Please help I-readyyyyyy

Answer:

The value of the derivative at (2, 3) is zero.

Step-by-step explanation:

Given function:

[tex]g(x)=x+\dfrac{4}{x^2}[/tex]

To differentiate the given function, use the power rule of differentiation.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Power Rule of Differentiation}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]

[tex]\textsf{Rewrite\;the\;function\;using\;the\;exponent\;rule\;\;$a^{-n}=\dfrac{1}{a^n}$}:[/tex]

[tex]\implies g(x)=x+4x^{-2}[/tex]

Apply the power rule:

[tex]\implies g'(x)=1+(-2) \cdot 4x^{-2-1}[/tex]

[tex]\implies g'(x)=1-8x^{-3}[/tex]

[tex]\implies g'(x)=1-\dfrac{8}{x^3}[/tex]

An extremum is a point where a function has a maximum or minimum value. From inspection of the given graph, the minimum point of the function is (2, 3).

To determine the value of the derivative at the minimum point, substitute x = 2 into the differentiated function.

[tex]\begin{aligned}\implies g'(2)&=1-\dfrac{8}{2^3}\\\\&=1-\dfrac{8}{8}\\\\&=1-1\\\\&=0\end{aligned}[/tex]

Therefore, the value of the derivative at (2, 3) is zero.

0-24-  Tally (1)

25-49   Tally (4)

50-74  Tally (5)

75-99  Tally (2)

the largest integer [tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]

To find the largest integer[tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$[/tex], we need to count how many factors of 3 are in the product of the odd integers from 1 to 99.

One way to do this is to factor each odd integer into its prime factors and count how many factors of 3 are present. However, this would be quite tedious and time-consuming.

A quicker approach is to use the fact that every third odd integer is a multiple of 3. Thus, we can count how many multiples of 3 are present in the product of the odd integers from 1 to 99.

Let [tex]$m$[/tex] be the number of multiples of 3 in the range from 1 to 99. Then we have:

[tex]m = \left\lfloor \frac{99}{3} \right\rfloor = 33[/tex]

This is because there are 33 multiples of 3 in the range from 1 to 99 (namely, 3, 6, 9, ..., 96, 99).

Each multiple of 3 contributes at least one factor of 3 to the product of the odd integers. However, some multiples of 3 contribute two or more factors of 3, depending on how many factors of 3 they contain.

To count how many multiples of 3 contribute two or more factors of 3, we need to count how many multiples of 9, 27, and 81 are present in the range from 1 to 99.

There are [tex]$\left\lfloor \frac{99}{9} \right\rfloor = 11$[/tex]multiples of 9, namely 9, 18, 27, ..., 81, 90, 99. Each multiple of 9 contributes at least two factors of 3 to the product of the odd integers.

There are [tex]$\left\lfloor \frac{99}{27} \right\rfloor = 3$[/tex] multiples of 27, namely 27, 54, 81. Each multiple of 27 contributes at least three factors of 3 to the product of the odd integers.

There is only one multiple of 81 in the range from 1 to 99, namely 81, which contributes at least four factors of 3 to the product of the odd integers.

Thus, the total number of factors of 3 in the product of the odd integers from 1 to 99 is:

[tex]n = m + 2\times\text{number of multiples of 9} + 3\times\text{number of multiples of 27} + 4\times\text{number of multiples of 81}[/tex]

[tex]n = 33 + 2\times 11 + 3\times 3 + 4\times 1 = 62[/tex]

Therefore, [tex]the $ largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]

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100 times the square root of 3 is also a possible value of a for this function.

In mathematics, the square root of a non-negative real number "a" is a non-negative real number that, when multiplied by itself, gives the original number "a". It is denoted by the symbol "√".

We can substitute each of the given values into the function f(a) = a² + 7 to determine if they are possible values of a.

Substituting the square root of 5:

f(√(5)) = (√(5))² + 7 = 5 + 7 = 12

So, the square root of 5 is not a possible value of a for this function.

Substituting the square root of 7:

f(√(7)) = (√(7))² + 7 = 7 + 7 = 14

So, the square root of 7 is a possible value of a for this function.

