(q6) A student wants to find the area of the surface obtained by rotating the curve
, about the x-axis. Which of the following gives the correct area?

This is the Law of Cosines, which relates the Lengths of the sides of a triangle to the cosine of one of its angles.CD² = AC² + (b - x)² - 2 * AC * (b - x) * (sin(ABD) / sin(ACD))

To derive the Law of Cosines, follow these steps:

Step 1: Consider the triangle AABD, where A and B are vertices and AB is the side opposite the angle ABD.

Apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:

AB² = AD² + BD²

Step 2: Now, consider the triangle ACBD, where C is another vertex and AC is the side opposite the angle ACD.

Apply the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all sides and angles in the triangle. In this case, we have:

AC / sin(ACD) = BD / sin(ABD)

Rearrange the equation to isolate AC:

AC = (BD / sin(ABD)) * sin(ACD)

Step 3: Notice that BD = b - x, where b is the length of AB and x is the length of CD.

Substitute this expression for BD in the equation from step 2:

AC = ((b - x) / sin(ABD)) * sin(ACD)

Step 4: Square both sides of the equation obtained in step 3:

AC² = ((b - x) / sin(ABD))² * sin²(ACD)

Step 5: Recall that sin²(ACD) = 1 - cos²(ACD). Substitute this expression in the equation from step 4:

AC² = ((b - x) / sin(ABD))² * (1 - cos²(ACD))

Step 6: Rearrange the equation to isolate cos²(ACD):

cos²(ACD) = 1 - (AC² / ((b - x) / sin(ABD))²)

Step 7: Simplify the equation:

cos²(ACD) = 1 - AC² / (b - x)² * (sin(ABD) / sin(ACD))²

Step 8: Finally, recall that cos²(ACD) = 1 - sin²(ACD) = 1 - (CD / AC)². Substitute this expression in the equation from step 7:

1 - (CD / AC)² = 1 - AC² / (b - x)² * (sin(ABD) / sin(ACD))²

Rearrange the equation to obtain the Law of Cosines:

CD² = AC² + (b - x)² - 2 * AC * (b - x) * (sin(ABD) / sin(ACD))

This is the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

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Answer:

B. 14,525

Step-by-step explanation:

If a tablet costs $35 and the school is purchasing tablets for every student, then the total cost to buy tablets for the whole school would be:

$35 x 415 = $14,525

Therefore, the answer is B. $14,525.

To set up the amortization table, we can use the mortgage and interest formulas as follows:

Mortgage formula:

M = P [ i(1 + i)^n / (1 + i)^n - 1]

where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (APR divided by 12), and n is the total number of payments (20 years multiplied by 12 months per year).

Interest formula:

I = P * i

where I is the monthly interest payment, P is the remaining principal balance, and i is the monthly interest rate.

Using these formulas, we can set up the following amortization table for the first two months:

Month Payment Principal Interest Balance

1    $400,000

2    

To fill in the table, we need to calculate the monthly payment (M) and the monthly interest payment (I) for the first month, and then use these values to calculate the principal payment for the first month. We can then subtract the principal payment from the initial balance to get the balance for the second month, and repeat the process to fill in the remaining columns.

To calculate the monthly payment (M), we can use the mortgage formula:

M = P [ i(1 + i)^n / (1 + i)^n - 1]

where P is the principal amount, i is the monthly interest rate, and n is the total number of payments.

Plugging in the given values, we get:

M = 400,000 [ 0.00279 (1 + 0.00279)^240 / (1 + 0.00279)^240 - 1]

M = $2,304.14

Therefore, the monthly payment is $2,304.14.

To calculate the interest payment for the first month, we can use the interest formula:

I = P * i

where P is the remaining principal balance and i is the monthly interest rate.

Plugging in the values for the first month, we get:

I = 400,000 * 0.00279

I = $1,116.00

Therefore, the interest payment for the first month is $1,116.00.

