Set up, but do not evaluate, the integral for the surface area of the solid cotained by rotating the curve y=4xe−8x on the interval 2≤x≤4 about the line x=−3, Set up, but do not evaluate, the integral for the surface area of the solid obtained by rotating the curve y=4xe−3x on the interval 2≤x s 44 about the line y=−3.

Answer: To find the capacity of the tin can, we can use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length is 5 cm, the width is 4 cm, and the height is 15 cm. So the volume of the tin can is 5 x 4 x 15 = 300 cubic cm.

To find the capacity of the plastic cylinder, we can use the formula for the volume of a cylinder, which is pi x radius squared x height. The diameter of the circular base is 7 cm, so the radius is half of that, or 3.5 cm. So the volume of the plastic cylinder is pi x (3.5 cm)^2 x 10 cm = 385.4 cubic cm.

So the plastic cylinder has a greater capacity by 385.4 - 300 = 85.4 cubic cm.

Step-by-step explanation:

The two towns are distance 60 miles apart in the real world if they are 3 inches apart on a map with a scale of 1 inch to 20 miles.

60 miles

1 inch = 20 miles

3 inches = 20 miles x 3 = 60 miles

The scale of a map is a way of expressing the relationship between the distances on the map and the actual distances in the world. If the scale on a map is 1 inch to 20 miles then it means that 1 inch on the map represents 20 miles in the real world. If two towns are 3 inches apart on the map, then this means that the actual distance between them is 3 times the scale, or 3 x 20 miles = 60 miles.

The two towns are 60 miles apart in the real world if they are 3 inches apart on a map with a scale of 1 inch to 20 miles.

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The 8 quadratic formulas are essential for solving quadratic equations. They are derived from the quadratic equation, which is expressed as ax² + bx + c = 0. The 8 quadratic formulas are:

1. Standard Quadratic Formula: x = [-b ± √(b² - 4ac)]/2a

2. Quadratic Formula for Negative Discriminant: x = [-b/2a] ± i√(-b² - 4ac)/2a

3. Quadratic Formula for Zero Discriminant: x = -b/2a

4. Quadratic Formula for One Real Root: x = -2c/b

5. Quadratic Formula for Two Real Roots: x = [-b ± √(b² + 4ac)]/2a

6. Quadratic Formula for Two Identical Real Roots: x = -b/a

7. Quadratic Formula for Two Imaginary Roots: x = [-b/2a] ± √(-b² + 4ac)/2a

8. Quadratic Formula for One Imaginary Root: x = [-b/2a] ± i√(b² + 4ac)/2a

By understanding these formulas, it's possible to solve for any unknowns in a quadratic equation.

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Answer: The perimeter of a rectangle is the sum of the lengths of its four sides which is given by the expression: P = 2l + 2w (where l is the length and w is the width)

The expression that does not show this relationship is P = l + w

It doesn't show the relationship because it doesn't take into account the two sides that are equal to the width and the two sides that are equal to the length.

P = 2l + 2w shows the relationship as it considers both length and width of the rectangle twice, once for each pair of sides.

Step-by-step explanation:

The rider has 141 laps left to finish the race.

If a rider has already cycled 4.75 km, and each lap measures 0.25 km, we can determine how many laps the rider has completed by dividing the distance already cycled by the distance per lap.

To find out how many laps the rider has left to finish the race, we will use the information on the total number of laps to complete the race: 160 laps.

The rider has completed:

4.75 km / 0.25 km = 19 laps

The rider has yet to finish:

160 laps - 19 laps = 141 laps

So the rider has 141 laps left to finish the race.

Therefore, the rider has 141 laps left to finish the race.

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Answer

-17

Step-by-step explanation:

5 times -17= -85 and then add 5 = -80

The response to claim A and Claim B on potential energy being stored in  a magnet in terms of the given options is that;

Claim A; I think So

Claim B; Definitely Not

Claim A; This claim is true because If we move a magnet against the magnetic force of a stronger magnet, the motion will make the magnetic field lines to be compressed and this would lead to an increase in potential energy since the magnetic force lines will now be compressed.

Thus, the claim is correct that there is more potential energy that can be stored by moving against the magnetic force of a stronger magnet.

Claim B; Unlike claim A where the magnets were being moved from each other, in this case they are moved closer to each other and therefore this causes a greater compression of space which will lead to a loss in potential energy. Therefore this claim is not true.

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Complete question

Claim A: More potential energy can be stored by moving against the magnetic force of a stronger magnet.

definitely

I think so

I don't know

I don't think so

definitely not

Explain why, using evidence from the activities you have done.