Substituting 100 times the square root of 3:

f(100√(3)) = (100√(3))² + 7 = 30000 + 7 = 30007

So, 100 times the square root of 3 is also a possible value of a for this function.

Therefore, the possible values of a for the given function are:

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Answer:

x = 37.5

Step-by-step explanation:

the top triangle has 2 congruent sides and is therefore isosceles with base angles being congruent, then

base angles = (180 - 75) ÷ 2 = 105 ÷ 2 = 52.5

the angle on the left of the outer triangle is right , then

x + 52.5 = 90 ( subtract 52.5 from both sides )

x = 37.5

this is just a quick addition to the superb reply above by "jimrgrant1"

Check the picture below.

Answer:

[tex]f(7.3)\approx9.9[/tex]

Step-by-step explanation:

Use point-slope form

[tex]y-y_1=m(x-x_1)\\y-9=3(x-7)\\y-9=3x-21\\y=3x-12[/tex]

[tex]f(7.3)=3(7.3)-12=21.9-12=9.9[/tex]

The value of the quadratic equation in the standard form is y = -x² -6x + 2.

y = ax² + bx + c, where a, b, and c are constants and an is not equal to 0, is a quadratic equation in standard form. A parabolic function's vertex, axis of symmetry, and intercepts with the x- and y-axes are all expressed by the quadratic equation in standard form. While the positions of the vertex and intercepts are determined by the factors b and c, the direction and form of the parabola are determined by the coefficient a. Every quadratic equation may be changed into standard form by applying the quadratic formula or the square method, which simplifies the analysis and comparison of various functions.

The standard form of the quadratic equation is given by:

y = ax² + bx + c

Substituting the values of x and y from the table we have:

For (-4, 10):

10 = a(-4)² + b(-4) + c

10 = 16a - 4b + c......(1)

For (-3, 11):

11 = a(-3)² + b(-3) + c

11 = 9a -3b + c......(2)

For (-2, 10):

10 = 4a - 2b + c .........(3)

Equation 1 can be written as follows:

10 = 16a - 4b + c

c = 10 - 16a + 4b

Substitute the value of c in equation 2 and 3:

11 = 9a -3b + c

11 = 9a - 3b + 10 - 16a + 4b

1 = - 7a + b .........(4)

And,

10 = 4a - 2b + c

10 = 4a - 2b + 10 - 16a + 4b

0 = -12a + 2b

12a = 2b

b = 6a .......(5)

Substitute the value of b in equation 4:

1 = - 7a + 6a

1 = -a

a = -1

Substitute the value of a in equation 5:

b = -6

Now, substitute the value of a and b in equation 1:

10 = 16a - 4b + c

10 = 16(-1) - 4(-6) + c

10 = -16 + 24 + c

10 = 8 + c

c = 2

Substituting the value in the quadratic equation we have:

y = -x² -6x + 2

Hence, the value of the quadratic equation in the standard form is y = -x² -6x + 2.

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If we cοnsider (x, y) tο be a pοint οn the unit circle, we get:

[tex]x^2 + y^2 = 1[/tex] (because the pοint is οn the unit circle) (since the pοint is οn the unit circle)

All real numbers must be determined in such a way that:

tan(s) = y / x

The trigοnοmetric identity can be applied:

Tan is equal tο Sin / Cοs.

We thus have:

Y/X = Tan(S), Sin(S), and Cοs (s)

Using the identity cοs(s) + sin(s) = 1, we square bοth sides tο οbtain:

[tex](y/x)^2 = sin^2(s) / cos^2(s) = 1 - cos^2(s)[/tex]

Rearranging and applying the equatiοn x2 + y2 = 1 results in:

cοs2(s) equals 1 - (y/x).

[tex]^2 = x^2[/tex]

Given that (x, y) is in the first οr fοurth quadrant and that x is pοsitive, we can take the square rοοt tο get the fοllοwing result:

cοs(s) = ± x

Sο, s is determined by:

S equals arccοs(x) + n, where n is any pοsitive integer.

