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The volume of the solid that is generated is: [tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]

Now, According to the question:

The formula for the shell method is :

[tex]=\int\limits^a_b {2\pi rh} \, dx[/tex]

where, a and b are the x - bound, which are  x=1 and x=2,

So, a = 1 and b = 2

r is the distance from a certain x-value in the interval [1, 2] and the axis of rotation, which is x = -1 .

r = x - (-1) = x + 1

h is the height of the cylinder at a certain x-value in the interval [1, 2],  which is [tex]\frac{1}{x^{2} } - 0[/tex] = [tex]\frac{1}{x^{2} }[/tex] (because [tex]\frac{1}{x^{2} }[/tex] is always greater than 0 and h must be positive).

Plugging it all in volume

[tex]\int\limits^2_1 {(2\pi (x + 1)(\frac{1}{x^2} ))} \, dx[/tex]

=  [tex]2\pi \int\limits^2_1 { (x + 1)(\frac{1}{x^2} ))} \, dx[/tex]

[tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]

Hence, The volume of the solid that is generated is: [tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]

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Rule: Y is equal to the square root of X.

Equation: Y = √X

What is algebraic expression?

An algebraic expression is when we use b and words in solving a particular mathematical question.

In this table, the relationship between the values of X and Y appears to be Y = √X.

This can be expressed as a mathematical rule and equation as follows:

Rule: Y is equal to the square root of X.

Equation: Y = √X

We can use this rule to complete the table as following figure.

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Answer:

x = 9

Step-by-step explanation:

(8x+16) + (9x+11) = 180

17x + 27 = 180

180 - 27 = 153

17x = 153

153/17 = 9

x = 9

Answer:

To solve the equation 8x+16+9x+11=180, add 8x and 9x to both sides to get 17x+27=180. Subtract 27 from both sides to get 17x=153. Divide both sides by 17 to get x=9.

The perimeter of Rebekah's new mural is 9 meters.

The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

A rectangular mural measures 1 meter by 3 meters.

Rebekah creates a new mural that is 0.5 meters longer.

The perimeter of Rebekah's new mural,

= 2 (1.5 + 3)

= 9 meters.

Therefore, the perimeter is 9 meters.

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Answer:

9

Step-by-step explanation:

Answer:

x = 7/2

y = 0

Step-by-step explanation:

–6x + y = –21

2x − 13y = 7

Times the second equation by 3

-6x + y = -21

6x - 39y = 21

-38y = 0

y = 0
Now put -0 back for y and solve for x

-6x = -21

x = 7/2

Answer:

I think it would be infinitely many solutions

Step-by-step explanation:

The bacteria will reach its maximum size at t = 8.94 weeks.

To find when the bacteria will reach its maximum size, we need to find the maximum value of p(t). The first step is to find the derivative of p(t):

dp(t)/dt = -8000(t^2 - 80)/(80 + t^2)^2

Next, we need to find the critical points of this derivative by setting it equal to 0 and solving for t:

dp(t)/dt = 0

-8000(t^2 - 80)/(80 + t^2)^2 = 0

t^2 - 80 = 0

t = √80

t = 4√5

t ≈ 8.94

Since t = 4√5 is the only critical point, we can see that it is a local maximum. To confirm this, we need to find the second derivative and evaluate it at t = 0:

d^2p(t)/dt^2 = 16000t (t^2 - 240) / (80 + t^2)^3

d^2p(t)/dt^2 = 160000 * -160 / (80 + 80)^3 < 0

Since the second derivative at t =  4√5 is less than 0, it is a local maximum.

--The question is incomplete, answering to the question below--

"The size of a bacteria population grows at a rate of p(t) = 8000t/ (80 + t^2) where t is measured in weeks. Determine when the bacteria will reach its maximum size."

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Multiply the mass in pounds by 0.45359237 to convert 145 lbs to kilogrammes.

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using the substitution u=5x−2, ∫x5x−2−−−−−√ⅆx is equivalent to  ∫u+2 /5 du/5

What is Derivative?

Calculus defines a derivative as the rate at which one quantity, y, changes in relation to another, x. The differential coefficient of y with respect to x is another name for it. Finding a function's derivative is the process of differentiation. A function's derivative is typically represented by d/dx (f(x)) (or df/dx (or Df(x) (or f')). Let's examine the technical definition of a derivative. Two points on a function f(x) curve are (x, f(x)) and ((x + h), f(x + h)), respectively. If so, [f(x + h) - f(x)]/(x + h - x) = [f(x + h) - f(x) / h] will be the slope of the secant line through these points. The second point overlaps the first point in the figure below when the distance between two points is nearly equal to 0 (i.e., as h approaches 0), and the secant line turns into the tangent line. Calculus refers to the slope of the tangent line as the function's derivative.

x = 1/y + 1

y + 1 = 1/x

y = 1/x - 1

differentiating y w.r.t to x

dy/dx=-1/x^2

using subsitution u= 5x-2

then x= u+2/5

∫u+2 /5 du/5

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Answer: 16

Step-by-step explanation:

274-50=224/14=16

Answer:

16

Step-by-step explanation:

Answer:

its "equally likely and unlikely" because since its 50% for the chocolate chip then its 25% for both oatmeal raisin, and sugar cookies, which both of their percentages are equivalent to 50% so its a 50/50 chance between getting chocolate chip cookies to getting oatmeal raisin and/or sugar cookies

Step-by-step explanation:

The solution to the inequality 5/w > 4/45, using interval notation, is given as follows:

(-∞, 56.25).

