Kristina paid mortgage interest of
$6,320.00 and Medical Expenses of
$$19,500.00 during 2022. Her
GROSS INCOME was $32,500.
17. Using the deduction that is
best for her, what are her federal
taxes owed for 2022. (She is a
single filer).

The values are given below:

Given :  S is a geometric sequence

(√x + 1) , 1 and (√x -1) are first three terms of the sequence

To Find : Value of x

Recall that a geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant and called the common ratio.

a , ar , ar² , ... , arⁿ⁻¹

The nth term of a geometric sequence with the first term a and the common ratio r is given by:   aₙ = arⁿ⁻¹

(√x + 1) , 1 and (√x -1) are first three terms of the sequence

=> r =  1/(√x + 1) = (√x -1) /1

1/(√x + 1) = (√x -1) /1

=> 1 = (√x + 1)  (√x -1)

=> 1 = x - 1

=> x = 2

Hence x =2

a = (√2 + 1)

r = 1/(√2 + 1)

5th term of the sequence = ar⁴

=  (√2 + 1)  (1/(√2 + 1))⁴

=  (√2 + 1) /(3 + 2√2)²

=  (√2 + 1) /(17 + 12√2)

= (√2 + 1)(17 - 12√2)  /(17 + 12√2) (17 - 12√2)

=   -7 + 5√2

a = 5 , b = - 7

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The appropriate hypotheses for the researcher are: Null hypothesis: p <= 0.5 and Alternative hypothesis: p > 0.5.

In statistics, a hypothesis is an assumption or proposition about a population parameter, based on sample data. A hypothesis is a statement that is tested to determine whether it is true or false. It is an important component of statistical inference, which involves drawing conclusions about a population based on a sample of data. There are two types of hypotheses in statistics: the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis that is tested against the alternative hypothesis. It is usually a statement of "no effect" or "no difference" between two groups or conditions. The alternative hypothesis is the hypothesis that is accepted if the null hypothesis is rejected. It is usually a statement of an effect or difference between two groups or conditions.

Here,

The null hypothesis states that the proportion of households in the city that gave a charitable donation in the past year is less than or equal to 50 percent. The alternative hypothesis states that the proportion of households that gave a charitable donation is greater than 50 percent. The researcher will test these hypotheses using the sample data to determine whether there is convincing statistical evidence to support the alternative hypothesis.

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The difference in population proportions of students who wish to study science in college between the two schools has a standard error for a confidence interval of about 0.0165.

One of the mathematical methods used in statistics to calculate variability is the standard error. It is referred to as SE. The standard deviation of a sample distribution serves as the standard error of a statistic or estimate of a parameter. It can be characterized as a projection of that standard deviation.

The standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college can be calculated as:

SE = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }

where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

For School G, p1 = 108/185 = 0.5838, and n1 = 185.

For School H, p2 = 92/165 = 0.5576, and n2 = 165.

Substituting these values into the formula, we get:

SE = sqrt{ [0.5838(1-0.5838)/185] + [0.5576(1-0.5576)/165] }

SE = sqrt{ [0.2365/185] + [0.2436/165] }

SE = sqrt{ 0.000125 + 0.000147 }

SE = sqrt{ 0.000272 }

SE = 0.0165

Therefore, the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college is approximately 0.0165.

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the value of the definite integral of (2x²2 + x - 1)/(x - 2) from 1 to 2 is -3.

How to solve it?

To solve this integral, we can use partial fraction decomposition. We first write:

(2x²2 + x - 1)/(x - 2) = A + B/(x - 2)

Multiplying both sides by (x - 2), we get:

2x²2 + x - 1 = A(x - 2) + B

Substituting x = 2, we get:

7A + B = 7

Substituting x = 1, we get:

-A + B = -2

Solving these equations simultaneously, we get:

A = -3 and B = 10

So we have:

(2x²2 + x - 1)/(x - 2) = -3 + 10/(x - 2)

Now we can integrate this expression:

∫[-3 + 10/(x - 2)] dx from 1 to 2

= [-3x + 10 ln|x - 2|] from 1 to 2

= [-3(2) + 10 ln|2 - 2|] - [-3(1) + 10 ln|1 - 2|]

Since ln|0| is undefined, we know that the natural logarithm term evaluates to zero. Therefore, we get:

= -6 + 3 + 0

= -3

So the value of the definite integral of (2x²2 + x - 1)/(x - 2) from 1 to 2 is -3.

