a homework assignment included 40 multiple choice questions Sabrina completed 65% of her assignment in David completed 4/5 of his assignment how many more questions did David complete compared to sabrina?​

The average cost per item over the interval (1,000,1,010] is (C(1010) - C(1000)) / (1010 - 1000) = (10,000 + 5(1010) - 10,000 - 5(1000)) / 10 = $5.50.

The average cost per item over the interval [999.5, 1000] is (C(1000) - C(999.5)) / (1000 - 999.5) = (10,000 + 5(1000) - 10,000 - 5(999.5)) / 0.5 = $5.00.

The given function C(x) represents the cost in dollars to manufacture x items. To find the average cost per item over a given interval, we use the formula: (C(b) - C(a)) / (b - a), where a and b are the endpoints of the interval.

For the interval (1,000,1,010], we substitute a = 1000 and b = 1010 into the formula to obtain (C(1010) - C(1000)) / (1010 - 1000). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1010) - $10,000 - $5(1000)) / 10 = $5.50 per item.

For the interval [999.5, 1000], we substitute a = 999.5 and b = 1000 into the formula to obtain (C(1000) - C(999.5)) / (1000 - 999.5). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1000) - $10,000 - $5(999.5)) / 0.5 = $5.00 per item.

To find C'(1000), we differentiate the function C(x) with respect to x, which gives C'(x) = 5. The value of C'(1000) is therefore 5, rounded to 1 decimal place.

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Answer:

42

Step-by-step explanation:

256 / 6 = 42.66666 since where only county full pots its 42

Answer

99

Step-by-step explanation:

Answer:

G. 14:5 is the correct answer.

Step-by-step explanation:

a:b = 4:5

a:c = 2:7

so,

here in first ratio a = 4

in second ratio a = 2

making them equal:

Taking LCM of 2 and 4 = 4

so

a:c = 2/7 = (2×2)/(7×2) = 4/14

so,

a = 4

c = 14

b = 5

so ratio c : b = 14:5

Answer:

I'm reading about it and mostly they're saying they were concerned with internal conflict within Russia. I'm not positive, it could be because of the loss of land, but it appears to be more politically motivated. uprisings with in the country. so my best guess would be none of the above

Answer:

x+3-12/8

Step-by-step explanation:

h(x)=-3/8x+12

y=h(x) let

y=-3/8x+12

here,

put at x at y and put y at x

x=-3/8y+12

8y=x+3-12

y=x+3-12/8

The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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I will break down the question into three parts and answer each one separately.

Part 1: sin 8x lim f(x)
There is no function f(x) provided in the question, so it is not possible to find the limit of f(x). The term "sin 8x" is also not relevant to this part of the question.

Part 2: find limx tan x
The limit of tan x as x approaches infinity does not exist because the function oscillates between positive and negative infinity. However, the limit of tan x as x approaches pi/2 from the left or right is equal to positive infinity, and the limit of tan x as x approaches -pi/2 from the left or right is equal to negative infinity.

Part 3: find f'(x) given that f(x)= (4x²-8), f(x)- Vox +2), and X-2 f(x) - j) given that 2x +1
To find the derivative of f(x), we need to differentiate each term separately and then combine the results. Using the power rule of differentiation, we have:

f(x) = 4x² - 8
f'(x) = 8x

f(x) = x^2 - Vox + 2
f'(x) = 2x - Vx

f(x) = (x - 2)f(x) - j
f'(x) = (x - 2)f'(x) + f(x) - j
       = (x - 2)(2x - Vx) + (x^2 - Vx + 2) - j
       = 2x^2 - 5x + 2 - Vx - j


a) To find the derivative of sin(8x) with respect to x, use the chain rule:
f'(x) = cos(8x) * 8 = 8cos(8x)

b) To find the derivative of f(x) = (4x^2 - 8) with respect to x, use the power rule:
f'(x) = 8x

c) To find the limit of f(x) = √(x + 2) as x approaches 1, simply substitute x = 1 into the function:
lim(x -> 1) f(x) = √(1 + 2) = √3

d) To find the limit of tan(x)/x as x approaches 0, use L'Hopital's rule. Since tan(x) -> 0 and x -> 0 as x -> 0, the conditions are satisfied:
lim(x -> 0) (tan(x)/x) = lim(x -> 0) (sec^2(x)/1) = sec^2(0) = 1

e) To find the derivative of f(x) = 2x + 1 with respect to x, use the power rule:
f'(x) = 2

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To solve for y, we can use the trigonometric identity:  sin(A+B) = sinA cosB + cosA sinB. The value of y depends on the value of x. We cannot determine the value of y without knowing x.