To calculate the principal payment for the first month, we can subtract the interest payment from the monthly payment:

Principal payment = Monthly payment - Interest payment

Principal payment = $2,304.14 - $1,116.00

Principal payment = $1,188.14

Therefore, the principal payment for the first month is $1,188.14.

To calculate the balance for the second month, we can subtract the principal payment from the initial balance:

Balance = Initial balance - Principal payment

Balance = $400,000 -$1,188.14

Balance = $398,811.86

Therefore, the balance for the second month is $398,811.86.

Using these values, we can complete the first two rows of the amortization table as follows:

Month Payment Principal Interest Balance

1 $2,304.14 $1,188.14 $1,116.00 $398,811.86

2    

To fill in the remaining columns for the second month, we can repeat the process using the new balance of $398,811.86 as the principal amount for the second month. We can calculate the interest payment using the same method as before, and then subtract the interest payment from the monthly payment to get the principal payment. We can then subtract the principal payment from the balance to get the new balance for the third month, and repeat the process for the remaining months of the amortization period.

Answer:

[tex]y=-\frac{4}{5}x-\frac{21}{5}[/tex]

Step-by-step explanation:

The fastest way is to use point-slope form with [tex]m=-\frac{4}{5}[/tex] and [tex](x_1,y_1)=(-4,-1)[/tex]:

[tex]y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}[/tex]

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

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

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

     |

     |

     |     *

     |    /

     |   /

     |  /

-----*--------

     |

     |

     |

     |

     |

The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

The reconciled balance is $600.13.

Answer:

-----------------------

Substitute 12 and 24 for n into formula and calculate.

So, the 12th term is 63 and 24th term is 123.

The set of all functions from X to Y, mathematicians can explore the relationships and Transformations between different sets.

"The set of all functions from X to Y" refers to the collection or group of all possible functions that can be defined from the set X to the set Y. In mathematics, a function is a relation between two sets, where each element in the first set (X) is associated with a unique element in the second set (Y).

When we talk about the set of all functions from X to Y, we are considering all the different ways in which elements from X can be mapped or related to elements in Y. Each function within this set represents a distinct mapping or correspondence between the elements of X and Y.

The set of all functions from X to Y can be denoted as F(X, Y) or sometimes written as Y^X, emphasizing that it represents the power set or the collection of all possible functions from X to Y.

The elements of this set are individual functions, where each function takes an input from X and produces an output in Y. These functions can have various properties, such as being continuous, differentiable, or having specific algebraic expressions.

By considering the set of all functions from X to Y, mathematicians can explore the relationships and transformations between different sets. This concept plays a fundamental role in various branches of mathematics, including analysis, algebra, topology, and more. It provides a framework for studying functions and their properties, enabling deeper insights into mathematical structures and their interconnections.

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Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis.

We are given Pentagon ABCDE, with vertices A (-4,-2) , at B(-6,-3) at C (-5,-6), at D (-2,-5) at E (-2,-3)

and the pentagon A'B'C'D'E' with vertices as:

A'(3,1) , B'(1,2) , C'(2,5) , D'(5,4) and E'(5,2).

Clearly we could observe that the image is formed by the translation and reflection of the pentagon ABCDE.

First the Pentagon is translated by the rule:

(x,y) → (x+7,y+1) so that the pentagon is shifted to the fourth coordinate  and then it is reflected across the x-axis to get the transformed figure in the first coordinate plane as Pentagon A'B'C'D'E'.

Hence, translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis.

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"Your question is incomplete, probably the complete question/missing part is:"

Pentagon ABCDE and pentagon A'B'C'D'E' are shown on the coordinate plane below:

Pentagon ABCDE and pentagon A prime B prime C prime D prime E prime on the coordinate plane with ordered pairs at A negative 5,

Which two transformations are applied to pentagon ABCDE to create A'B'C'D'E'?

Translated according to the rule (x, y) →(x + 8, y + 2) and reflected across the y-axis.

Translated according to the rule (x, y) →(x + 2, y + 8) and reflected across the x-axis.