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Answer:Il y a 2 configurations de Thalès La première donne BC/CE = AC/CD = 1/2

la seconde donne BC/CE = CF/CA => CF = CA/2 = 3/2

Step-by-step explanation:

The dimension of the square metal sheet is x = 4 ft

Dimensions are the measure of a physical property of an object such as length, width or height.

Since an open box is to be constructed from a square sheet of metal with dimensions x feet by x feet by removing a square of side 1 foot from each corner and turning up the edges.

The volume V of the box is V(x) = (x - 2)².

To find the dimensions of the sheet metal needed to make a box that will hold 4 cubic feet by solving the equation V(x) = 4, we make V(x) = 4 and solve the equation.

So,  V(x) = (x - 2)².

(x - 2)² = 4

Taking square roots of both sides, we have that

√(x - 2)² = ±√4

x - 2 = ±2

x = 2 ± 2

x = 2 - 2 or x = 2 + 2

x = 0 or x = 4

Since the dimension cannot be 0, x = 4

So, the dimension of the sheet is x = 4 ft

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The solution is, y = 2x + 5+4 when graph would shift by 4 unit.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Given  : y = 2x + 5 .

To find :

If you wanted to shift the graph up what would be equation .

Solution : We have given that y = 2x + 5 .

BY the transformation rule ;

if f(x) +k then graph would shift up by k units .

Then to shift the graph of y = 2x + 5 up we need to add something in 5

Like   y = 2x + 5+4

Then graph would shift by 4 unit.

Therefore,   y = 2x + 5+4 graph would shift by 4 unit.

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Answer:

a. The fare for a 9-mile journey =  £ 10.6

Step-by-step explanation:

Fare = £2.50 + £0.90 x miles

Fare(9) = £2.50 + £0.90 x ( 9 miles) = £2.50 +  £ 8.1 =  £ 10.6

a. The fare for a 9-mile journey =  £ 10.6

So, in response to the above question, we can state thatThe equilibrium interest rate is 5.0% as a result (determined by equation adding $50 in interest to a $1000 bond over a year). The right response is thus 5.3%.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

We must locate the point at which the supply and demand for bonds are equal in order to determine the equilibrium interest rate. To do this, we may solve for Q by setting the demand and supply equations to equal values.

1000 - 0.5Q = 450 + 5Q

5.5Q = 550

Q = 100

We can calculate the equilibrium price (interest rate) by putting Q=100 into either the demand or supply equations now that we are aware of the quantities that are requested and supplied at equilibrium:

P = 1000 - 0.5Q = 1000 - 0.5(100) = $950

The equilibrium interest rate is 5.0% as a result (determined by adding $50 in interest to a $1000 bond over a year).

The right response is thus 5.3%.

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The rate of spreading in one year is approximately 0.00001 km/year.

To find the rate of spreading in one year, we need to divide the total distance of 927 km by the time it took to spread, which is 71 million years. However, it's important to convert the time unit from million years to years:

71 million years = 71,000,000 years

So, the rate of spreading in one year is:

927 km ÷ 71,000,000 years ≈ 0.00001307 km/year

Rounding to the nearest hundredth, we get:

0.00001307 km/year ≈ 0.00001 km/year

Therefore, the rate of spreading in one year is approximately 0.00001 km/year.

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The solution of the system x + y ≥ 75 and 2.5x + 10.5y ≤ 800  of the equation is

The system of equation x + y ≥ 75 and 2.5x + 10.5y ≤ 800 will have a solution that is as written in the equation.

This is done by substituting each value

Using (250, 10)

250 + 10 ≥ 75

260 ≥ 75 correct

2.5x + 10.5y ≤ 800

2.5 * 250 + 10.5 * 10 ≤ 800

730 ≤ 800 correct

since the the values are correct for the equations,  (250, 10) is the solution

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Answer:

In the given triangle.

Base= 3

Perpendicular=4

Hypotenuse=5

Step-by-step explanation:

CosB = B/H

=3/5

Sin B = P/H

= 4/5

Tan B = P/B

= 4/3

The perimeter of the triangle is 24 units.

what is perimeter ?

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.

Given by the question:

To find the perimeter of the triangle, we need to find the distance between each pair of vertices and then add them up.