The range οf x's value is limited tο [-1, 1] because it is οn the unit circle. As a result, the values οf s are prοvided by:

S = arccοs(x) + n, where n is any pοsitive integer and x is within the range [-1, 1].

The pοssible values οf s in exact radian measure in [0, 2] are as fοllοws:

S = arccοs(-1) + = S = arccοs(1) = 0

S is equal tο arccοs(0) + n + (n + 1/2)

where any integer n is used.

As n can be any integer, the pοssible pοssibilities οf s are s = 0,, and (n + 1/2).

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According to the given information, the missing side measure is 14.

What is triangle?

A triangle is a polygon with three sides, three angles, and three vertices. It is the simplest polygon and the fundamental shape used in geometry. A triangle can be classified based on the length of its sides and the measure of its angles.

To find the missing side measure, we can set up a proportion between the corresponding sides of the two similar triangles:

(x + 5) / x = 9.5 / 7

We can then solve for x by cross-multiplying:

7(x + 5) = 9.5x

7x + 35 = 9.5x

35 = 2.5x

x = 14

Therefore, the missing side measure is 14.

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Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

Using the properties of  absolute value function, proved that |x - y| > |x| - |y| is true for all x and y.

To prove that |x - y| > |x| - |y|, we can consider two cases

Case 1

x >= 0 and y >= 0

In this case, |x - y| = x - y and |x| - |y| = x - y. So we have

|x - y| = x - y

| x | - | y | = x - y

Substituting these expressions into the original inequality, we get:

x - y > x - y

This inequality is true for all x and y where x >= 0 and y >= 0, since the difference between x and y is always greater than or equal to zero.

Case 2

x < 0 and y < 0

In this case, |x - y| = -(x - y) and |x| - |y| = -x + y. So we have:

|x - y| = -(x - y)

| x | - | y | = -x + y

Substituting these expressions into the original inequality, we get

-(x - y) > -x + y

Simplifying both sides, we get

y - x > -x + y

Adding x to both sides, we get

y > 0

This inequality is true for all x and y where x < 0 and y < 0, since both x and y are negative and the difference between x and y is always less than or equal to zero.

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Answer:

Step-by-step explanation:

subtract 434-46

The point of intersection of the two lines is (-3.4, -1.2).

Step 1: The slope of a line passing through two points (x1,y1) and (x2,y2) can be found using the formula:

m = (y2-y1)/(x2-x1)

Using this formula, we can find the slope of the first line:

m1 = (−2−3)/(-5 -5) = −5/(-10) = 1/2

And the slope of the second line:

m2 = (−4−4)/(2 -(-6)) = -8/4 = -2

Step 2: Find the y-intercept of each line

The y-intercept of a line in slope-intercept form (y = mx + b) is the value of y when x=0. We can use one of the two given points on each line to find the y-intercept:

For the first line passing through points (5,3) and (−5,−2):

y = mx + b

3 = (1/2)(5) + b

b = 3 - 5/2

b = 1/2

So the first line can be written as y = 1/2x + 1/2

For the second line passing through points (−6,4) and (2,−4):

y = mx + b

4 = (-2)(−6) + b

b = 4 - 12

b = -8

So the second line can be written as y = -2x - 8

Step 3: Each line in slope-intercept form (y = mx + b):

First line: y = 1/2x + 1/2

Second line: y = -2x - 8

Step 4: To find the point of intersection of the two lines, we need to solve the system of equations. We can solve for x by setting the two right-hand sides equal to each other:

1/2x + 1/2 = -2x - 8

(x + 1)/2 = -2x - 8

x + 1 = -4x - 16

5x = -16 - 1

5x = -17

x = -17/5

x = -3.4

Now that we know x, we can find y by substituting x=10 into one of the two equations:

y = -2x - 8

y = -2(-3.4) - 8

y = - 1.2

Thus, the point of intersection of the two lines is (-3.4, -1.2).

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Step-by-step explanation:

See Venn diagram below

(a) Negation: C) This vertex is connected to at least one other vertex in the graph. (b) Negation: D) This number is related to at least one even number.