Comparing this to the given equation, we can see that:  A = x+y

B = x
sinA = sin(x+y)
cosB = cosx
sinB = sinx

Plugging these values in, we get:  sin(x+y) = sinA cosB + cosA sinB = sin(x+y) cosx + cos(x+y) sinx
We can simplify this using the sum-to-product identity:  sin(x+y) = sinx cos(x+y) + cosx sin(x+y) = sinx cosx + sin(x+y) cosx

Moving all the terms involving sin(x+y) to one side and factoring, we get:  sin(x+y) - sin(x+y) cosx = sinx cosx
sin(x+y) (1 - cosx) = sinx cosx
sin(x+y) = (sinx cosx)/(1-cosx)

We can simplify further using the identity:  2 sinA cosB = sin(A+B) + sin(A-B).

Thus, 2 sinx cosx = sin(2x)
sinx cosx = (1/2) sin(2x)

Substituting this into the previous equation, we get:  sin(x+y) = (1/2) sin(2x)/(1-cosx)
We can now solve for y: sin(x+y) = (1/2) sin(2x)/(1-cosx)
sin(y) cosx + cos(y) sinx = (1/2) sin(2x)/(1-cosx)
(sin(y)/cos(y)) = (1/2) sin(2x)/(1-cosx) - (sinx/cosx)

Using the identity tan(A-B) = (tanA - tanB)/(1+tanA tanB), we can simplify this to:  tan(y - pi/4) = (sinx - \(\sqrt{(3) cosx)/(1+2sinx) }\)
We can now solve for y - pi/4:
tan(y - pi/4) = (sinx - \(\sqrt{(3) cosx)/(1+2sinx) }\)
y - pi/4 = atan((sinx - \(\sqrt{(3) cosx)/(1+2sinx)) }\)

Adding pi/4 to both sides, we get:
y = atan((sinx - \(\sqrt{(3) cosx)/(1+2sinx)) }\)) + pi/4

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The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

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Answer:

4044.32

Explanation:

6506.08 (total) - 2461.76 (top)=

4044.32 (lateral+top)

Formulae:

total = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)

top= T= πr2

The student who is correct is Oscar. The average cost would be determined first and the average cost would be multiplied by 9.

The first step is to determine the cost of one cup of coffee. In order to determine the cost of one cup of coffee, divide the total cost paid for a certain cup by the number of cups bought.

The average cost is the cost per unit produced during a production run. It denotes the average amount of money spent to manufacture a product. This amount varies according to the number of units produced.

The average cost (AC) or average total cost (ATC) is the cost per unit of output. To calculate it, divide the total cost (TC) by the quantity produced by the firm (Q).

Cost per cup = total cost / number of cups bought $10.60 / 4 =  $2.65

In order to determine the cost of 9 cups of coffee, multiply the cost per cup by the total number of cups bought.

Total cost of 9 cups of coffee = cost per cup x total number of cups $2.65 x 9 = $23.85

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The equation of a parabola is a quadratic equation.

The equation of the parabola is: \(\mathbf{y = 4x^2 + 32x -32}\)

The points are given as:

\(\mathbf{(x,y) = (-5,-224),(-3,-92),(1,4)}\)

Substitute these values in:

\(\mathbf{y = ax^2 + bx +c}\)

So, we have:

\(\mathbf{-224 = a(-5)^2 + b(-5) +c}\)

\(\mathbf{-224 = 25a - 5b +c}\) ------ (1)

\(\mathbf{-92 = a(-3)^2 + b(-3) +c}\)

\(\mathbf{-92 = 9a -3b +c}\) ---- (2)

\(\mathbf{4 = a(1)^2 +b(1) +c}\)

