Find g'(x) for the given function. Then find ​g'(-3),g'(0) ​, and g'(2).

g(x)=√3x

The equation of the line that passes through the points (1,0) and (3,6) is y = 3x - 3.

The formula for equation of line is expressed as:

y = mx + b

Where m is slope and b is the y-intercept.

Given that, the line passes through points  (1,0) and (3,6).

First, we determine the slope:

[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{6 - 0}{3 - 1} \\\\Slope\ m = \frac{6}{2} \\\\Slope\ m = 3[/tex]

Now we plug the  slope m = 3 and one point (1,0)into the point-slope form to find the equation:

( y - y₁ ) = m( x - x₁ )

( y - 0 ) = 3( x - 1 )

y = 3x - 3

Therefore, the equation of the line is y = 3x - 3.

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Answer:

  26.1°

Step-by-step explanation:

You want the value of angle x° in a right triangle that has the side adjacent to x being 53 cm, and the side opposite being 26 cm.

The tangent ratio is ...

  Tan = Opposite/Adjacent

The side opposite the angle is 26 cm; the side adjacent is 53 cm. The ratio of these is ...

  tan(x) = 26/53

The arctangent function is used to find the angle when the tangent is known.

  x = arctan(26/53) ≈ 26.1°

The angle x° is approximately 26.1°.

__

Additional comment

The calculator must be in degrees mode.

<95141404393>

Answer:

{e, 24}

Step-by-step explanation:

U = {a, b, c, d, e, f, 19, 20, 21, 22, 23, 24}

X = {a, b, c, 20, 21, 22}

Y = {b, d, f, 19, 21, 23}

X' ∩ Y' = (X U Y)'

= ({a, b, c, 20, 21, 22} U {b, d, f, 19, 21, 23})'

= ({a, b, c, d, f, 19, 20, 21, 22, 23})'

={e, 24}

Since each child buys a double scoop with 2 flavors and no two children choose the same combination, we can determine the number of children by finding the number of unique flavor combinations possible.

To calculate the number of unique flavor combinations, we can use the concept of combinations without repetition. The formula for this is given by nCr = n! / ((n-r)! * r!), where n is the total number of flavors and r is the number of flavors chosen for each double scoop.

In this case, there are 9 flavors available and each child chooses 2 flavors. Using the formula, we have:

9C2 = 9! / ((9-2)! * 2!) = 9! / (7! * 2!) = (9 * 8) / 2 = 36 / 2 = 18.

Therefore, there are 18 children in the group, as each child can choose from 18 unique flavor combinations without repetition.

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The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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Therefore, BC is equal to 4 cm.

To solve this problem, we can use the Angle Bisector Theorem and the Pythagorean Theorem.

Let's start by applying the Angle Bisector Theorem. According to the theorem, the ratio of the segments of the hypotenuse formed by the altitude is equal to the ratio of the corresponding sides of the triangle.

In triangle ABC, we have:

AD/DB = AC/CB

Given that AD = 8 cm, we need to find DB. Let's denote DB as x.

8/x = AC/CB

Since AC is the altitude, it can be determined by applying the Pythagorean Theorem in right triangle ACH.

AC^2 = AH^2 + HC^2

AC^2 = (AB - BH)^2 + HC^2

AC^2 = (BC - 4)^2 + HC^2

Now, let's apply the Pythagorean Theorem in right triangle BCH.

BC^2 = BH^2 + HC^2

BC^2 = 4^2 + HC^2

Since AC = BC - 4, we can substitute these expressions into the equation:

(BC -4)^2 + HC^2 = BC^2

Expanding and simplifying this equation, we get:

BC^2 - 8BC + 16 + HC^2 = BC^2

Simplifying further, we have:

-8BC + 16 + HC^2 = 0

Now, let's substitute the value of HC = AD - AH = 8 - 4 = 4 into the equation:

-8BC + 16 + 4^2 = 0

-8BC + 16 + 16 = 0

-8BC + 32 = 0

-8BC = -32

BC = -32 / -8

BC = 4

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Answer:

a. 0.9375, 0.46875

b. geometric sequence

c. equation: [tex] 7.5 * (\frac{1}{2})^(n-1)[/tex]

Step-by-step explanation:

a.

The table can be finished as follows:

n t(n)

1 7.5

2 3.75

3. 1.875

4. 0.9375

5 0.46875

b.

The type of sequence is a geometric sequence.