Distance between (-4, -2) and (2, -2):

[tex]d = sqrt[(2-(-4))^2 + (-2-(-2))^2] = sqrt[6^2 + 0^2] = 6[/tex]

Distance between (2, -2) and (2, 6):

[tex]d = sqrt[(6-(-2))^2 + (2-2)^2] = sqrt[8^2] = 8[/tex]

Distance between (2, 6) and (-4, -2):

[tex]d = sqrt[(-4-2)^2 + (-2-6)^2] = sqrt[(-6)^2 + (-8)^2] = sqrt[36 + 64] = sqrt[100][/tex]= 10

Now we add up the distances:

Perimeter = 6 + 8 + 10 = 24

Therefore, the perimeter of the triangle is 24.

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The rock has an instantaneous velocity of 16 meters per second.

In this problem we need to determine the average velocity of the rock, represented by a secant line, and estimate its instantaneous velocity, represented by a tangent line. The average speed is defined by the following expression:

u = [y(t + Δt) - y(t)] / Δt

Where:

The instantaneous speed is the average speed when Δt ⇒ 0.

Part A

Case I

y(1) = 20 · 1 - 1.87 · 1²

y(1) = 20 - 1.87

y(1) = 18.13 m

y(2) = 20 · 2 - 1.87 · 2²

y(2) = 40 - 7.48

y(2) = 32.52 m

u = (32.52 m - 18.13 m) / 1 s

u = 14.39 m / s

Case II

y(1.1) = 20 · 1.1 - 1.87 · 1.1²

y(1.1) = 19.737 m

u = (19.737 m - 18.13 m) / 0.1 s

u = 16.07 m / s

Case III

y(1.01) = 20 · 1.01 - 1.87 · 1.01²

y(1.01) = 18.292 m

u = (18.292 m - 18.13 m) / 0.01 s

u = 16.2 m / s

Case IV

y(1.001) = 20 · 1.001 - 1.87 · 1.001²

y(1.001) = 18.146 m

u = (18.146 m - 18.13 m) / 0.001 s

u = 16 m / s

And the instantaneous velocity of the rock is approximately 16 meters per second.

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Answer:

Step-by-step explanation:

Let's start by finding the total number of women in the company. We know that 40% of the employees are women, so if we let x be the total number of employees, we can write:

Number of women = 40% of x = 0.4x

Let's then use the given ratio to determine the number of single women in the company. If the ratio of single women to married women is 2:5, we can write:

Number of single women = (2/7) * Number of women = (2/7) * 0.4x = 0.114x

We are also given that there are 30 married women. Since the total number of women is 0.4x, we can write:

Number of married women = 30

0.6x = 30

x = 50

Therefore, there are a total of 50 employees in this company.

SINE OF A TRIANGLE

16/34

The sine of an angle is the opposite divided by the hypotenuse,

In the given triangle, the opposite is the side facing the longest side(hypotenuse)

This will give us the answer 16/34

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We can write the given limits as -

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is the graph of the function f(x) as shown in the image.

We can write the limits as -

{ 1 } -

[tex]$ \lim_{x \to 2^{-} } f(x)[/tex] = 0

{ 2 } -

[tex]$ \lim_{x \to 2^{+} } f(x)[/tex] = -1

{ 3 } -

[tex]$ \lim_{x \to 2 } f(x)[/tex] = -1

Therefore, we can write the given limits as -

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The maximum time that tony can park his car at the garage if he wants to pay less than $8 is 5.6 hours

Let's start by setting up an inequality that represents the situation:

Total cost for parking x hours <= $8

We know that the first hour costs $2.75, and each additional hour or part thereof costs $1.25. So the cost for x hours can be expressed as:

Cost = $2.75 + $1.25 × (x - 1)

Note that we subtract 1 from x because the first hour is already accounted for in the flat fee.

Now we can substitute this expression into the inequality:

$2.75 + $1.25 × (x - 1) <= $8

Simplifying this inequality, we get:

$1.25x <= $7

Dividing both sides by $1.25, we get:

x <= 5.6

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From density, the probability that X>1.6 or X<0.36 is 1 - (0.36 + 0.64) = 0.00.

Density in mathematics is a measure of how much of a certain quantity is contained within a given area or volume. It is defined as the ratio of the mass of the object to the volume of the object.

For example, the density of water is 1 gram per cubic centimeter (1 g/cm3). Density can be used to measure the concentration of a substance in a given area, such as the amount of salt in a given volume of water. Density can also help to identify different substances, such as air, oil, and water. It is an important concept in physics, chemistry, and engineering.