Do you agree with Claim B, More potential energy can be stored by moving against the magnetic force closer to a magnet?

definitely

I think so

I don't know

I don't think so

definitely not

Explain why, using evidence from the activities you have done.

On the other hand, it is not impossible for an equation to have only one solution, an infinite number of solutions, or none at all. Any value for the variable would make the equation true, but an equation with infinite solutions suggests that there is no answer to the equation.

What is  infinite solution?

Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".

What is an infinite number?

There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.

                    The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.

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The median age of the presidents at their death is 69.

The median is the value that is exactly in the middle of a dataset when it is arranged in order. It is a measure of central tendency which separates the lowest 50% from the highest 50% of values.

The median formula is {(n + 1) / 2}th, where “n” is the number of items in the set and “th” means the (n)th number. To find the median, first arrange the data points from smallest to largest.

The steps for finding the median differ depending on whether we have an odd or an even number of data points. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.

In this case, the number of data points is even, that is 38. So, the median is:

= {(n + 1) / 2}th

= {(38 + 1) / 2}th

= 19,5th

Thus, it means the median is the average of the 19th and 20th in the data points. So, it will be:

Median = (68 + 70) / 2

Median = 138 / 2

Median = 69

Hence, the median age of the presidents at their death is 69.

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Although part of your question is missing, you might be referring to this full question: This list shows the age at which 38 U.S. Presidents died.

46 58 64 68 73 80 90

49 60 65 70 74 81 93

53 60 66 71 77 83

56 63 67 71 78 85

56 63 67 71 78 88

57 64 67 72 79 90

What is the median age of the presidents at their death?

A. 69

C. 68

b. 67.5

d. 70

Answer:

2145

Step-by-step explanation:

Here is the formula for the sum of the first n terms.

[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]

Here is the formula for the nth term.

[tex]a_n=a_1+(n-1)d[/tex]

We are given

[tex]a_6=13[/tex]

[tex]S_{40}=3420[/tex]

[tex]3420=\frac{40}{2}(2a_1+(40-1)d)[/tex]

[tex]13=a_1+(6-1)d[/tex]

We don't have a lot to work with but we can get it done.

Lets solve for [tex]a_1[/tex] in [tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex].

Multiply each term by [tex]\frac{2}{n}[/tex].

[tex]\frac{n}{2}(2a_1+(n-1)d)\frac{2}{n} =S_n\frac{2}{n}[/tex]

Simplify.

[tex]\frac{n}{2}*(2a_1+nd-d)\frac{2}{n} =S_n\frac{2}{n}[/tex]

Apply the distributive property.

[tex][\frac{n}{2} (2a_1)+\frac{n}{2} (nd)+\frac{n}{2} (-d)]\frac{2}{n} =S_n\frac{2}{n}[/tex]

Simplify.

[tex](2\frac{n}{2}a_1+\frac{n^2d}{2} -\frac{n}{2}d)\frac{2}{n} =S_n\frac{2}{n}[/tex]

[tex](na_1+\frac{n^2d}{2} -\frac{n}{2}d)\frac{2}{n} =S_n\frac{2}{n}[/tex]

[tex](na_1+\frac{n^2d}{2} -\frac{dn}{2})\frac{2}{n} =S_n\frac{2}{n}[/tex]

[tex]\frac{(na_1+\frac{n^2d}{2} -\frac{dn}{2})*2 }{n}=S_n\frac{2}{n}[/tex]

[tex]\frac{n(2a_1+nd-d)}{n} =S_n\frac{2}{n}[/tex]

[tex]2a_1+nd-d=S_n\frac{2}{n}[/tex]

[tex]2a_1+nd-d=\frac{2S_n}{n}[/tex]

[tex]2a_1=\frac{2S_n}{n}-nd+n[/tex]

Divide each term by 2.

[tex]\frac{2a_1}{2}=\frac{\frac{2S_n}{n} }{2} +\frac{-nd}{2} +\frac{d}{2}[/tex]

Simplify.

[tex]a_1=\frac{S_n}{n} -\frac{nd}{2} +\frac{d}{2}[/tex]

Insert our answer for [tex]a_1[/tex] into [tex]a_n=a_1+(n-1)d[/tex]

[tex]a_n=\frac{S_n}{n_{40} } -\frac{n_{40} d}{2} +\frac{d}{2}+(n_6-1)d\\[/tex]

I continued my work on paper. I will attach it below.

The Exponential formula for the given expression "5 × 5 × 5" can be represented as 5³ , and the value is 125 .

What is an Exponential Form ?

An Exponential Form is a way of writing large or very small numbers succinctly .