A geometric sequence is a sequence of numbers where the ratio between any two consecutive terms is constant.

In this case, the ratio between any two consecutive terms is 3.75/7.5=½ ,

so the sequence is geometric.

c.

The equation for the sequence is t(n) = 7.5 * (1/2)^n.

This equation can be found by looking at the first term of the sequence (7.5) and the common ratio (1/2).

t(1) = 7.5

t(2) = 7.5 * (1/2) = 3.75

t(3) = 7.5 * (1/2)^2 = 1.875

The equation can also be found by looking at the general formula for a geometric sequence,

which is [tex]t(n) = a*r^{n-1}[/tex]

In this case,

t(n) =[tex] 7.5 * (\frac{1}{2})^{n-1}[/tex]

This is the required equation.

Answer:

[tex]\textsf{a.}\quad \begin{array}{|c|c|c|c|c|c|}\cline{1-6}\vphantom{\dfrac12} n&1&2&3&4&5\\\cline{1-6}\vphantom{\dfrac12}t(n)&7.5&3.75&1.875&0.9375&0.4687\\\cline{1-6}\end{array}[/tex]

[tex]\textsf{b.} \quad \textsf{Geometric sequence.}[/tex]

[tex]\textsf{c.} \quad t(n)=7.5(0.5)^{n-1}[/tex]

Step-by-step explanation:

Before we can complete the table, we need to determine if the sequence is arithmetic or geometric.

To determine if a sequence is arithmetic or geometric, examine the pattern of the terms in the sequence.

Calculate the difference between consecutive terms by subtracting one term from the next:

[tex]t(2)-t(1)=3.75-7.5=-3.75[/tex]

[tex]t(3)-t(2)=1.875-3.75 = -1,875[/tex]

As the difference is not common, the sequence is not arithmetic.

Calculate the ratio between consecutive terms by dividing one term by the previous term.

[tex]\dfrac{t(2)}{t(1)}=\dfrac{3.75}{7.5}=0.5[/tex]

[tex]\dfrac{t(3)}{t(2)}=\dfrac{1.875}{3.75}=0.5[/tex]

As the ratio is common, the sequence is geometric.

To complete the table, multiply the preceding term by the common ratio 0.5 to calculate the next term:

[tex]t(4)=t(3) \times 0.5=1.875 \times 0.5=0.9375[/tex]

[tex]t(5)=t(4) \times 0.5=0.9375 \times 0.5=0.46875[/tex]

Therefore, the completed table is:

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}\vphantom{\dfrac12} n&1&2&3&4&5\\\cline{1-6}\vphantom{\dfrac12}t(n)&7.5&3.75&1.875&0.9375&0.4687\\\cline{1-6}\end{array}[/tex]

To find an equation for the sequence, use the general form of a geometric sequence:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

In this case, the first term is the value of t(n) when n = 1, so a = 7.5

We have already calculated the common ratio as being 0.5, so r = 0.5.

Substitute these values into the formula to create an equation for the sequence:

[tex]t(n)=7.5(0.5)^{n-1}[/tex]

The left-hand side of the equation represents the logarithm of 64 with base x, and it is not possible to find a real value of x that satisfies the equation.

solve the equation logₓ(64) + 5 = 2, we can follow these steps:

Step 1: Move the constant term to the other side of the equation:

logₓ(64) = 2 - 5

logₓ(64) = -3

Step 2: Rewrite the equation in exponential form:

x^(-3) = 64

Step 3: Rewrite 64 as a power of x:

x^(-3) = x^6

Step 4: Set the exponents equal to each other:

-3 = 6

The equation -3 = 6 is not true, which means there is no real solution to the given equation.

Therefore, the equation logₓ(64) + 5 = 2 has no solution in the real number system.

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The triangles are congruent because of S.A.A

Congruent triangles are triangles having corresponding sides and angles to be equal. This means that for two triangles to be congruent, the corresponding angles must be equal and the corresponding sides must also be equal.

In the triangles the corresponding angles are equal.

In triangle ABC, the third angle is calculated as;

180-(90+30)

= 180-120

= 60°

I'm triangle DCE, the third angle is calculated as;

180-(90+30)

= 180-120

= 60°

Therefore the two triangles are congruent because the corresponding angles are equal.

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To find the rate at which the light projected onto the wall is moving along the wall, we can use trigonometry and calculus. Let's denote the angle between the rotating light and the wall as θ.