The probability that X>1.6 or X<0.36 is 0.00 because the density function is 0 for values outside the range from 0.36 to 1.6. The density function is a measure of how likely it is for a value of X to be within a certain range, and since the density of X is 0 for values outside the range, the probability of X being outside that range is also 0.

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Answer:

E. none​

Step-by-step explanation:

Let's use algebra to solve the problem:

Let's start by defining some variables. We'll use T for Tim's current age, and M for Mary's current age.

According to the first sentence of the problem, "Tim's age was three-quarters of Mary's age 5 years ago." In other words, we can write:

T - 5 = (3/4)(M - 5)

We can simplify and rearrange this equation to get:

4T - 20 = 3M - 15

4T = 3M + 5

According to the second sentence of the problem, "Tim will be five-sixth of Mary's age in 3 years." In other words, we can write:

T + 3 = (5/6)(M + 3)

Again, we can simplify and rearrange this equation to get:

6T + 18 = 5M + 15

6T = 5M - 3

Now we have two equations with two variables (4T = 3M + 5 and 6T = 5M - 3). We can use these equations to solve for T and M.

Multiplying the first equation by 2, we get:

8T = 6M + 10

Multiplying the second equation by 3, we get:

18T = 15M - 9

We can now solve for M by subtracting the first equation from the second:

10T = 21

T = 2.1

Substituting this value of T into one of the equations (e.g. 4T = 3M + 5), we can solve for M:

4(2.1) = 3M + 5

M = 8.3

Therefore, Tim's current age is 2.1 years and Mary's current age is 8.3 years.

The sum of their ages right now is T + M = 2.1 + 8.3 = 10.4 years.

So the sum of Tim and Mary's ages right now is 10.4 years.

it takes 24 minutes for the rock climber to climb 288 feet.

How to determine?

The correct equation to represent this situation is:

$$\frac{720}{60}m=288$$

Here, we first convert the rate from feet per hour to feet per minute by dividing by 60. Then, we set up the equation where the product of the rate and the time in minutes equals the distance climbed.

Simplifying this equation, we get:

$$12m=288$$

Dividing both sides by 12, we get:

$$m=24$$

Therefore, it takes 24 minutes for the rock climber to climb 288 feet.

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The graph provides a visual representation of the cost of book printing services for each bid, allowing Bruno to easily compare the two options.

To graph the linear equations, we will use the values in the table to plot points on the coordinate plane, and then connect the points to form lines.

For Bid 7:

X y

0 5

3 50

5 80

7 110

10 155

For Bid 8:

X y

0 40

3 70

5 90

7 110

10 140

We can now plot these points on the coordinate plane and connect them to form two lines. Hence we obtain  Graph of Bid 7 and Bid 8

The x-axis represents the number of books, and the y-axis represents the cost. The title of the graph is "Comparison of Bids for Book Printing Services." We can see that Bid 7 is represented by the blue line, while Bid 8 is represented by the orange line.

To create the legend, we can add a key that explains which line represents which bid. For example, we could add a note at the bottom of the graph that says "Blue line: Bid 7, Orange line: Bid 8."

Overall, the graph provides a visual representation of the cost of book printing services for each bid, allowing Bruno to easily compare the two options.

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The given function can also be represented as,

[tex]f(x) =3x^2+6x-24[/tex]  

and

[tex]f(x) =3(x+4)(x-2)[/tex]

A relationship between several inputs and outputs is called a function. Simply described, a function is a relation between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for each function. A function is usually referred to as f(x), where x is the input . Typically, a function is written as y = f. (x).

Given function is ,

[tex]f(x) =3(x+1)^2-27[/tex]

This function can also be expressed as,

[tex]f(x) =3(x+1)^2-27\\\\f(x) =3(x^2+1+2x)-27\\\\f(x) =3x^2+3+6x-27\\\\f(x) =3x^2+6x-24\\\\f(x) =3(x^2+2x-8)\\\\f(x) =3(x^2+(4-2)x-8)\\\\f(x) =3(x^2+4x-2x-8)\\\\f(x) =3(x+4)(x-2)[/tex]

So, the given function can also be stated as,

[tex]f(x) =3x^2+6x-24[/tex]  

and

[tex]f(x) =3(x+4)(x-2)[/tex]

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The equation of the line in point slope form is y + 6 = 3 (x + 3), and the line in slope intercept form is y = 3x + 3.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

We have the points on the line given.