The given expression is : ⇒ [tex]5 \times 5 \times5[/tex] ;

here we can observe that the number 5 is multiplied by itself 3 times ,

So , the base of the exponential form is 5 ; and

the exponent/power of exponential form is 3 .

So ,the exponential form is written as [tex]5^{3}[/tex] ,and the value of this form is 125 .

Therefore , the exponential formula of [tex]5 \times 5 \times5[/tex] is [tex]5^{3}[/tex] .

The given question is incomplete , the complete question is

How do you find the exponential formula of the the expression 5 × 5 × 5 ?

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The equation for the nth term of this sequence is  [tex]a_{n}[/tex] = 8n - 14. The solution has been obtained by using the concept of arithmetic progression.  

What is arithmetic progression?

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

We are given that the third term is 10.

This means that [tex]a_{3} =10[/tex]

So, n=3

Substituting this value in the given equations, we get

1)  [tex]a_{n}[/tex] = 8*3+10 = 34

2)  [tex]a_{n}[/tex] = 8*3 - 14 = 10  

3)  [tex]a_{n}[/tex] = 16*3+10 = 58

4)  [tex]a_{n}[/tex] = 16*3 - 38 = 10

So, the second and the fourth equation satisfy the condition.

We are also given that the fifth term is 26.

This means that [tex]a_{5} =26[/tex]

So, n=5

Substituting this value in the given equations, we get

2)  [tex]a_{n}[/tex] = 8*5-14 = 26  

4)  [tex]a_{n}[/tex] = 16*5 - 38 = 42

So, the second equation satisfies the condition.

Hence,the equation for the nth term of this sequence is  [tex]a_{n}[/tex] = 8n - 14.

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Answer:

Let x be the cost of the phone.

we know that the cost of the phone case is 10 times cheaper than the phone so the cost of the case is x/10

We also know that the total cost of the phone and the case is 660.

so we can write an equation:

x + (x/10) = 660

We can solve this equation for x by multiplying both sides by 10:

10x + x = 6600

11x = 6600

x = 600

So the cost of the phone is 600 and the cost of the phone case is 600/10 = 60

The solution to the expression when x = 3 is 0

An equation is an expression that shows the relationship between variables and numbers.

Given the diagram, the small white squares represent 1, while the big shaded rectangle represent -x.

The diagram shown represents the expression:

-x + 1 + 1 + 1  (they is one big shaded rectangle and three white small squares)

= -x + 3

Substituting x = 3 gives:

= -(3) + 3

= 0

The solution is 0

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The domain of a function is the set of all possible input values for which the function produces a valid output.

The domain of a function is the set of all possible input values for which the function produces a valid output. To find the domain of a specific function, you will need to look at the equation and determine what values are acceptable for the inputs. For example, if the equation is y = x2 + 5, then the domain of the function would be all real numbers, since any real number can be plugged in for x and the equation will produce a valid output.

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The expression that is an element of AxBxB is (1,2,3)

The given data is A= (a, b}, B = {1,2,3}

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined.

[tex]& \ A \times B=\left\{\begin{array}{c}(a, 1),(a, 2),(a, 3),(b, 1) \\(b, 2),(b, 3)\end{array}\right. \\[/tex]

[tex]& A \times B \times B=\left\{\begin{array}{l}(a, 1,1),(a, 1,2),(a, 1,3), \\(a, 2,1),(a, 2,2),(a, 2,3),\end{array}\right. \\& (a, 3,1),(a, 3,2),(a, 3,3) \\ & (b, 1,1),(b, 1,2),(b, 1,3) \\& \left.\begin{array}{l}(b, 2,1),(b, 2,2),(b, 2,3) \\(b, 3,1),(b, 2),(b, 3,3)\end{array}\right\} \\[/tex]

[tex]& \therefore(b, 2,3) \in D \times B \times B \\\\& (a, a, 1) \notin A \times B \times B \\\\& \left(b, 2^2\right) \quad \forall A \times B \times B \\\\& (2,1,1) \notin A \times B \times B \\\\&=(b, 2,3) \in \cap \times B \times B \\&\end{aligned}[/tex]

The union of two sets X and Y is equal to the set of elements that are present in set X, in set Y, or in both the sets X and Y.

The intersection of sets can be denoted using the symbol ‘∩’. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.

Therefore, the expression that is an element of AxBxB is (1,2,3).

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Exponent 2 means the number of times one number is multiplied. The number of time the base is multiplied.

The Exponents refers to the repeated multiplication of the same thing by itself.

For example, [tex]x^{2}[/tex] . here 2 is the exponent and x is the base. Then we can write it as x . x . The base is multiplied by 2 time by itself.