Given:

Distance from the light to the wall, r = 15 feet

Rate of rotation, dθ/dt = 1 rotation every 4 seconds

We need to find the rate at which the light's projection moves along the wall, which is represented by dx/dt.

Using trigonometry, we know that the tangent of the angle θ is equal to the ratio of the distance along the wall (dx) to the distance from the light to the wall (r).

tan(θ) = dx / r

Differentiating both sides of the equation with respect to time t, we get:

sec^2(θ) * dθ/dt = dx/dt

Since we are given that the angle θ is 15 degrees, we can substitute the values and solve for dx/dt.

sec^2(15°) * (1 rotation / 4 seconds) = dx/dt

Simplify and calculate the value to find the rate at which the light's projection moves along the wall in feet per second.

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The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

If Delaware was proportional to Alabama in enrollment to the district, it would have approximately 37 districts.

The ratio of students to districts in Alabama is 630,683/137 = 4,603 students per district. If Delaware had the same ratio of students to districts, it would have 120,475/4,603 = 26.16 districts. Rounding to the nearest whole number, Delaware would have approximately 26 districts if it was proportional to Alabama in enrollment to the district.

The time taken for 1414 people to paint 14 walls is 6,430.44 minutes.

To find out how many minutes it would take 1414 people to paint 14 walls, we can use the information given to find the ratio.

We know that it takes 9 people 41 minutes to paint 9 walls.

Let's find the ratio:

(9 people) : (1414 people) = (41 minutes) : (x minutes)

Use the mutual multiplication property of the resulting ratio:

9 * x = 1414 * 41

Right simplification:

9x = 57974

To solve this problem, create a ratio using the information provided:

(9 people) : (1414 people) = (41 minutes) : (x minutes)

We can multiply the ratios:

9 * x = 1414 * 41

On the right side of the equation, calculate the product of 1414 and 41, which equals 57974.

4 444 So:

444 9x = 57974 To separate

4 share both sides of the equation with 9:

4 x = 57974/9

share both sides with 9:

4 x = 6430.44

It will take 6,430.44 minutes for 1,414 people to paint 14 walls.

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These lines are not sufficient for me to evaluate their content and determine their truthfulness or accuracy.

In order to provide a meaningful response, I would need you to provide the specific lines or statements you would like me to evaluate.

However, I can assure you that as an AI language model, I generate responses based on the data I have been trained on up until September 2021. I do not have real-time information or access to the internet to verify the accuracy of specific statements made after that time.

I generate responses based on patterns and information from the training data, but I do not copy content from specific sources without attribution.

However, if you copy and paste any responses I provide without proper attribution, that would be considered plagiarism.

It is always important to provide proper citations and references when using information from any source, including AI-generated content.

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The element of A n B is { 7, 8}

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind.

For example, if the element of P is even numbers from 1 to 20 and element of Q is factor of 6 from 1 to 20 then we can say that set Q is a subset of set P.

The sign 'n' means intersection and this means what is common to two or more set.

If set A = { 1,2,5,7,8}

set B = { 6,7,8,9}

then we can see that 7 and 8 are common to both sides, then

A n B = { 7,8}

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Answer:

24 u jus gotta multiply by 3 cuz it is 1 out of 3

Step-by-step explanation: hi :)

The roster method of the set A' = {14, 15, 20}

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

A typical example of the roster method is to write the set of numbers from 1 to 5 as {1, 2, 3, 4, 5}.

Therefore,

U = universal sets = {14, 15, 16, 17, 18, 19, 20}

A = {16, 17, 18, 19}

Therefore, let's find A' as follows:

A' is the value not in A. Hence, in roster method.

A' = {14, 15, 20}

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The rest of the amount, represented by R, is $2000 in this case.

If the total amount is $3000 and a certain amount, c, is deposited in one investment, we can represent the remaining amount in dollars by subtracting the deposited amount from the total.

Let's denote the remaining amount as R.

R = Total amount - Deposit amount

R = $3000 - c

Here, R represents the rest of the amount in dollars after the deposit of c dollars. By subtracting the deposit amount from the total amount, we can determine the value of the remaining amount.

For example, if $1000 is deposited in one investment (c = $1000), we can find the remaining amount as follows:

R = $3000 - $1000

R = $2000

Therefore, the rest of the amount, represented by R, is $2000 in this case.