(a)

A) Some vertex is connected to some other vertex in the graph.

B) At least one vertex is not connected to any other vertex in the graph.

C) This vertex is connected to at least two other vertices in the graph.

D) There exists at least one vertex that is not connected to at least one other vertex in the graph.

E) This vertex is connected to some other vertices in the graph, but not necessarily to all of them.

(b)

A) This number is related to at least one odd number.

B) There exists at least one number that is not related to any even number.

C) All numbers are related to at least one even number.

D) This number is not related to at least one even number.

E) All numbers are related to at least one even number.

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Complete question:

Find a negation for each of the statements in (a) and (b).

(a) This vertex is not connected to any other vertex in the graph.

A) No vertex is connected to any other vertex in the graph.

B) All vertices are connected to all other vertices in the graph.

C) This vertex is connected to at least one other vertex in the graph.

D) All vertices are connected to at least one other vertex in the graph.

E) This vertex is connected to all other vertices in the graph.

(b) This number is not related to any even number.

A) This number is not related to any odd number.

B) All numbers are related to at least one even number.

C) All numbers are not related to any even number.

D) This number is related to at least one even number.

E) No number is related to any even number.

The equation representing the money or balance (y) in your savings account any time (x) is y = z - 25x.

An equation is an algebraic statement showing the equality of two or more mathematical expressions.

Mathematical expressions combine variables with numbers, values, and constants without the equal symbol (=).

The monthly withdrawals = $25

The number of months (x) = 4

Account balance (y) = $75

Let z = the initial balance in the savings account.

y = z - 25x

75 = z - 25x

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Answer:

(2u - 1) (3u + 10)

Step-by-step explanation:

Let's Check

(2u - 1) (3u + 10)

6u² + 20u - 3u + 10

6u² + 17u + 10

So, (2u - 1) (3u + 10) is the correct answer.

Solving a system of equations we the length and width of the playground is length = 9 yards, width = 12 yards

Remember that the area of a rectangle of length L and width W is:

Area = L*W

Here we know that the area is 108 square yards, and we know that he width is 3 yards longer than the length, then we can write a system of equations:

W =L + 3

108 = L*W

Replacing the first equation into the second one we will get:

108 = (L + 3)*L

108 = L² + 3L

Then we have the quadratic equation:

L² + 3L - 108 = 0

Using the quadratic formula we get the solutions:

[tex]L = \frac{-3 \pm \sqrt{3^2 - 4*1*-18} }{2}[/tex]

We only care for the positive solution, which is:

L = 9

Then the width is:

W = L + 3 = 9 + 3 = 12

Then the correct option is:

•length = 9 yards, width = 12 yards

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Answer: 2s²(39 - 74s - 280s)(s - 2)(s + 7/2)

Step-by-step explanation:

To factor the polynomial 78s - 148s³ - 560s² completely, we can first factor out a common factor of 2s²:

2s²(39 - 74s - 280s)

Then, we can factor the quadratic expression inside the parentheses using the quadratic formula:

s = [-(-74) ± √((-74)² - 4(39)(-280))] / 2(39)

s = [74 ± √(54724)] / 78

s = [74 ± 2√13681] / 78

s = [74 ± 2×117] / 78

Therefore, the roots of the quadratic expression are:

s = 2 or s = -7/2

Substituting these values back into the factored expression, we get:

2s²(39 - 74s - 280s) = 2s²(39 - 74(2) - 280(2)) = -1240s²

2s²(39 - 74s - 280s) = 2s²(39 - 74(-7/2) - 280(-7/2)) = 2450s²

So the completely factored form of the polynomial is:

2s²(39 - 74s - 280s)(s - 2)(s + 7/2)

Answer:

The formula to calculate the amount of loan with flat rate interest is:

Amount = Principal + (Principal x Rate x Time)

Where,

Principal = the amount of loan

Rate = the interest rate per year

Time = the time period in years

Given,

Principal = K40,000.00

Rate = 9% per year

Time = 2.5 years

Substituting the values in the formula, we get:

Amount = K40,000.00 + (K40,000.00 x 0.09 x 2.5)

Amount = K40,000.00 + K9,000.00

Amount = K49,000.00

Therefore, the amount he will pay the bank is K49,000.00.

Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.

What is the slope?

In mathematics, the slope is a measure of the steepness of a line.

The solution provided involves three steps to find the slope of the line that passes through two points: (-2, 8) and (4, 6).

Step 1 involves finding the change in y-coordinates, which is the difference between the y-coordinate of the second point and the y-coordinate of the first point. In this case, the second point has a y-coordinate of 6 and the first point has a y-coordinate of 8.

Therefore, the change in y-coordinates is 6 - 8 = -2.

Step 2 involves finding the change in x-coordinates, which is the difference between the x-coordinate of the second point and the x-coordinate of the first point. In this case, the second point has an x-coordinate of 4 and the first point has an x-coordinate of -2.

Therefore, the change in x-coordinates is 4 - (-2) = 6.

Step 3 involves dividing the change in y-coordinates by the change in x-coordinates to find the slope of the line. In this case, the change in y-coordinates is -2 and the change in x-coordinates is 6, so the slope is -2/6 or -1/3.

Since all the steps are correct and properly executed, there is no error.

Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.

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Answer:

B. 2.1

Step-by-step explanation:

If you draw a line from C to intersect AB perpendicularly at point D so we have 2 right triangles ACD and BCD.

For △ACD, AC is hypotenuse so sinA = CD/AC

=> CD = 5 x sin(20) = 5 x 0.342 = 1.71

then we have AB = AD + BD

Pythagorean theorem: c^2 = a^2 + b^2

for △ACD, 5^2 = 1.71^2 + AD^2

AD^2 = 5^2 - 1.71^2 = 22.0759

AD = 4.70

BD = AB - AD = 6 - 4.70 = 1.30

for △BCD, BC is hypotenuse

BC^2 = BD^2 + CD^2 = 1.30^2 + 1.71^2 = 4.61

BC = √4.61 = 2.1

The value of function f(0) after putting the value of x = 0 we get the value o which is not DNE.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

Given function is

f(x)=5x

we have to find the value of the f(0)

so putting the value of 0 as x we get,

f(x)=5x

f(0) = 5(0)

f(0) = 0

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Answer:

20 units

Step-by-step explanation:

Point 1 (-9, 4)

Point 2 (3, -12)

Distance Formula

d=√((x2-x1)²+ (y2-y1)²)

d=√((3+9)²+ (-12-4)²)

d=√(12²+ (-16)²)

d=√(144+ 256)

d=√400

d=20

Answer:

[tex]\textsf{To\;add\;(or subtract)\;in\;Scientific\;Notation,\;you\;must\;have\;the\;same\;$\boxed{\sf power\;of\;10}$\:.}\\\textsf{Then\;you\;can\;$\boxed{\sf add\;or\;subtract}$\;the\;coefficients\;and\;$\boxed{\sf keep}$\;the\;power\;of\;10.}[/tex]

[tex]\textsf{To\;multiply\;in\;Scientific\;Notation,\; you\;must\;$\boxed{\sf multiply}$\;the\;coefficients}\\\textsf{and\;$\boxed{\sf add}$\;the\;powers\;of\;10.}[/tex]

[tex]\textsf{To\;divide\;in\;Scientific\;notation,\;you\;must\;$\boxed{\sf divide}$\;the\;coefficients}\\\textsf{and\;$\boxed{\sf subtract}$\;the\;powers\;of\;10.}[/tex]

Step-by-step explanation:

To add (or subtract) in Scientific Notation, you must have the same power of 10. Then you can add or subtract the coefficients and keep the power of 10.

Example expression:

[tex]2.3 \times 10^3 +3.2 \times 10^3[/tex]

Factor out the common term 10³:

[tex]\implies (2.3 +3.2) \times 10^3[/tex]

Add the numbers:

[tex]\implies (5.5) \times 10^3[/tex]

[tex]\implies 5.5\times 10^3[/tex]

Therefore, we have added the coefficients and kept the power of 10.