\(\mathbf{4 = a +b +c}\) ---- (3)

Subtract (3) from (2)

\(\mathbf{9a - a - 3b - b + c - c =-92 - 4}\)

\(\mathbf{8a - 4b =-96}\)

Multiply by 3

\(\mathbf{24a - 12b = -288}\)

Subtract (3) from (1)

\(\mathbf{25a -a - 5b -b +c - c = -224 - 4}\)

\(\mathbf{24a - 6b = -228}\)

Subtract \(\mathbf{24a - 6b = -228}\) from \(\mathbf{24a - 12a = -288}\)

\(\mathbf{24a- 24a - 12ba +6b = -288 + 96}\)

\(\mathbf{- 6b = -192}\)

Divide through by -6

\(\mathbf{b = 32}\)

Substitute \(\mathbf{b = 32}\) in \(\mathbf{8a - 4b =-96}\)

\(\mathbf{8a - 4 \times 32 = -96}\)

\(\mathbf{8a - 128 = -96}\)

Collect like terms

\(\mathbf{8a = 128 -96}\)

\(\mathbf{8a = 32}\)

Divide both sides by 8

\(\mathbf{a = 4}\)

Substitute \(\mathbf{a = 4}\) and \(\mathbf{b = 32}\) in \(\mathbf{4 = a +b +c}\)

\(\mathbf{4 + 32 + c = 4}\)

\(\mathbf{36 + c = 4}\)

Subtract 36 from both sides

\(\mathbf{c = -32}\)

Substitute values of a, b and c in: \(\mathbf{y = ax^2 + bx +c}\)

\(\mathbf{y = 4x^2 + 32x -32}\)

Hence, the equation of the parabola is: \(\mathbf{y = 4x^2 + 32x -32}\)

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The time plot of the populations (P and Q) for t=1 to t=4 is as follows:Figure: Time plot of P and Q for t=1 to t=4.Phase-plane plot: The phase-plane plot of the populations (P and Q) is as follows:Figure: Phase-plane plot of P and Q.

An interaction model is given by AP

=P(1-P) - 2uPQ AQ

= -2uQ+PQ. where r and u are positive real numbers. A) Rewrite the model in terms of populations (Pt+1, Q+1) rather than changes in populations (AP, AQ).B) Let r

=0.5 and u

= 0.25. Calculate (Pr. Q) for t

= 1, 2, 3, 4 using the initial populations (Po. Qo)

= (0, 1). Finally sketch the time plot and phase-plane plot of the model.A) To rewrite the model in terms of populations, add P and Q on both sides to obtain Pt+1

= P(1-P)-2uPQ + P

= P(1-P-2uQ+1) and Q(t+1)

= -2uQ + PQ + Q

= Q(1-2u+P).B) Let's calculate Pr and Qr with the given values. We have, for t

=1: P1

= 0(1-0-2*0.25*1+1)

= 0Q1

= 1(1-2*0.25+0)

= 0.5for t

=2: P2

= 0.5(1-0.5-2*0.25*0.5+1)

= 0.625Q2

= 0.5(1-2*0.25+0.625)

= 0.65625for t

=3: P3

= 0.65625(1-0.65625-2*0.25*0.65625+1)

= 0.57836914Q3

= 0.65625(1-2*0.25+0.57836914)

= 0.52618408for t

=4: P4

= 0.52618408(1-0.52618408-2*0.25*0.52618408+1)

= 0.63591760Q4

= 0.52618408(1-2*0.25+0.63591760)

= 0.66415737Time plot. The time plot of the populations (P and Q) for t

=1 to t

=4 is as follows:Figure: Time plot of P and Q for t

=1 to t

=4.Phase-plane plot: The phase-plane plot of the populations (P and Q) is as follows:Figure: Phase-plane plot of P and Q.

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For the given matrix A, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. The determinant det(A) is 68.

To find the minors of a matrix, we need to find the determinants of the submatrices obtained by removing the row and column corresponding to the element of interest. In this case, the minors M13, M23, and M33 correspond to the determinants of the 2x2 submatrices obtained by removing the first row and the third column, second row and third column, and third row and third column, respectively.