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The total cost of membership for both Club A and Club B will be the same, amounting to $74.

To determine after how many months the total cost of each health club will be the same, we can set up an equation where the total cost of Club A is equal to the total cost of Club B.

Let's assume the number of months is represented by 'm'. The total cost of Club A after 'm' months can be calculated as:

Total Cost of Club A = $18 + $14m

Similarly, the total cost of Club B after 'm' months can be calculated as:

Total Cost of Club B = $26 + $12m

We want to find the value of 'm' where the total costs are equal, so we can set up the following equation:

$18 + $14m = $26 + $12m

Now, we can solve this equation for 'm':

$14m - $12m = $26 - $18

$2m = $8

m = $8 / $2

m = 4

Therefore, after 4 months, the total cost of each health club will be the same.

To find the total cost for each club after 4 months, we substitute 'm' into the total cost equations:

Total Cost of Club A = $18 + $14(4) = $18 + $56 = $74

Total Cost of Club B = $26 + $12(4) = $26 + $48 = $74

So, the total cost for each club after 4 months will be $74.

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(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.

(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.

(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.

(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.

Similar triangles have the same corresponding angle measures and proportional side lengths.

The triangle similarity criteria are:

(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.

12/8 = 9/6

1.5 = 1.5

(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.

(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.

14/10 = 21/15

1.4 =

(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.

SMK = 90⁰, 60⁰, 30⁰

QTR =  90⁰, 30⁰, 60⁰

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a. The vertical shift of the graph of G(x) compared to the graph of F(x) is an upward shift of 1 unit.

b. The vertical shift of the graph of G(x) compared to the graph of F(x) is an upward shift of 1 unit, while there is no horizontal shift between the two graphs.

In the functions G(x) = 2^(-x) and F(x) = 2^x:

Vertical Shift:

The vertical shift refers to the movement of a graph up or down along the y-axis. In this case, comparing G(x) = 2^(-x) to F(x) = 2^x, there is a vertical shift present.

The graph of F(x) = 2^x has its vertex (the lowest point of the graph) at the point (0, 1) on the coordinate plane.

The graph of G(x) = 2^(-x) is obtained by reflecting the graph of F(x) about the x-axis. This reflection results in a vertical shift of the graph. The graph of G(x) will have its vertex (the highest point of the graph) at the point (0, 1).

Therefore, the vertical shift of the graph of G(x) compared to the graph of F(x) is an upward shift of 1 unit.

Horizontal Shift:

The horizontal shift refers to the movement of a graph left or right along the x-axis. In this case, comparing G(x) = 2^(-x) to F(x) = 2^x, there is no horizontal shift present.

Both G(x) = 2^(-x) and F(x) = 2^x have their graphs centered at the y-axis, passing through the point (0, 1). Therefore, there is no horizontal shift between the two functions.

To summarize, the vertical shift of the graph of G(x) compared to the graph of F(x) is an upward shift of 1 unit, while there is no horizontal shift between the two graphs.

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The following question may be like this:

Consider the functions G(x) = 2^(-x) and F(x) = 2^x.

State the vertical shift of the graph of G(x) compared to the graph of F(x).

State the horizontal shift of the graph of G(x) compared to the graph of F(x). explain

The statement "there exists x ∈ S ∖ m" means that there exists an element x that belongs to the set S but does not belong to the set m. In other words, x is an element that is present in S but is not present in m.

The phrase "m ⊊ m ∪ {x} ∈ X" states that the set m is a proper subset of the set m ∪ {x}, and this union belongs to the set X. This implies that the set m ∪ {x} contains all the elements of m along with the additional element x.

The phrase "a contradiction" indicates that the statement or assumption being made leads to a logical inconsistency or contradiction. In this context, the contradiction arises from the fact that the assumption that x is not in m contradicts the statement that m ∪ {x} is a proper superset of m.

Overall, the given statement implies that the existence of an element x in S, which is not in m, leads to a contradiction when considering the relationship between m and m ∪ {x}.

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The absolute extrema of the function f(x) = 6[tex]x^4[/tex] - 8[tex]x^3[/tex] on the closed interval (-∞, ∞) are: the minimum value of -2 at x = 1 and no maximum value.

To find the absolute extrema of the function f(x) = 6[tex]x^4[/tex]- 8[tex]x^3[/tex] on a closed interval, we need to evaluate the function at its critical points and endpoints and compare their values.