Translated according to the rule (x, y) →(x + 2, y + 8) and reflected across the y-axis.

Translated according to the rule (x, y) →(x + 8, y + 2) and reflected across the x-axis.

The Probabilities are:

1. 3/10, 0.3, 30%

2. 7/10, 0.7, 70%

3. 9/10, 0.9, 90%

4. 1/10, 0.1, 10%

From the data,

Total people = 20

Number of Female Candidate = 6

Number of Male Candidate = 6

1. Probability of Women could win

= 6/20

= 3/10

In decimal = 0.3

In Percentage = 30%

2. Probability of Men could win

= 14/20

= 7/10

In decimal = 0.7

In Percentage = 70%

3. Probability of Democrat win

= 18/20

= 9/10

In decimal = 0.9

In Percentage = 90%

4. Probability of Republican win

= 2/20

= 1/10

In decimal = 0.1

In Percentage = 10%

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The points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane.

To prove that the points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane, we need to show that the distances between these points are equal.

Let's calculate the distances between the points using the distance formula:

Distance between 2 and -1+i√3:

d₁ = |2 - (-1+i√3)|

= |3 - i√3|

= √(3² + (√3)²)

= √(9 + 3)

= √12

= 2√3

Distance between -1+i√3 and -1-i√3:

d₂ = |-1+i√3 - (-1-i√3)|

= |-1+i√3 + 1+i√3|

= |2i√3|

= 2√3

Distance between -1-i√3 and 2:

d₃ = |-1-i√3 - 2|

= |-3 - i√3|

= √((-3)² + (√3)²)

= √(9 + 3)

= √12

= 2√3

We have shown that the distances between the three pairs of points are all equal to 2√3.

Therefore, the points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane.

To find the length of a side of this equilateral triangle, we can take any of the distances calculated above. In this case, each side of the triangle has a length of 2√3.

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Since a kite is a quadrilateral, it has the value of 360 total degrees.

To calculate the number of different CD-Rs that the computer user can create with 15 songs from the available 35 songs, we need to calculate the number of permutations.

The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items taken at a time.

In this case, the computer user has 35 songs available, and they want to create a CD-R with 15 songs.

Number of permutations = 35P15 = 35! / (35 - 15)!

Calculating this:

35! / (35 - 15)! = (35 * 34 * 33 * ... * 21) / 15!

However, the factorial calculation for 35! / 15! is extensive and can be challenging to compute directly. Instead, we can simplify the expression using cancelations:

35! / (35 - 15)! = (35 * 34 * 33 * ... * 21) / (15 * 14 * 13 * ... * 1)

Many terms will cancel out:

(35 * 34 * 33 * ... * 21) / (15 * 14 * 13 * ... * 1) = 35 * 34 * 33 * ... * 21

Now, we can calculate the simplified expression:

35 * 34 * 33 * ... * 21 ≈ 5.0477859e+19

Therefore, the computer user can create approximately 5.0477859e+19 different CD-Rs with 15 songs from the available 35 songs.

Answer:The correct graph for the given system of equations is:

graph of two lines, one with a positive slope and one with a negative slope, that intersect at the point negative 1, 1 with text on graph that reads One Solution -1, 1.

Step-by-step explanation:

The equation of the absolute value function set on Cartesian plane is f(x) = - |(1 / 2) · x|.

In this problem we need to find the equation behind the representation of an absolute value function on Cartesian plane, whose definition is shown below:

f(x) = - |m · x + b|

Where:

First, determine the slope of the absolute value:

m = (1 - 0) / (2 - 0)

m = 1 / 2

Second, find the intercept of the function:

b = 0

Third, define the absolute value function:

f(x) = - |(1 / 2) · x|

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The simplified form of[tex]-6ru^2 -ur^2 - 22u^2r^2[/tex]is [tex]-u^2(7r + 22r^2)[/tex].