To find the cofactors, we multiply each minor by a positive or negative sign based on its position in the matrix. The signs alternate starting with a positive sign for the top left element. In this case, the cofactors C13, C23, and C33 correspond to the minors M13, M23, and M33 respectively.

Finally, the determinant of a 3x3 matrix can be found by using the formula det(A) = a11C11 + a12C12 + a13C13, where a11, a12, and a13 are the elements of the first row of the matrix and C11, C12, and C13 are their corresponding cofactors. In this case, the determinant det(A) is 68.

Therefore, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. And the determinant det(A) is 68.

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Answer:

∠ ACD = 130°

Step-by-step explanation:

∠ ABC = 180° - 120° = 60° ( adjacent angles on a straight line )

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ACD is an exterior angle of the triangle , then

∠ ACD = 70° + 60° = 130°

To find the center of mass of a cone of uniform density with radius R at the base, height h, and mass M, we need to use the formula:

x_cm = (1/M)∫∫∫xρdV
y_cm = (1/M)∫∫∫yρdV
z_cm = (1/M)∫∫∫zρdV

where x_cm, y_cm, and z_cm are the coordinates of the center of mass, ρ is the density, and V is the volume of the cone.

We can simplify the integral by using cylindrical coordinates, where the density is constant and equal to M/V, and the limits of integration are:

0 ≤ r ≤ R
0 ≤ θ ≤ 2π
0 ≤ z ≤ h(r/R)

Thus, the center of mass of the cone is:

x_cm = 0
y_cm = 0
z_cm = (3h/4)(r/R)^2

Therefore, the center of mass of the cone is located at (0, 0, (3h/4)(r/R)^2) with respect to the origin at the center of the base of the cone and +z going through the cone vertex.

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One of the benefits of representing data sets using frequency distributions is; Organizing the data into a frequency distribution can make patterns within the data more evident.

Frequency distributions are usually portrayed as frequency tables or graphs or charts. Frequency distributions may likely show either the actual number of observations falling in each range or the percentage of observations and this distribution is called a relative frequency distribution.

There are three types of frequency distributions namely;

Looking at the options, the most appropriate one showing a benefit of using graphs of frequency distributions is; Option A

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Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

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The scale factor is given as follows:

5/3.

The value of x is given as follows:

x = 7.

Two triangles are defined as similar triangles when they share these two features listed as follows:

Equivalent side lengths for this problem are given as follows:

YZ and BC.

Hence the scale factor is given as follows:

10/6 = 5/3.

Then the value of x can be obtained as follows:

(12x - 59)/(2x + 1) = 5/3

Applying cross multiplication, we have that:

3(12x - 59) = 5(2x + 1)

26x = 182

x = 182/26

x = 7.

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Answer: 12pi + 140

Step-by-step explanation:

Area of the trapezoid: (1/2)(7)(16+24)=(20)(7)=140

Area of semicircle: (pi)(12)=12pi

So total area = 12pi + 140

Answer:

Step-by-step explanation:

Number of seats = number of rows * number of seat in each row

                            = (3c + 8 )*(4c -1)

                            = 3c*(4c - 1) + 8(4c - 1)

                             = 3c*4c - 3c*1 + 8*4c - 1*8

                             = 12c² - 3c + 32c - 8

                             =12c² + 29c - 8

A $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.  A $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

The formula to calculate the value of a CD after a specific duration at a specific interest rate compounded annually is given by:

A = P(1 + r/n)^(nt)

where P is the principal,

r is the annual interest rate,

n is the number of times compounded per year,

t is the number of years, and

A is the value of the CD at maturity.

Here, we need to calculate the value of a $1,000 initial investment in each bank's CD at maturity.

Let's calculate the value of a $1,000 investment in Bank ABC's CD.

P = $1,000

r = 5.0% compounded annually

t = 10 years

n = 1

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.05/1)^(1x10)A = $1,628.89

Therefore, a $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.

Let's calculate the value of a $1,000 investment in Bank XYZ's CD.

P = $1,000

r = 4.95% compounded daily

t = 10 years

n = 365

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.0495/365)^(365x10)A = $1,622.82

Therefore, a $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

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The negation of the statement "All coffee beans contain coffee" is "There exists a coffee bean that does not contain coffee."