The inequality for this problem is defined as follows:

5/w > 4/45.

Applying cross multiplication, we have that the solution can be obtained as follows:

4w < 45 x 5

w < 45 x 5/4

w < 56.25.

The solution is found similarly to an equality, isolating the desired variable, and finding the desired range of values.

The solution w < 56.25 is composed by values to the left of x = 56.25 on the number line, that is, values between negative infinity and 56.25, hence the interval is given as follows:

(-∞, 56.25).

The problem is incomplete, hence it was adapted to show the solution to an inequality, and then written in interval notation.

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Answer: y=2x+3

Step-by-step explanation:

2x−y=−3

Step 1:

Add -2x to both sides.

2x−y+−2x=−3+−2x−y=−2x−3

Step 2: Divide both sides by -1.−y−1=−2x−3−1y=2x+3

Surface area of the cylinder would be 231.1 sq ft.

How do you find a surface area of a cylinder?

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

The surface area of a cylinder with height h and radius r can be found using the formula:

2πr^2 + 2πrh

Given a cylinder with height 6 ft and radius 7 ft, the surface area is:

2π * 7^2 + 2π * 7 * 6 = 147.1 + 84 = 231.1 sq ft (rounded to the nearest tenth).

Therefore, Surface area of the cylinder would be 231.1 sq ft.

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The average acceleration over the given time interval is option C -10 m/s²

By dividing the change in velocity by the change in time, the average acceleration will be determined. Therefore, let's first determine the velocity function:

x = 4t² - 3t³

v = dx / dt

v = d( 4t² - 3t³) / dt

v = 8t - 9t²

Then,

at t = 0 sec , v = 0 m/s.

at t = 2 sec , v = 8(2) - 9(2²) = 16 - 36 = -20 m/s.

Average acceleration;

The rate of change in velocity is referred to as the average acceleration. To calculate the average acceleration of anything, we divide the change in velocity by the time since the initial measurement. A crazy ball's average acceleration, for instance, would be 20 cm/s/s if its velocity rose from 0 to 60 cm/s in 3 seconds.

avg.acc = (- 20 - 0) / (2 - 0) = -20 / 2 = -10 m/s²

That is,

-10 m/s² (option c) will be the average acceleration over the given interval.

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The given question is incomplete. Completed question is here;

The coordinates of an object is given as a function of time by x=4t^2-3t^3,where x is in meter and t is in second .what is its average acceleration over the time interval from 0 to 2 seconds

If the area of the triangle is 50m² the length of it's other two sides is 10m each and hypotenuse is 14.1m

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

A right angled triangle is a triangle with 90°. Since of one of the angle is 45° , this means that the triangle is isosceles and the other two sides will be equal. This means a= b

Area of triangle = 1/2absinC

50 = 1/2 b²sin90

50× 2 = b²× 1

b² = 100

b = √ 100

b =10m

b = 10m

a= 10m

using Pythagoras theorem

c² = 10²+10²

c² =100+100

c²= 200

c =√200

c = 14.1m

therefore the measure of the other two sides is 10m each and the hypotenuse is 14.1m

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The density and uncertainty in the density of the sphere is (1828.28 ± 0.0984)  kg/m³

The radius of a sphere is (6.20 ± 0.30)  cm

Mass of the sphere is (1.81 ± 0.09)  kg

We know that the formula for the density,

Density = mass/volume

d = m/V

As we know tha volume of the sphere is, [tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]V=\frac{4}{3} \pi r^3\\\\V=\frac{4}{3} \pi (6.2\times 10^{-2})^3\\\\V=0.00099~m^3[/tex]

So, the density would be,

d = (1.81) / (0.00099)

d = 1828.28 kg/m³

We can find the uncertainty in volume as follows :

[tex]\frac{\delta V}{V}=3\frac{\delta r}{r}\\\\\frac{\delta V}{V}=3\times \frac{0.003}{0.0620} \\\\\frac{\delta V}{V}=0.0484[/tex]

and the uncertainty in the mass would be,

[tex]\frac{\delta m}{m}=\frac{0.09}{1.81} \\\\\frac{\delta m}{m}=0.05[/tex]

