Simplifying the equation:

354 = 2L + 166

Subtracting 166 from both sides:

188 = 2L

Dividing both sides by 2:

L = 94

The length of the parking lot is 94 m.

Answer:

Step-by-step explanation:

Formula for perimeter = (2 * length) + (2* width) = Perimeter

2l + (83 * 2) = 354

2l + 166 = 354

2l = 354 - 166

2l = 188

l = 188/2

l = 94 m

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

We should know that a circle is a set of points on a circle that are equal from a fixed point

The standard form for finding the equation of a circle is expressed as;

(x-a)² + (y-b)² = b=r²

where; (a, b) is the center of the circle

r is the radius of the circle

Given the following

Diameter = 12 units

radius = 12/2 = 6 units

If the center lies on the y-axis, the center will be at (0, 3)

Therefore, Substituting into the formula, we will have (x-0)² + (y-3)² = 6² which is equivalent to x²+ (y-3)² = 36

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Answer: D - 14

Step-by-step explanation:

1 gallon = 2.15

So to find how many gallons is worth 30.10, divide by 2.15

30.10 ÷ 2.15 = 14

Answer:

Step-by-step explanation:

To find the required gallons of gas for 30.10$, you can use the following formula:

Required gallons of gas=Cost of required gallons of gas/cost of one gallon of gas

Here given that, the cost of required gallons of gas is 30.10$ and the cost of one gallon of gas is 2.15$

Now apply the formula:

Required gallons of gas = 30.10$/2.15$ = 14

Therefore, the required gallons of gas = 14

So 14 gallons of gas costs 30.10$

Option D is the correct answer.

Because there is a 16% chance of getting that many babies born female if the method had no effect, the method has no statistical significance. Hence couples would likely use a procedure that raises the likelihood of a baby born female from the approximately 50% rate expected by chance to the 51.13% produced by this method.

This means that the method has practical significance.

Depends on if the p-value is less or more than the significance level:

The p-value for this problem is given as follows:

0.16.

As the p-value is greater than the standard significance level of 0.05, the method has no statistical significance.

The percentage of females born is given as follows:

1066/2085 x 100% = 51.13%.

As this percentage is an increase from the usual 50%, the method has practical significance.

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So on solving the provided question, we can say that n the graphs we have A at origin; B at origin; C in 3rd quadrant; D in the 2nd quadrant

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here in the graphs we have

A at origin

B at origin

C in 3rd quadrant

D in the 2nd quadrant

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Without the specific function it is not possible to give you the exact solution and also without knowing the specific limits of the integral, it is not possible to evaluate the definite integral.

The solid in the figure is a rectangular prism with a cutout, the cutout is a cylinder with radius 2. The volume of the solid can be found by using a double integral.

The first integral represents the volume of the rectangular prism, and the second integral represents the volume of the cylinder cut out of it. The limits of the double integral are determined by the dimensions of the rectangular prism and the cylinder.

The volume of the rectangular prism = (x-coordinate max - x-coordinate min) * (y-coordinate max - y-coordinate min) * (z-coordinate max - z-coordinate min)

The volume of the cylinder = ∫∫[2<= [tex]\sqrt{x^{2} + y^{2} }[/tex] <= 2.5] dA

The limits of the double integral are determined by the dimensions of the rectangular prism and the cylinder

The x-coordinate min is 0, x-coordinate max is 4, y-coordinate min is 0, y-coordinate max is 6, z-coordinate min is 0, and z-coordinate max is 6.

The volume of the solid

= (4 - 0) * (6 - 0) * (6 - 0) - ∫∫[2<= [tex]\sqrt{x^{2} + y^{2} }[/tex] <=2.5] dA

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The length of measurement would be in a scale drawing of 180 m is 24 cm.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, the scale is 2 cm = 15 m.

So, 1 m =2/15

A scale drawing of 180 m

Now, 180 m = 2/15 ×180

= 2×12

= 24 cm

Therefore, the length of measurement would be in a scale drawing of 180 m is 24 cm.

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Answer:

  29°

Step-by-step explanation:

In given parallelogram LMNQ, you want the measure of angle LMQ when angle MQN is given as 29°.

Angles LMQ and MQN are alternate interior angles where transversal MQ crosses parallel lines LM and NQ. As such, they are congruent.

  m∠LMQ = 29°

Answer:

A) 14

Step-by-step explanation:

When a small is gear connected to a larger gear, the smaller gear makes more revolutions than the larger gear. Use the ratio of the numbers of teeth to find the ratio of the numbers of revolution.