Exponents are  also called powers or orders. This is the shorthand for repeated multiplication of the same thing by itself. This process of using exponents is called "raising to a power" where the exponent is the "power". The expression [tex]4^{3}[/tex] is pronounced as four raised to the third power", "four, raised to the power three", or "four to the third". It stands for many times the value is being multiplied.

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Answer:  32

Step-by-step explanation: because the line has to add up to 180 degrease

Answer:

he has 86.36% percent out of 100

Answer:

4 or t = -8

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are solving for the variable, t. Note the equal sign, what you do to one side, you do to the other.

To isolate t, add 7 to both sides of the equation:

21 = t - 7

21 (+7) = t - 7 (+7)

21 + 7 = t

t = 28

t = 28 is your answer.

Check: Plug in 28 for t in the given equation:

21 = t - 7

21 = (28) - 7

21 = 21 (True).

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An equation that has one solution for y for each value of x is referred to be a function. A function pairs each input of a particular type with exactly one output.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function.  Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

An equation that has one solution for y for each value of x is referred to be a function.

A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.

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Answer:12

Step-by-step explanation:

dive 36 plates by by the amount of plates per stack (3)

Answer:

I'(-0.5, 0.25), J'(0.5,0.5), K'(0.5, -0.25)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

The coordinates of the vertices for the figure after the given transformation Dilation of 0.25. is solved to be

I' (-0.5, 0.25)

J' (-1, 1)

K' (1, -0.25)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

In the given problem the coordinates of the image is solved when r = 0.25

preimage                                       image

I (-2, 1)   → (0.25 * -2, 0.25 * 1) →   I' (-0.5, 0.25)

J (2, 2)   → (0.25 * 2, 0.25 * 2) →   J' (-1, 1)

K (2, -1)   → (0.25 * 2, 0.25 * -1) →   K' (1, -0.25)

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Answer:

no the points shown would not be part of y =0.5x

Answer:

D- 22

Step-by-step explanation:

The rectangle would be 9 units tall and 2 units wide.     2 x 2 = 4   9 x 2 = 18     4 + 18 = 22

The blue rectangle is what the rectangle would look like.

The distance between the points E(3, 7) and F(6, 5) is 3.605 units.

Algebraic expression that gives the distances between pairs of points in terms of their coordinates.

The distance between two points having coordinates P(a, b) and Q(c, d) is,

D= √(c-a)² + (b-d)².

Given:

Points E(3, 7) and F(6, 5).

Now, using Distance Formula

D= √(6-3)² + (5-7)²

D = √(3)² + (2)²

D= √9+4

D= √13 units

D= 3.605 unit

Hence, the distance is 3.605.

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The perimeters of the two composite figures are listed below:

Case C: 50.913π mm

Case D: 20.310 cm

In this problem we find two composite figures, whose perimeter have to be found. Perimeter is the length of all borders of the figure. The first figure is formed two semicircles and the second figure is formed by two semicircles and two right triangles, whose perimeter formulas are:

Semicircle

s = π · r

Triangle

s = b + h + p

Where:

Case c - The perimeter of the shape is:

s = π · (28 mm) + π · (14 mm) + 28 mm

s = 50.913π mm

Case d - The perimeter of the shape is:

s = 2π · (1.8 cm) + 2 · (4.5 cm)

s = 20.310 cm

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The measure of the sixth angle of the given convex hexagon is 54 degrees.

We know that the sum of all the interior angles of a convex hexagon is:

720 degrees

Given that three interior angles of the given hexagon measure 140 degrees each.

The fourth angle is 84 degrees.

Let us consider the sixth angle to be x degrees.

Then as per the question, the fifth angle is 3 x (sixth angle) = 3x

Hence, sum of all the angles of the given convex hexagon is:

(3 x 140) + 84 + 3x + x = 720

504 + 4x = 720

4x = 720 - 504 = 216

x = 54 degrees.

Therefore the measure of the sixth angle of the given convex hexagon is 54 degrees.

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Karmyn has 56 tablespoons of vinegar for a salad dressing recipe.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

Karmyn is making a salad dressing using vinegar. She has three and a half glasses of vinegar. She understands that one cup contains 16 tablespoons.

First, we need to convert the 3 1/2 cups of vinegar to tablespoons.

We know that there are 16 tablespoons in 1 cup, so we can multiply the number of cups by the number of tablespoons per cup to convert the measurement.

3 1/2 cups × 16 tablespoons/cup = 56 tablespoons.

Therefore, she has 56 tablespoons of vinegar.

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