To simplify the expression[tex]-6ru^2 -ur^2 - 22u^2r^2[/tex], we can combine like terms and factor out common factors.

First, let's look at the variables r and u separately:

For r:

We have terms[tex]-6ru^2[/tex] and [tex]-ur^2.[/tex] We can factor out r from these terms:

[tex]r(-6u^2 - u^2)\\r(-7u^2)[/tex]

For u:

We have term[tex]-22u^2r^2[/tex]. We can factor out[tex]u^2[/tex]from this term:

[tex]u^2(-22r^2)[/tex]

Combining the simplified terms for r and u, we get:

[tex]r(-7u^2) + u^2(-22r^2)[/tex]

Now, we can factor out the common factor of[tex]-u^2[/tex]:

[tex]u^2(7r + 22r^2)[/tex]

Therefore, the simplified expression is[tex]-u^2(7r + 22r^2)[/tex] .

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Insufficient funding creates systemic barriers that hinder service providers from delivering services at the desired level of quality, accessibility, and effectiveness.

Lack of funds indicates a lack of financial resources to fully provide the tools, materials, and infrastructure required to offer services. This may lead to a lack of necessary equipment, resources, or technology needed to deliver effective and efficient services.

Lack of funds frequently results in understaffing or the inability to recruit and retain a sufficient pool of qualified workers. Overloading current employees due to insufficient personnel numbers can result in increasing workloads, burnout, and decreased productivity.

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Answer:

A. z+50

Step-by-step explanation:

Friday => z visitors

Saterday => z+100 visitors

sunday => (z visitors + z+100 visitors) /2 = (z+z+100)/2 = (2z+100)/2 =
2z/2 + 100/2 = z+50  

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

To determine which set of side measurements could form a triangle, we need to check if the sum of the lengths of the two shorter sides is greater than the length of the longest side. This is known as the Triangle Inequality Theorem.

Let's check each set of side measurements:

13, 19, 7:

The sum of the two shorter sides is 7 + 13 = 20, which is greater than the longest side (19). Therefore, this set of side measurements could form a triangle.

25, 12, 13:

The sum of the two shorter sides is 12 + 13 = 25, which is equal to the longest side (25). Therefore, this set of side measurements could form a triangle.

18, 2, 24:

The sum of the two shorter sides is 2 + 18 = 20, which is greater than the longest side (24). Therefore, this set of side measurements could form a triangle.

3, 1, 5:

The sum of the two shorter sides is 1 + 3 = 4, which is less than the longest side (5). Therefore, this set of side measurements could not form a triangle.

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

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The graph of the function f(x) = (2)ˣ is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = (2)ˣ

The above function is an exponential function that has been transformed as follows

Initial value = 1

Growth factor = 2

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

Step-by-step explanation:

To determine which man had the more extreme height, we can calculate the z-scores for both individuals and compare their values. The z-score indicates how many standard deviations a particular value is from the mean.

For the tallest man with a height of 247 cm, we can calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (247 cm), μ is the mean (175.97 cm), and σ is the standard deviation (7.46 cm).

z = (247 - 175.97) / 7.46 ≈ 9.50

For the shortest man with a height of 122.8 cm, we can calculate the z-score using the same formula:

z = (x - μ) / σz = (122.8 - 175.97) / 7.46 ≈ -7.14

The z-score for the tallest man is approximately 9.50, and the z-score for the shortest man is approximately -7.14.

Since the z-score measures how many standard deviations a value is from the mean, the man with the z-score of 9.50 (the tallest man) has the more extreme height. A higher z-score indicates a more extreme deviation from the mean.

Answer:

16

Step-by-step explanation:

find volume of pool

(multiply everything together)

since each otter needs 30 m^3 of space, divide the volume by 30

answer comes to 16.8. however since we can't put 0.8 of an otter in the pool, you round down to 16

A. For the function f(x) = -2x³ - x² + 5x - 1:

- Degree: The degree of a polynomial is the highest power of the variable. In this case, the degree is 3 since the highest power of x is ³ (cubed).