1 gear has 9 teeth

1 gear has 27 teeth

27/9 = 3

The ratio is 3:1.

The small gear makes 3 revolutions for each revolutuion of the large gear.

The large gear makes 1/3 revolution for each revolution of the small gear.

Here, the small gear makes 42 revolutions.

42/3 = 14

The large gear makes 14 revolutions.

Answer: A) 14

The larger gear has made 14 revolutions when the smaller gear has made 42 revolutions. This is because the ratio of the teeth on the gears is 1:3, which is also the ratio of their revolutions.

The ratio of the number of teeth on the two gears is also the ratio of the number of rotations they make. In this case, the smaller gear has 9 teeth and the larger gear has 27 teeth. So, the ratio is 9:27, which simplifies to 1:3.

This means that for every one rotation of the larger gear, the smaller gear will make three rotations.

Since the smaller gear has made 42 rotations, to figure out the number of rotations the larger gear has made, you would divide 42 by 3. (because of the 1:3 ratio). The answer is 14.

Therefore, the larger gear has made 14 revolutions when the smaller gear has made 42 revolutions. So, the correct answer is A) 14.

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Answer:

$1688.40

Step-by-step explanation:

1% of 1608 = 16.08

16.08 (5) = 80.40

1608+ 80.40= 1688.40

Answer: The discount percentage is 23.4%

Step-by-step explanation:

The discount percentage can be calculated by taking the difference between the original price and the sale price, dividing that by the original price, and then multiplying by 100 to get a percentage.

Answer:

1540$!$($9$

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Marcella would need to sell at least 40 office machines each month to earn at least $4,000.

To find the least number of office machines Marcella would need to sell each month to earn at least $4,000, we need to know the price of each office machine and the commission she receives for each sale.

We can use following formula:

Rearranging this formula to solve for the number of machines sold, we get:

Plugging in the values we know:

Number of Machines Sold = 4000 / (1000 x 0.1)

Number of Machines Sold = 4000 / 100

Number of Machines Sold = 40

Therefore, Marcella would need to sell at least 40 office machines each month to earn at least $4,000.

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Answer: The constant of proportionality is 12.

Step-by-step explanation: You can start by dividing 36 by 3 60 divided by 5 then 72 divided by 6 and then 84 divided by 7. All of the division problems have an answer of 12. So the constant of proportionality is 12.

The value of the z is 6√6 units. The triangles follow similar triangle property.

What are similar triangles?

Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.

Consider △BDC and △ABC:

∠C = ∠C

∠ABC = ∠BDC = right angle

If two angles of a triangle are equal to two angles of another triangle, then third angle of the triangles also equal.

∠BAC =∠DBC

According to A-A-A rule △BDC and △ABC are similar to each other.

Thus the ratio of corresponding sides is also equal.

Therefore:

AB/BD = BC/DC = AC/ BC

Consider the last two ratios:

BC/DC = AC/ BC

z/12 = z/18

z² = 12 × 18

z² = 6×2×6×3

z = 6√6

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Answer:

No it is not

Step-by-step explanation:

In an additive relationship, two quantities can be expressed as related to each other through addition. It can be written as y = x + a, where y is related to x through the addition of a constant, “a”.

In this scenario, the "a" is not constant

1+2=3, 5+3=8, and 9+4=13

the number is increasing by one each time

Answer: c

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be a=6 and b=17.

An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.

Here,

Given : A right triangle ,

=> 8²+a²= 10²

=> a² = 100 -64

=>  a² =36

=> a =6

For b,

=> b²  = 8² + 15²

=> b²  = 64 + 225

=> b² = 289

=> b = 17

Therefore , the solution of the given problem of triangle comes out to be a=6 and b=17.

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Answer: x = 15

Step-by-step explanation: Combine like terms

7 x plus 4 x plus x equals 180

12 x equals 180

2

Divide both sides by the same factor

12 x equals 180

the fraction with numerator 12 x and denominator 12 end fraction equals the fraction with numerator 180 and denominator 12 end fraction

3

Simplify

Solution

x equals 15

Evelyn’s enlarged photo will not retain the same proportions as the original one.

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  "::" or "=".

Given,

Length of the original photograph L = 5''

Width of the original photograph W = 7''

Ratio between length and width of original photograph

L/W = 5/7

Length of the enlarged photograph L' = 16''

Width of the enlarged photograph W' = 20''

Ratio between length and width of enlarged photograph

L'/W' = 16/20 = 4/5

Comparing both ratios

L/W = L'/W'

5/7 ≠ 4/5

so, proportion is not same.

Hence, proportion of the enlarged photo is not same as the original photo.

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