Find an expression which represents the sum of (-8x+7y)(−8x+7y) and (2x-2y)(2x−2y) in simplest terms.

The solution of the differential equation is \(y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6]\) .

According to the given question.

We have a differential equation

\(y^{"} + 4y^{'} + 4y = 2x^{3}\)

The above differerntial equation acn be written as

\((D^{2} +4D+ 4)= 2x^{3}\)

Now, the auxillary equation for the above differential equation is given by

\(m^{2} + 4m + 4 = 0\)

\(\implies m^{2} + 2m + 2m + 4 = 0\)

⇒ m (m + 2) + 2(m + 2) = 0

⇒ m(m + 2)(m + 2) = 0

Therefore,

\(C.F = (C_{1} + C_{2}x)e^{-2x}\)

Now,

\(PI = \frac{1}{D^{2} +4D+4} 2x^{3}\)

\(\implies PI = \frac{1}{4(1+\frac{D^{2}+4D }{4} )} 2x^{3}\)

\(\implies PI = \frac{1}{4} [1+(\frac{D^{2}+4D }{4} )]^{-1} 2x^{3}\)

\(\implies PI = \frac{1}{4} [ 1 - (\frac{D^{2} +4D}{4} )+(\frac{D^{2} +4D}{4} )^{2} -(\frac{D^{2}+4D }{4}) ^{3} ...]2x^{3}\)

\(\implies PI =\frac{1}{2} [ x^{3} -\frac{1}{4} (6x)-3x^{2} +3x^{2} -6]\)

\(\implies PI = \frac{1}{2} [x^{3} -\frac{3}{2} x-6]\)

Therefore, the solution of the differential equation will be

y = CI + PI

\(y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6]\)

Hence, the solution of the differential equation is \(y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6]\) .

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Answer:

See below. Graphs attached

Step-by-step explanation:

Let's first list out the rules of reflection over the x and y axes as well as over a line y = x

1.The reflection of the point A(x, y) across the x-axis is the point A'(x,-y).
In other words,, the x-coordinate does not change, the new y-coordinate is the negative of the original y-coordinate.

2.The reflection of the point A(x, y) across the line y = x is the point
A'(y, x). The x and y coordinates are interchanged

3.The reflection of the point A(x, y) across the y-axis is the point A'(-x, y). The y-coordinate is unchanged, the new x-coordinate is negative of the original x-coordinate

Given these rules:

1) Reflection across the x-axis (x, y) ⇒ (x, -y)

U(-2, -5)  ==> U'(-2, 5)

V(-1, -3) ==>  V'(-1, 3)

W(0, -3) ==> W'(0, 3)

X(3, -5)  ==>  X'(3, 5)

2) Reflection across the line y = x

U(2, 0)  ==> U'(0, 2)

V(1,  3) ==>  V'(3, 1)

W(2, 4) ==>  W'(4, 2)

X(3, 0) ==>   X'(0, 3)

3) Reflection across the y-axis (x, y)--> (-x, y)

Q(-3, -5) ==> Q'( 3, -5)

R(-2, -3) ==>R'( 2, -3)

S( 2, -2) ==> S'(-2, -2)

T(-1, -5) ==>  T'( 1, -5)

Graphs Attached

Answer:

e

Step-by-step explanation:

61/3 ÷ 1/6

Convert the mixed fraction to an improper fraction

to convert to an improper fraction : (6 x 3) + 1 = 19 = 19/3

19/3 ÷ 1/6 = 19/3 x 6/1 = 38

To find the volume of a triangular prism with a right angle, multiply the area of the base triangle by the height of the prism.

Start with a triangular prism that has a right angle. The base of the prism is a right-angled triangle.

Measure the lengths of the two perpendicular sides of the right-angled triangle, which are typically referred to as the base (b) and the height (h) of the triangle.

Calculate the area of the base triangle using the formula: Area = (1/2) * base * height.

Measure the height (H) of the prism, which is the perpendicular distance between the two parallel bases.

Multiply the area of the base triangle by the height of the prism to find the volume:

Volume = Base Area * Height = (1/2) * base * height * H.

If the dimensions are given in different units, make sure to convert them to the same unit before performing the calculations.

The volume of a triangular prism with a right angle can be found by multiplying the area of the base triangle by the height of the prism. Ensure that the base dimensions and the height are measured accurately and in the same unit.

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a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

We have,

a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:

P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))

Where:

P(t) = Pressure at time t

Pi = Initial reservoir pressure

Q = Flow rate

K = Permeability

h = Reservoir thickness

ϕ = Porosity

μ = Viscosity

Ct = Total compressibility

t = Shut-in time (12 hours)

Δt = Time since the start of the flow period

Bo = Oil formation volume factor

ΔP = Pressure drop during the flow period

Given:

Pi = 3100 psi

Q = 200 STB/day

K = 45 md

h = 60 ft

ϕ = 15%

μ = 1.2 cp

Ct = 15x10^-6 psi^-1

Bo = 1.3 bbl/STB

t = 12 hours

Δt = 48 hours

ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))

Substituting the given values into the equation:

ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x\(10^{-6}\) * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x \(10^{-6}\) * (48 + 48)) / (1.3 * (0 + 48))))))

After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.

b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.