The critical points occur where the derivative of the function is equal to zero or undefined. Let's find the derivative of f(x) first. Taking the derivative of f(x) = 6[tex]x^4[/tex] - 8[tex]x^3[/tex], we get f'(x) = 24[tex]x^3[/tex] - 24[tex]x^2[/tex].

Setting f'(x) equal to zero, we have 24[tex]x^3[/tex] - 24[tex]x^2[/tex] = 0. Factoring out 24[tex]x^2[/tex]from the equation, we get 24[tex]x^2(x - 1)[/tex] = 0. This equation is satisfied when x = 0 or x = 1.

Now we evaluate the function at these critical points and the endpoints of the interval. The given interval is not specified, so we'll assume it as the entire real number line (-∞, ∞).

For x = 0, f(0) = 6[tex](0)^4[/tex] - 8[tex](0)^3[/tex] = 0.

For x = 1, f(1) = 6[tex](1)^4[/tex] - 8[tex](1)^3[/tex] = -2.

Since the function is a fourth-degree polynomial, it approaches negative infinity as x approaches negative infinity and approaches positive infinity as x approaches positive infinity.

Therefore, the absolute extrema of the function f(x) = 6[tex]x^4[/tex] - 8[tex]x^3[/tex] on the closed interval (-∞, ∞) are: the minimum value of -2 at x = 1 and no maximum value.

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Answer:

Domain: x [tex]\geq[/tex] -5

Range: y [tex]\geq[/tex] -3

Step-by-step explanation:

The domain is all the possible inputs or x value.  x will be greater than -5.

The range is all of the possible outputs or y value.   y will be greater than -3

Answer:

Domain:  [-5, ∞)

Range:  [-3, ∞)

Step-by-step explanation:

The given graph shows a continuous curve with a closed circle at the left endpoint (-5, -3) and an arrow at the right endpoint.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

The domain of a function is the set of all possible input values (x-values).

As the leftmost x-value of the curve is x = -5, and it continues indefinitely in the positive direction, the domain of the  graphed function is:

The range of a function is the set of all possible output values (y-values).

From observation, it appears that the minimum y-value of the curve is y = -3. The curve continues indefinitely in the positive direction in quadrant I. Therefore, the range of the graphed function is:

Answer:

[tex]\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66[/tex]

Step-by-step explanation:

[tex]\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta[/tex]

[tex]\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66[/tex]

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Answer: 4 pages

Step-by-step explanation:

To solve this problem, we need to use the formula:

Rate = Output/Time

Let's use "p" to represent the number of pages Ethan can type and "t" to represent the time he has before the meeting starts.

Rate = 2 pages/(1/8 hour) = 16 pages/hour

Since the meeting starts 3/4 hour later than the scheduled time, Ethan has t = 1 - 3/4 = 1/4 hour to type pages before the meeting starts.

Output = Rate * Timep = (16 pages/hour) * (1/4 hour) = 4 pages

Therefore, Ethan can type 4 pages before the meeting starts.

Answer: 4 pages

Q1- The annual depreciation for the equipment is $2,000.

Q2- The book value of the equipment at the end of Year 3 is $6,500.

Q1: What is the annual depreciation for the equipment?

To calculate the annual depreciation, we need to determine the difference between the initial value and the salvage value, and divide it by the number of years.

Initial value = $12,500

Salvage value = $2,500

Number of years = 5

Annual depreciation = (Initial value - Salvage value) / Number of years

= ($12,500 - $2,500) / 5

= $10,000 / 5

= $2,000

Therefore, the annual depreciation for the equipment is $2,000.

Q2: What is the book value of the equipment at the end of Year 3?

The book value of the equipment at the end of a specific year can be calculated by subtracting the accumulated depreciation from the initial value.

Initial value = $12,500

Annual depreciation = $2,000

Number of years = 3

Accumulated depreciation = Annual depreciation * Number of years

= $2,000 * 3

= $6,000

Book value at the end of Year 3 = Initial value - Accumulated depreciation

= $12,500 - $6,000

= $6,500

Therefore, the book value of the equipment at the end of Year 3 is $6,500.

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Answer:

D. √3

Step-by-step explanation:

The tangent ratio is given by:

tan (θ) = opposite/adjacent, where

Thus, we plug in 8√3 for the opposite side and 8 for the adjacent side, which gives us:

tan (60) = (8√3) / 8

Thus reduces down to √3 so D. is the correct answer.