We have,

Understanding the negation of a statement, it helps to break down the original statement and analyze its logical structure.

The original statement is "All coffee beans contain coffee."

This statement is a universal statement because it uses the word "all" to refer to every coffee bean.

It asserts that every coffee bean contains coffee.

The negation of a universal statement is an existential statement, which asserts the existence of at least one case that contradicts the original statement.

So, the negation of the statement "All coffee beans contain coffee" is "There exists a coffee bean that does not contain coffee."

This means that we are asserting the existence of at least one coffee bean that goes against the original statement, indicating that not all coffee beans contain coffee.

By using the concept of negation, we switch the emphasis from the universality of the original statement to the existence of a counterexample, providing a contradictory claim to challenge the original assertion.

Thus,

The negation of the statement "All coffee beans contain coffee" is "There exists a coffee bean that does not contain coffee."

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To determine the points of intersection we first equate the expressions, then we solve for x. Once we have the values of x for which the functions are equal we plu them on one of the function to find its corresponding value of y.

a)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=3:

Hence the functions intersect at (3,11)

When x=2:

Hence the functions intersect at (2,6)

Therefore the function intersect at the points (3,11) and (2,6).

b)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=7:

Hence the functions intersect at (7,-26)

When x=-1:

Hence the functions intersect at (-1,-2)

Therefore the function intersect at the points (7,-26) and (-1,-2).

Answer:

See below

Step-by-step explanation:

Evaluate the expressions if x = 10, y = 5, and z = 1.

Answer:

see below

Step-by-step explanation:

⇒  -7y - (-12y) = -7y + 12y =  5y

⇒  15xy - (-6xy) = 15xy + 6xy = 21xy

⇒  -53va - 32va =    - 85av

⇒  64 / 0.8 -5.6 / 7

   = 448 - 7.48

          5*6

    = 79.2

⇒    -(x -3) + 6

   = -x + 3 + 6

   = -x + 9

⇒  6 + 3 (9)

   = 6 + 27

   = 33

Evaluate the expressions if x = 10, y = 5, and z = 1.

⇒  x/y = 10 / 5 = 2

⇒  xy + z = 10*5 + 1 = 51

⇒  5 (z - x) = 5(1 - 10) = 5 - 50 = 45

Step-by-step explanation:

x = 2 , y = 7

ans, y = 11 - 2x and 4x - 3y = -13

→ 7 = 11 - 2(2) → 7 = 11 - 4 → 7 = 7

→ 4(2) - 3(7) = -13 → 8 - 21 = -13 → -13 = -13

x = 5 , y = 2

→ 2x + y = 12 and x = 9 - 2y

as, 2(5) + 2 = 12 → 10 + 2 = 12 → 12 = 12

x = 9 - 2y → 5 = 9 - 2(4) → 5 = 9 - 4 → 5 = 5

x = 3 , y = 5

ans. 2x + y = 11 , x - 2y = -7

2(3) + 5 = 11 → 6 + 5 = 11 → 11 = 11

3 - 2(5) = 7 → 3 - 10 = 7 → 7 = 7

x = 7 , y = 3

ans. x + 3y = 16 and 2x - y = 11

7 + 3(3) = 16 → 7 + 9 = 16 → 16 = 16

2(7) - 3 = 11 → 14 - 3 = 11 → 11 = 11

hope this answer helps you dear....take care may u have a great day ahead!

To find the polar coordinate equation for the special line passing through point P(1, 5) such that P is closer to the origin than any other point on that line, we need to determine the equation in the form r = f(θ).

We can start by expressing point P in Cartesian coordinates:

P(x, y) = (1, 5)

To convert this to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = arctan(y/x)

Applying these formulas to point P, we have:

r = √(1² + 5²)

 = √(1 + 25)

 = √26

θ = arctan(5/1)

   = arctan(5)

   ≈ 1.373

Therefore, the polar coordinate equation for the special line is:

r = √26

The angle θ can take any value since the line extends infinitely in all directions. Thus, θ remains as a variable.

The polar coordinate equation for the special line passing through point P(1, 5) is:

r = √26, where θ is any real number.

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