(-3, -6) and (2, 9)

Slope of the line = (9 - -6) / (2 - -3) = 15/5 = 3

Equation of a line in point slope form is,

y - y₁ = m (x - x₁)

where (x₁, y₁) is a point on the line and m is the slope.

Substituting a point (-3, -6) and the slope = 3, we get,

y - -6 = 3 (x - -3)

y + 6 = 3 (x + 3), which is the point slope form.

Equation of a line in slope intercept form is,

y = mx + c

where m is the slope and c is the y intercept.

Substituting m = 3 and (x, y) = (2, 9),

9 = (3 × 2) + c

c = 9 - 6 = 3

Equation in slope intercept form becomes,

y = 3x + 3

Hence the point slope form and slope intercept form of the given line are y + 6 = 3 (x + 3) and y = 3x + 3 respectively.

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Answer:

(0.0301, 0.1733)

Step-by-step explanation:

[tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\\\CI_{98\%}=\biggr(\frac{287}{522}-\frac{233}{520}\biggr)\pm 2.326\sqrt{\frac{\frac{287}{522}(1-\frac{287}{522})}{522}+\frac{\frac{233}{520}(1-\frac{233}{520})}{520}}\\\\\\CI_{98\%}\approx\{0.0300,0.1734\}[/tex]

Hence, the best choice is (0.0301, 0.1733) which tells us that we are 98% confident that the difference between the two proportions of men and women who successfully found Egypt on the map when highlighted is between 0.0301 and 0.1733

Answer:

there are 720 ways to arrange the 7 friends around the circular table at the wedding reception

Step-by-step explanation:

The number of ways to arrange n distinct objects in a circle is (n-1)!, since there are n ways to choose the starting point, and then (n-1)! ways to arrange the remaining objects in a circle.

In this case, we have 7 friends seated around a circular table, so the number of ways to arrange them is:

(7-1)! = 6! = 720

Therefore, there are 720 ways to arrange the 7 friends around the circular table at the wedding reception.

Answer:

720

Step-by-step explanation:

(7-1)! = 6! = 720

Answer: If the new or compared value is P% more than the reference value, you can calculate the reference value as follows:

Reference value = New or compared value / (1 + P/100)

For example, if the new value is 120% of the reference value, then P = 20 and the reference value can be calculated as:

Reference value = New value / (1 + 20/100) = New value / 1.2

If the new or compared value is P% less than the reference value, you can calculate the reference value as follows:

Reference value = New or compared value / (1 - P/100)

For example, if the new value is 80% of the reference value, then P = 20 and the reference value can be calculated as:

Reference value = New value / (1 - 20/100) = New value / 0.8

Step-by-step explanation:

A quadratic equation in standard form to represent the data in the table is as follows;

y = 0.5x² - 4x + 9

In order to determine a quadratic equation in standard form for the line of best fit that models the data points described above, we would use a scatter plot (graphing calculator).

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a quadratic equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the data set, a quadratic equation for the line of best fit is given by:

y = 0.5x² - 4x + 9

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2) The equation of tangent line is,

⇒ y = 324x log 3  + 84 - 648 log 3

3) And, The value of x is,

⇒ x = nπ ± π/6

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

2) The equation of curve is,

y = 3ˣ² + 3

At x = 2

y = 3⁴ + 3

y = 84

Hence, The value of point = (3, 84)

Now, Find dy/dx as;

y = 3ˣ² + 3

dy/dx = 3ˣ² log 3 × 2x

dy/dx = 2x × 3ˣ² log 3

At x = 2

dy/dx = 2 × 2 × 81 × log 3

m = dy/dx = 324 log 3

We know that;

The slope intercept form of equation of line is,

y = mx + c

y = 324x log 3  + c

At point (x, y) = (2, 84)

84 = 324 × 2 log 3 + c

⇒ c = 84 - 648 log 3

Hence, The equation of tangent line is,

⇒ y = 324x log 3  + 84 - 648 log 3

3) We know that;

Horizontal tangent will have a slope of 0.

Hence, The derivative represent the rate of change of a function.

The equation of graph is,

y = 4x - 3 tan x

y' = 4 - 3 sec²x = 0

sec²x = 4/3

sec²x = (2/√3)²

x = nπ ± π/6

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