[tex]\hrulefill[/tex]

To multiply in Scientific Notation, you must multiply the coefficients and add the powers of 10.

Example expression:

[tex]2.3 \times 10^3 \times 3.2 \times 10^3[/tex]

Collect like terms:

[tex]\implies 2.3 \times 3.2 \times 10^3 \times 10^3[/tex]

Multiply the numbers (coefficients):

[tex]\implies 7.36 \times 10^3 \times 10^3[/tex]

[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 7.36 \times 10^{(3+3)}[/tex]

[tex]\implies 7.36 \times 10^{6}[/tex]

Therefore, we have multiplied the coefficients and added the powers of 10.

[tex]\hrulefill[/tex]

To divide in Scientific notation, you must divide the coefficients and subtract the powers of 10.

Example expression:

[tex]\dfrac{8.6 \times 10^6}{2.15 \times 10^2}[/tex]

Collect like terms:

[tex]\implies \dfrac{8.6}{2.15} \times \dfrac{10^6 }{10^2}[/tex]

Divide the numbers (coefficients):

[tex]\implies 4\times \dfrac{10^6 }{10^2}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad \dfrac{a^b}{a^c}=a^{b-c}[/tex]

[tex]\implies 4\times 10^{(6-2)}[/tex]

[tex]\implies \implies 4\times 10^{4}[/tex]

Therefore, we have divided the coefficients and subtracted the powers of 10.

Answer: In the table x part, it increases from -2 all the way to 4. In the table y part, it decreases from 17 to -1, but then increases back from -1 to 17.

The length of h in the attached composite figure where all the angles are right angles is equal to 4m.

In the attached diagram of composite figure,

All are right angles.

Composite figure consist two rectangles,

Upper and lower rectangles.

length of the upper rectangle is equal to 5m

Width of the upper rectangle is equal to 'h' m

Width of the lower rectangle is equal to 2m

Length of each dash '-' mark  is equals to 1m.

length of 'h'm  is equals

= 2 m + 2 dash marks

= 2m + 2m

= 4m

Therefore, the length of the h in the composite figure ( attached diagram ) is equals to 4m.

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The above question is incomplete, the complete question is:

What is the length of h in the following composite figure? All angles are right angles.

5 m

4 m

3 m

2 m

Diagram is attached.

Answer:

4 m is ur answer

Step-by-step explanation:

hope this helps

Step-by-step explanation:

Original job = x men * 40 days = 40x man days  to complete

  now add 8 men     =    x+8  men

                                           man days now is   (x+8) (30)  to complete job

so     40x = (x+8)(30)

        40x = 30x + 240

          10 x = 240

              x = 24 men originally

(a) The function x as a function of t is t = 250ln(499x/998)

(b) Half the population will have heard the rumor approximately 109.86 units of time after it was started.

(a) To solve the differential equation dt/dx = kx(N−x), we can separate the variables and integrate

dt/dx = kx(N−x)

dt/(N-x) = kx dx

Integrating both sides, we get

t = -1/k × ln(N-x) - 1/k × ln(x) + C

where C is the constant of integration.

To find C, we can use the initial condition that two people start the rumor at t=0, so x=2:

0 = -1/k * ln(N-2) - 1/k * ln(2) + C

C = 1/k * ln(N-2) + 1/k * ln(2)

Substituting C back into the equation, we get:

t = -1/k * ln(N-x) - 1/k * ln(x) + 1/k * ln(N-2) + 1/k * ln(2)

Simplifying, we get

t = 1/k * [ln((N-2)x/(2(N-x)))]

Substituting k=1/250 and N=1000, we get:

t = 250ln(499x/998)

(b) We want to find the time t when half the population has heard the rumor, so x = N/2 = 500. Substituting this into the equation we obtained in part (a), we get

t = 250ln(499(500)/998) = 250ln(249/499)

t ≈ 109.86

Therefore, half the population will have heard the rumor approximately 109.86 units of time after it was started.

Learn more about differential equation here

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