- Leading coefficient: The leading coefficient is the coefficient of the term with the highest power. In this case, the leading coefficient is -2.

- Constant: The constant term is the term without a variable. In this case, the constant term is -1.

B. For the function g(x) = 3(x + 2)(x - 4):

- Degree: The degree of a polynomial is determined by the highest power of the variable. In this case, the degree is 2 since the highest power of x is ² (squared).

- Leading coefficient: The leading coefficient is the coefficient of the term with the highest power. In this case, the leading coefficient is 3.

C. For the function f(x) = -x² + 5x + 3:

- Degree: The degree of a polynomial is determined by the highest power of the variable. In this case, the degree is 2 since the highest power of x is ² (squared).

- Leading coefficient: The leading coefficient is the coefficient of the term with the highest power. In this case, the leading coefficient is -1.

- Constant: The constant term is the term without a variable. In this case, the constant term is 3.

D. For the function f(x) = 3x⁵ - x¹⁰:

- Degree: The degree of a polynomial is determined by the highest power of the variable. In this case, the degree is 10 since the highest power of x is ¹⁰ (tenth power).

- Leading coefficient: The leading coefficient is the coefficient of the term with the highest power. In this case, the leading coefficient is 3.

- Constant: The constant term is the term without a variable. In this case, there is no constant term (it is 0).

Answer:

50 people

Step-by-step explanation:

After removing the people who liked neither, we are left with,

320 - 72 = 248

now, out of these 248, 196 like cats

248 - 196 = 52 so 52 dont like cats

also, 102 like dogs so 248 - 102 = 146

so 146 dont like cats

these 146 cannot be included in liking both

similarly the 52 cannot be included in liking both

so we are left with 248 - 52 - 146 = 50

so 50 people like both cats and dogs

There are two elements in A' ∩ B.

The given sets are: U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 4, 5}, B = {1, 3, 5, 7}To find the number of elements in A' ∩ B, we first need to find the complement of A,

which is the set of all elements that are not in A.Complement of A: A' = {3, 6, 7}

Now, we need to find the intersection of A' and B.Intersection of A' and B: A' ∩ B = {3, 7}

Therefore, there are two elements in A' ∩ B, which are 3 and 7.

To summarize, we have U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 4, 5}, and B = {1, 3, 5, 7}. The complement of A is A' = {3, 6, 7}.

The intersection of A' and B is A' ∩ B = {3, 7}.

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Based on the information we can infer that the pool cover costs: $1568.25

To find the price of the pool cover we must take into account the pool area. In this case, being an irregular polygon, we must divide it into regular polygons to find its area.

According to the above, the pool area is 697 square meters. So the value of the cover would be:

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Answer:

2m - 72

Step-by-step explanation:

2x Malik's age = 2 × m, m represents his age because it is unknown

72 less means -72

Answer:
Final Price: $318.50
You save: $136.50

Step-by-step explanation:

To find the discount for a $455 designer purse that is on sale for 30% off, we can follow these steps:

Step 1: Calculate the discount amount

Discount Amount = Original Price * Discount Percentage

= $455 * 30% = $455 * 0.3 = $136.50

Step 2: Calculate the final price after the discount

Final Price = Original Price - Discount Amount

= $455 - $136.50 = $318.50

The discount for the $455 designer purse that is on sale for 30% off is $136.50. The final price after the discount is $318.50.

Answer:

Step-by-step explanation:

Discount: subtract the percentage from the sale price:

$455.00 x 30% = $136.50

then you subtract the amount $136.50 from the original price of $455.00 = $318.50  The customer will pay $318.50 because a discount was for 30% off from the original price.

Answer:

x = 130°

Step-by-step explanation:

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

x is an exterior angle of the triangle , then

x = 40° + 90° = 130°

Answer: Your answer is 130

Step-by-step explanation: 40 degrees (bottom right) + 90 degrees (bottom left) = 130 degrees which is the answer.

Hope it helped :D