It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.

The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.

Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.

It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.

Thus,

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

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Write and solve an equation to find the missing dimension of the prism.

Volume = 1620 cm³

width = 9 cm

length = 9 cm

Equation =

Height =

For calculating the height, the formula is,

Substituting the values given above in the formula, We get,

⇒ \( \sf height = \frac{1620}{9 \times 9} \)

⇒ \( \sf height = \frac{1620}{81} \)

⇒ \( \sf height = 20 \:cm \)

The height of the prism is 20 cm.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

Volume is sometimes referred to as capacity.

We have,

Volume = 1620 cm³

length= 9 bm

width= 9 cm

So, Volume of cuboid = l w h

1620 = 9 x 9 x h

1620 = 81 x h

h = 1620 /81

h= 20 cm

Thus, the height is 20 cm.

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Heritability is a statistic that quantifies the proportion of observed variance in a group of individuals that can be attributed to genetic variance.

Heritability is a fundamental concept in genetics and behavioral sciences that helps understand the extent to which genetic factors contribute to observed variations in a particular trait within a population. It measures the proportion of phenotypic variation (differences in traits) that can be explained by genetic variation. Heritability estimates range from 0 to 1, where a value of 0 indicates that all observed variation is due to environmental factors, and a value of 1 suggests that all observed variation is due to genetic factors.

To calculate heritability, researchers typically study populations with varying degrees of genetic relatedness, such as twins or family members. By comparing the similarity of traits between individuals with known genetic relatedness, it is possible to estimate the contribution of genetic factors to the observed variance. Environmental factors that contribute to phenotypic variation are considered as part of the non-genetic or "environmental" component.

It is important to note that heritability estimates are population-specific and apply only to the particular group being studied. Additionally, heritability does not provide information about specific genes or the precise mechanisms by which genetic factors influence traits. Nonetheless, heritability serves as a valuable tool in understanding the relative importance of genetic and environmental factors in shaping individual differences within a population.

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Answer:

13 pounds

Step-by-step explanation:

0.35x = 4.55

x = 13

Answer:

13

Step-by-step explanation:

Divide $4.55/$0.35

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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Answer:

X=4

Step-by-step explanation:

Given mean =8,

Total number given including X is 5

5×8= 40

40-(Given number)

40-6-7-13-10=4

x=4 Is the final answer

Answer:

\((3.4)\)

Step-by-step explanation:

Answer:

1 - sec (x)

Step-by-step explanation:

Write the problem as a mathematical expression

tan (x) (cot(x)−csc(x)

Apply the distributive property

tan (x) cot(x) +tan (x) (−csc(x)

Rewrite in terms of sines and cosines, then cancel the common factors

1+tan (x) (−csc(x)

Then u get 1 - sec (x)

Answer:+0.82 and -0.8

Step-by-step explanation:

The probability that the ace of diamonds and a black card will come is 1 / 51 .

Case A :

probability of first getting an ace of diamonds = 1 / 52

probability of getting a black card given first card is ace of diamond = 26 / 51

Hence , probability that the ace of diamonds and a black card will come is  ( 1 / 52 ) * ( 26 / 51 ) = ( 1 / 102 )

Case B :

probability of first getting a black card = ( 26 / 52 )

probability of getting an ace , given first card is a black card = ( 1 / 51 )

Hence , the probability that the ace of diamonds and a black card will come is  ( 26 / 52 ) * ( 1 / 51 ) = ( 1 / 102 )

P ( A ∪ B ) = P ( A ) + P (B ) + P ( A ∩ B )

                  = ( 1 / 102 ) + ( 1 / 102 )

                = 1 / 51 .

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Answer:

b

Step-by-step explanation:

i did it in my head

Answer:

?

Step-by-step explanation:

c

Step-by-step explanation:

this is correct

Answer:

Answer:

C.12

Step-by-step explanation:

Answer:

i dont exactly know but the answer is C ?

Step-by-step explanation:

Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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Answer:

x=0 and y=2

Step-by-step explanation:

12.5x+ 2.5(5x+2)=5

12.5x +12.5x +5= 5

x=0

Subsitute x into equation

y=5(0) +2

y= 2

Answer:

B

Step-by-step explanation:

(m^-2 n^-3)^-4

-2 x -4 = 8

-3 x -4 = 12

m^8n^12

The given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

Given is the expression -

(m − 2n − 3) − 4

The given expression is -

(m − 2n − 3) − 4

m - 2n - 3 - 4

m - 2n - 7

Therefore, the given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

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Answer: wait how much was her allowance

Step-by-step explanation:

The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

Answer:

A = 10² + 2π(5²) = 100 + 50π

= about 257.1 units²

Switch the variable x and y with each other. Then the correct option is B.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = 3x – 10

Then the inverse function of the f(x) will be

Put y in place of f(x).

    x = 3y – 10

  3y = x + 10

    y = (x + 10) / 3

Switch the variable x and y with each other.

Then the correct option is B.

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Answer:

-1

Step-by-step explanation:

The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.

A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:

Angle 2 = (Angle 1) / 0.25

For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.

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Answer:

13 - The first option

11 - (x+1)

16 - first option

Step-by-step explanation: