Fed the partial fraction decomposition of 1/(2x+1)(x-8).

[tex]\left(x-2\right)^{2}+\left(y-4\right)^{2}=25[/tex]

Hope this helps!

The equation of circle is [tex](x-2)^{2}+(y-4)^{2} =25[/tex]

The equation of circle is given as,

                 [tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]

Where [tex](h,k)[/tex] is the coordinate of center and r is radius.

From the given figure,

It is observed that, the center of circular pool is (2, 4)

and radius is 5.

substitute the value of center and radius in above equation.

                  [tex](x-2)^{2}+(y-4)^{2} =5^{2}\\\\(x-2)^{2}+(y-4)^{2} =25[/tex]  

The equation of circle is [tex](x-2)^{2}+(y-4)^{2} =25[/tex]

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The limit of the sequence as n approaches infinity is ln(8). The sequence converges, and the limit is ln(8).

To determine whether the sequence given by an = ln(8n² + 9) − ln(n² + 9) converges or diverges, we can examine the behavior of the terms as n approaches infinity.

Taking the limit as n approaches infinity, we have:

lim(n→∞) ln(8n² + 9) − ln(n² + 9)

We can simplify this expression using logarithmic properties. The natural logarithm of a quotient is equal to the difference of the logarithms:

= lim(n→∞) ln[(8n² + 9)/(n² + 9)]

Now, let's analyze the behavior of the numerator and denominator as n approaches infinity:

As n becomes larger and larger, the higher-order terms dominate. In this case, the leading term in both the numerator and denominator is n².

In the numerator, 8n² dominates, and in the denominator, n² dominates. Therefore, as n approaches infinity, the ratio (8n² + 9)/(n² + 9) approaches 8.

Taking the natural logarithm of 8, we have ln(8).

Therefore, the limit of the sequence as n approaches infinity is ln(8).

Hence, the sequence converges, and the limit is ln(8).

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Question:

2 people A and B travel from X to Y along different routes. Their journeys take the same amount of time. B's route is 100km at an average speed of 40km/hour A's route is 60km. What is A's average speed?

Answer:

Person A's average speed is 24km/hr

Step-by-step explanation:

Given

Person B

[tex]Distance = 100km[/tex]

[tex]Speed = 40km/hr[/tex]

Person A

[tex]Distance = 60km[/tex]

Required

Average speed of person A

Speed is calculated as:

[tex]Speed = \frac{Distance}{Time}[/tex]

For person B

[tex]40 = \frac{100}{Time}[/tex]

Make Time the subject

[tex]Time= \frac{100}{40}[/tex]

[tex]Time= 2.5hr[/tex]

For person A

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]Speed = \frac{60}{Time}[/tex]

The journeys last for the same duration.

So;

[tex]Speed = \frac{60}{2.5}[/tex]

[tex]Speed = 24[/tex]

Person A's average speed is 24km/hr

The image of the vector (1, -3, 0) under the linear transformation T is (-4, -5, 8).

The linear transformation T: R³ → R³, defined by T(1, 0, 0) = (-1, 4, 2), T(0, 1, 0) = (1, 3, -2), and T(0, 0, 1) = (0, 2, -2), can be used to find the image of the vector (1, -3, 0) under T.

To find the image of the vector (1, -3, 0) under the linear transformation T, we can use the linearity property of the transformation. Since T is a linear transformation, we can express any vector v = (x, y, z) as a linear combination of the standard basis vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1).

The given information states that T(1, 0, 0) = (-1, 4, 2), T(0, 1, 0) = (1, 3, -2), and T(0, 0, 1) = (0, 2, -2). Using these values, we can express (1, -3, 0) as a linear combination:

T(1, -3, 0) = T(1, 0, 0) - 3T(0, 1, 0) + 0T(0, 0, 1)

           = (-1, 4, 2) - 3(1, 3, -2) + 0(0, 2, -2)

           = (-1, 4, 2) - (3, 9, -6) + (0, 0, 0)

           = (-1 - 3 + 0, 4 - 9 + 0, 2 + 6 + 0)

           = (-4, -5, 8)

Therefore, the image of the vector (1, -3, 0) under the linear transformation T is (-4, -5, 8).

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Rewrite equations:

y=2;y=

−4

3

x+6

Step: Solvey=2for y:

y=2

Step: Substitute2foryiny=

−4

3

x+6:

y=

−4

3

x+6

2=

−4

3

x+6

2+

4

3

x=

−4

3

x+6+

4

3

x(Add 4/3x to both sides)

4

3

x+2=6

4

3

x+2+−2=6+−2(Add -2 to both sides)

4

3

x=4

4

3

x

4

3

=

4

4

3

(Divide both sides by 4/3)

x=3

Answer:

x=3 and y=2

Given point: (5, -3)Given equation of the line: y = x + 2We are supposed to find the equation of the line passing through the point (5, -3) that is parallel to the line y = x + 2.

First, we need to find the slope of the given line y = x + 2. Here, the slope is 1 as the coefficient of x is 1.Now, a line parallel to this line will also have the same slope. Therefore, the slope of the required line is also 1.Now we have the slope and the point (5, -3) that the line passes through. Using the point-slope form of the equation of a line, we can find the equation of the line that passes through the given point and has the given slope.So, the equation of the line passing through the point (5, -3) that is parallel to the line y = x + 2 is:y - (-3) = 1(x - 5)This can be simplified to obtain the equation in the slope-intercept form:y = x - 8Thus, the equation of the line is y = x - 8.

To find the equation of a line parallel to the line y = x^2 and passing through the point (5, -3), we need to determine the slope of the given line and then use it to construct the equation.

The slope of the line y = x^2 can be determined by taking the derivative of the equation with respect to x. In this case, the derivative is:

dy/dx = 2x

Since the derivative represents the slope of the original line, we know that the slope of the line y = x^2 is 2x. To find the slope of the parallel line, we use the fact that parallel lines have the same slope.

Therefore, the slope of the parallel line is also 2x.

Now, using the point-slope form of a linear equation, we can write the equation of the parallel line:

y - y1 = m(x - x1)

where (x1, y1) is the given point (5, -3) and m is the slope.

Plugging in the values, we have:

y - (-3) = 2x(x - 5)

Simplifying further:

y + 3 = 2x^2 - 10x

Rearranging the equation to the standard form:

2x^2 - 10x - y - 3 = 0

So, the equation of the line passing through the point (5, -3) and parallel to the line y = x^2 is 2x^2 - 10x - y - 3 = 0.

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We have to find the equation of the line passing through the point [tex]$(5,-3)$[/tex] that is parallel to the line [tex]$y=x+2$[/tex].

Therefore, the equation of the line passing through the point [tex]$(5,-3)$[/tex] and parallel to the line [tex]$y=x+2$[/tex] is:

[tex]$y=x-8$[/tex].

As we know, the parallel lines have the same slope. Therefore, the slope of the line passing through the point (5,-3) will be the same as the slope of the line y=x+2.

Thus, we can write the slope-intercept form of the equation of the line y = mx + b as follows:

y = mx + b ------(1)

Here, m is slope of the line, b is y-intercept of the line. For the line y=x+2, slope of the line is:

m=1

Now, we will find the value of b for the line y = mx + b passing through the point (5,-3).

[tex]$$-3=1\times5+b$$$$[/tex]

[tex]b=-8$$[/tex]

Therefore, the equation of the line passing through the point (5,-3) and parallel to the line y=x+2 is:

y=x-8

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Answer:b

Step-by-step explanation:

the solution of system of linear equations is x = 27/2, y = 21/2, z = -1/2

To solve the system of linear equations using the Gaussian Elimination Method with Partial Pivoting, we'll perform the following steps:

Step 1: Set up the augmented matrix for the system of equations.

Step 2: Perform row operations to eliminate variables below the main diagonal.

Step 3: Back-substitute to find the values of the variables.

Let's proceed with the calculations:

Step 1: Augmented matrix setup

The augmented matrix for the system of equations is:

[ 0.5  -0.5   1 |  1 ]

[-0.5   1   -0.5 |  4 ]

[  1   -0.5  0.5 |  8 ]

Step 2: Row operations

[ 0.5  -0.5   1 |  1 ]

[-0.5   1   -0.5 |  4 ]

[  1   -0.5  0.5 |  8 ]

R₂ -> R₂ + R₁

[ 0.5  -0.5   1 |  1 ]

[0   0.5   0.5 |  5 ]

[  1   -0.5  0.5 |  8 ]

R₃ -> R₃ - 2R₁

[ 0.5  -0.5   1 |  1 ]

[0   0.5   0.5 |  5 ]

[  0   0.5  -1.5 |  6 ]

R₃ -> R₃ - R₂

[ 0.5  -0.5   1 |  1 ]

[0   0.5   0.5 |  5 ]

[  0   0  -2 |  1 ]

The new augmented matrix after the row operations is:

[ 0.5  -0.5   1 |  1 ]

[0   0.5   0.5 |  5 ]

[  0   0  -2 |  1 ]

Step 3: Back-substitution

Now, we'll back-substitute to find the values of the variables. Starting from the last row, we can directly determine the value of z:

-2z = 1

z = - 1/2

Substituting z = - 1/2 into the second equation, we can find the value of y:

0.5y + 0.5z = 5

0.5y + 0.5(-1/2) = 5

y = 21/2

0.5x - 0.5y + z = 1

0.5x - 0.5(21/2) + (-1/2) = 1

x = 27/2

Therefore, the solution of system of linear equations is x = 27/2, y = 21/2, z = -1/2

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Answer:

Look for 75% of 1 1/2, I got 1.125 or 1 1/8

Step-by-step explanation:

(a) The ball's height when it leaves the child's hand is 3 feet.

(b) The maximum height of the ball is 3.5625 feet.

(c) The ball strikes the ground approximately 32 feet away from the child.

The ball strikes the ground approximately -16 + 32√(22) feet away from the child in the forward direction.

(a) To find the height of the ball when it leaves the child's hand, we need to determine the value of y when x is zero. Plugging x = 0 into the equation y = -1/16x^2 + 2x + 3, we get:

y = -1/16(0)^2 + 2(0) + 3

y = 3

Therefore, the ball is 3 feet high when it leaves the child's hand.

(b) The maximum height of the ball can be found by finding the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, the equation is y = -1/16x^2 + 2x + 3, so a = -1/16 and b = 2. Plugging these values into the formula, we get:

x = -(2)/(2(-1/16))

x = -16/32

x = -1/2

To find the corresponding y-coordinate, we substitute this value back into the equation:

y = -1/16(-1/2)^2 + 2(-1/2) + 3

y = -1/16(1/4) - 1 + 3

y = 1/64 - 64/64 + 192/64

y = 129/64

Therefore, the maximum height of the ball is 129/64 feet.

(c) The ball strikes the ground when its height is zero. To find the distance from the child where this occurs, we set y = 0 and solve for x:

0 = -1/16x^2 + 2x + 3

This equation can be solved using various methods such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula here:

x = (-2 ± √(2^2 - 4(-1/16)(3)))/(2(-1/16))

x = (-2 ± √(4 + 3/2))/(2(-1/16))

x = (-2 ± √(11/2))/(2(-1/16))

x = (-2 ± √(11/2))/(-1/8)

x = (-2 ± 4√(22))/(1/8)

Since we're interested in the positive value of x (the ball strikes the ground in the forward direction), we take the positive square root and simplify:

x = (-2 + 4√(22))/(1/8)

x = 8(-2 + 4√(22))

x = -16 + 32√(22)

Therefore, the ball strikes the ground approximately -16 + 32√(22) feet away from the child in the forward direction.

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Answer:

I think it's the first one

Answer:

to my knowledge I would pick A

Answer:

there

Step-by-step explanation:

Answer:

khan

Step-by-step explanation:

Answer:

11 oranges in each box

Step-by-step explanation:

99/9=11

Answer: 11 oranges in each box.

Step-by-step explanation:

Division is used to evenly separate totals into groups (total/#of groups= Quotient per group).

In this case, we divide the total, 99 oranges, by the amount of groups we want, which is 9 boxes, in order to find an even amount for each box from the total oranges.

So, 99/9= 11 oranges per box

Answer:

since it is Right angled isosceles triangle it's base side are equal

by using Pythagoras law

x²+x²=1²

2x²=1

x=√{1/2}or 0.707 or 0.71

.186915888

that is the answer

if I meant 2.675 divided by .5 it is 5.35

Answer:

you can use a calculator but, its 0.1869158878504672897196261682243

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

Well 3 friends and 45 dollars each

45*3=135

Answer:

Large number =52

small number =13

Step-by-step explanation:

4x + x =65

5x=65

x=13

4x=52

Answer:

Malcolm owes the greatest amount.

Step-by-step explanation:

The question is asking for the amount owed by each person. That just means you take the absolute value of their bank balance if their bank balance is negative. Absolute value is just how far away the number is from zero (basically when a number is negative, you're just making it positive).

Sophia owes $150, Malcolm owes $325, and Oren owes $275.

325 > 275 > 150

Thus Malcolm owes the most, since his amount owed is the highest.

Answer:

This question is clearly incomplete, so i will answer it in a really general way.

Suppose that for a quadratic function, we know that the x-intercepts are a and b.

And we also know that this function passes through the point (c, d).

First a definition, for a n-degree polynomial with the x-intercepts {x₁, x₂, ...,xₙ}  and a leading coefficient K, we can write this polynomial in the factorized form as:

p(x) = K*(x - x₁)*(x - x₂)*...*(x - xₙ)

Now let's do the same for our quadratic function, we can write it as:

f(x) = K*(x - a)*(x - b)

(where a and b are known numbers)

Now we also know that this function passes through the point (c, d)

This means that:

f(c) = d

then:

d = K*(c - a)*(c - b)

With this equation we can find the value of K,

K = d/( (c-a)*(c - b))

Then the quadratic function is:

[tex]f(x) = d\frac{(x-a)}{(c-a)} \frac{(x-b)}{(c-b)}[/tex]

Where again, it is supposed that you know the values of a and b, and also the point (c, d)

Answer:

A

Step-by-step explanation:

The required surface area is multiplied by a factor of 25 or 5 to 2. Option C is correct.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,

The lateral surface area of a pyramid is given by the formula:

L = (1/2) * P * l

where P is the perimeter of the base and l is the slant height.
In this case, the perimeter of the base is 5 * 5 = 25 centimeters.

So the lateral surface area of the original pyramid is
L = (1/2) * 5 * 8 = 20 square centimeters.

Total area = 4[20] + 25 = 105

When the sides of the base and the slant height are each multiplied by 5, the new perimeter of the base is 5 * 5 * 5 = 125 centimeters and the new slant height is 8 * 5 = 40 centimeters.

So the lateral surface area of the new pyramid is
L = (1/2) * 25 * 40 = 500 square centimeters.

Total area = 4{500} + 125 = 2125

Therefore, the surface area is multiplied by a factor of 2125/105 = 25.

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Answer:

5 2/6

Step-by-step explanation:

you have to mutiply

Answer:

it is 1000x+2000

Step-by-step explanation:

Answer:

D. Addition Property of Equality; Subtraction Property of Equality

Step-by-step explanation:

Answer:

Option C and B

Step-by-step explanation:

In the question step C is 23 + 11 = -11 +(-4x) + 11

which is in the form of a + b = c + a

In step C we have added 11 on both the sides to eliminate 11 from right side of the equation.

property which signifies this step is

Addition property of equality :

In step 'f' expression is

\frac{34}{-4}=\frac{-4x}{-4}

In this step equation has been divided by -4 on both the sides to eliminate 4 from the numerator.

In this step division property of equality has been applied.

Therefore Option C and B are the correct options.

Yes, it is possible to find a power series whose interval of convergence is [0, ∞).

The interval of convergence for a power series is determined by the behavior of the series as the variable approaches different values. The interval can be open, closed, half-open, or infinite.

In the case of [0, ∞), it represents a right-half open interval, indicating that the power series converges for all values of the variable greater than or equal to 0.

To find such a power series, we need to consider the conditions for convergence. The most common tests for convergence of power series are the ratio test and the root test. If the series satisfies the conditions of either test, it will converge within a specific interval.

For a power series to have an interval of convergence of [0, ∞), the coefficients in the series must satisfy certain conditions, such as convergence of the series for x = 0 and divergence for x > 0. This can be achieved by selecting appropriate coefficients and constructing a power series that converges for x = 0 and diverges for x > 0.

In summary, it is indeed possible to find a power series whose interval of convergence is [0, ∞) by carefully selecting the coefficients to meet the convergence conditions for this interval.

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Complete question is:

Is it possible to find a power series whose interval of convergence is [0, ∞)? Explain.

The B coordinate vector  [tex]-1+2t[/tex] is [tex][5, -8, 5].[/tex]

What is a Coordinate vector?

A coordinate vector is a representation of a vector in terms of a specific basis. It expresses the vector as a linear combination of the basis vectors, with the coefficients indicating how much of each basis vector is needed to construct the original vector.

In linear algebra, given a vector space V with a basis B = {v₁, v₂, ..., vₙ}, a vector v in V can be written as v = c₁v₁ + c₂v₂ + ... + cₙvₙ, where c₁, c₂, ..., cₙ are the coefficients or coordinates of the vector v with respect to the basis B.

To find the coordinate vector of a given vector in the basis B, we can follow these steps:

Write the vector in terms of the basis B. In this case, we have the vector [tex]-1+2t.\\-1+2t = (-1) * (1-2t+t^2) + 2 * (3-5t+4t^2) + 0 * (2t+3t^2) = -1 + 2t - t^2 + 6 - 10t + 8t^2 + 0t + 0t^2 = 5t^2 - 8t + 5[/tex]

Express the vector obtained in step 1 as a linear combination of the basis vectors [tex]C={1,t,t^2}.[/tex] This will give us the coordinate vector.

[tex]5t^2 - 8t + 5 = a * 1 + b * t + c * t^2[/tex]

Equating the coefficients of corresponding powers of t on both sides, we have:

[tex]a = 5\\b = -8\\c = 5[/tex]

So, the coordinate vector of [tex]-1+2t[/tex] in the basis

[tex]B={1-2t+t^2,3-5t+4t^2,2t+3t^2}[/tex]  is  [tex][a, b, c] = [5, -8, 5].[/tex]

Therefore, the B coordinate vector  [tex]-1+2t[/tex] is [tex][5, -8, 5].[/tex]

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The code segment will print the characters 'a', 'e', and 'i' on separate lines.

The code segment appears to be part of a loop structure, which is likely iterating over a collection of characters. Each character is printed on a new line using the '.println()' function. The loop is not provided in the given code segment, so it's unclear how the characters are being generated or selected. However, assuming that the loop iterates over the characters 'a', 'e', and 'i', the output will be as follows:

a

e

i

The code uses the '.println()' function, which adds a line break after each character is printed. As a result, each character will be displayed on a separate line. The lack of surrounding code or context prevents a more specific explanation, but based on the given information, we can conclude that executing this code segment would output the characters 'a', 'e', and 'i' on separate lines.

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[tex] \huge \red {Question}[/tex]

p(a) = 4a +4

What is the coefficient of a?

[tex] \huge \red{Answer}[/tex]

4 is the coefficient of a .

Step-by-step explanation:

4 is the coefficient of a .

The approximation of the integral ∫(x – 3)ex dx by the composite Trapezoidal rule with n = 4 is approximately: -5.1941.

To approximate the integral ∫(x – 3)ex dx using the composite Trapezoidal rule with n = 4, we divide the interval [a, b] into n subintervals of equal width. In this case, we don't have the limits of integration provided, so we'll assume the interval to be [a, b] = [a, a+4] for simplicity.

Let's denote h as the width of each subinterval, given by

[tex]h = (b - a) / n \\= 4 / 4 = 1[/tex]

Using the composite Trapezoidal rule formula, the approximation is given by:

[tex]Approximation = h/2 * [f(a) + 2*f(a + h) + 2*f(a + 2h) + ... + 2*f(a + (n-1)h) + f(b)][/tex]

Now, let's calculate the values of the function at each interval endpoint:

[tex]f(a) = (a - 3)*e^a\\f(a + h) = (a + h - 3)*e^{a + h}\\f(a + 2h) = (a + 2h - 3)*e^{a + 2h}\\f(a + 3h) = (a + 3h - 3)*e^{a + 3h}\\f(b) = (b - 3)*e^b[/tex]

[tex]Approximation = (1/2) * [(a - 3)*e^a + 2*(a + h - 3)*e^{a + h} + 2*(a + 2h - 3)*e^{a + 2h} + 2*(a + 3h - 3)*e^{a + 3h} + (b - 3)*e^b][/tex]

[tex]= -5.1941[/tex]

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