The uncertainty in the density of the sphere would be,

[tex]\frac{\delta d}{d}=\frac{\delta V}{V}+\frac{\delta m}{m}\\\\\frac{\delta d}{d}=0.0484+0.05\\\\\frac{\delta d}{d}=0.0984[/tex]

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Answer:

Step-by-step explanation:

To evaluate g(-5), you simply plug in -5 for x in the equation:

g(-5) = (-5)²-10 which is 25 - 10 which is 15. Therefore, g(-5) = 15

Since Polygon X is a scaled copy of Polygon Y using a scale factor of 3, a statement which is true include the following: D. The area of Polygon X is 9 times the area of Polygon Y.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Therefore, the area of Polygon X with respect to Polygon Y based on the given scale factor of 3 is as follows;

Area of Polygon X/Area of Polygon Y = 3²

Area of Polygon X/Area of Polygon Y = 9.

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The statement that must be true is (c) x² = a/b

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

√a/√b = x

Take the square root of both sides

So, we have the following representation

a/b = x²

Rewrite the equation as

x² = a/b

Hence, the solution is x² = a/b

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The formula v · v = kvk2 can be seen to hold for all vectors in Rn, as the dot product of a vector and itself is equal to the magnitude of the vector squared.

The formula v · v = kvk2 is true for all vectors v in Rn. This is because the dot product of a vector and itself is equal to the magnitude of the vector squared. The dot product of two vectors is defined as the sum of the products of their components. Therefore, when a vector v is multiplied by itself, the result is the sum of the squares of all its components. The magnitude of a vector is defined as the square root of the sum of the squares of its components. Thus, the formula v · v = kvk2 can be seen to hold for all vectors in Rn, as the dot product of a vector and itself is equal to the magnitude of the vector squared.

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Step-by-step explanation:

the triangle GAS is congruent with the triangle IOL (I know, it is tempting to say OIL, but it is important to show the sequence of the corresponding corners, so G corresponds to I, A to O and S to L) by AAS (angle-angle-side) : 2 angles and a not included but corresponding side are equal between the 2 triangles.

The factorization is given as 9x² - 9x - 44

Factorize fully 3 ( x − 4 )² + 15 ( x − 4 )

(3x - 4)² + 15(x-4)

(3x - 4)(3x - 4) + 15(x-4)

we have to open the bracket

9x² - 12x - 12x + 16 + 15x - 60

take the like terms in the equation

9x² - 24x + 15x +16 - 60

9x² - 9x - 44

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The expressions for the real part, imaginary part, and magnitude of the complex function f(x) = 1/(1-ix) are: Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2), Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2) and |f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|

Given the complex function f(x) = 1/(1-ix), where I = √-1, we can find the real part, imaginary part, and magnitude as follows:

Real part: The real part of a complex number is equal to the real part of the numerator divided by the real part of the denominator. Here, the numerator is 1, so the real part of the numerator is 1. The denominator is 1-ix, so the real part of the denominator is 1, and the imaginary part of the denominator is -x. The real part of the complex function is then given by:

Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2)

Imaginary part: The imaginary part of a complex number is equal to the imaginary part of the numerator divided by the real part of the denominator. Here, the numerator is 1, so the imaginary part of the numerator is 0. The denominator is 1-ix, so the real part of the denominator is 1, and the imaginary part of the denominator is -x. The imaginary part of the complex function is then given by:

Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2)

Magnitude: The magnitude of a complex number is equal to the square root of the sum of the squares of the real and imaginary parts. The magnitude of the complex function is then given by:

|f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|

Therefore, the expressions for the real part, imaginary part, and magnitude of the complex function f(x) = 1/(1-ix) are: Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2), Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2)

and |f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|.

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Answer:

The volume of each cylinder is given by the formula: V = πr^2h, where r is the base radius and h is the height of the cylinder.

When 25 cylinders are put into the half-filled container, the water level rises to the top of the container, which means that the total volume of the 25 cylinders is equal to the volume of the container. Let's assume the volume of the container is V_container.

So, 25 * πr^2 * h = V_container

Dividing both sides by 25πh gives: r^2 = V_container / (25πh)

Taking the square root of both sides gives: r = √(V_container / (25πh))

Since h = 10 cm, we can substitute this value in the formula above: r = √(V_container / (25π * 10))

Since r is the base radius of the cylinder, it must be positive. So, the final equation becomes:

r = √(V_container / (25π * 10)) cm = 5√(5/π) cm. shown

By using 3.14 for the value of π, we can calculate the value of r:

r = 5√(5/π) = 5√(5/3.14) = 5 * √(5/3.14)

= 5 * √(1.5873) = 5 * 1.259 = 6.295 cm (rounded to the first decimal place)

So, the base radius of the cylinder is approximately 6.3 cm.

The solution to the inequality in question is less than or equal to 4300 pounds and 2.6875 cubic yards of sand can be hauled in the truck to still classify as a passenger vehicle.

From the question itself, we can deduce that the inequality is -

Let us assume that the amount of stuff carried by the vehicle is = x

So, the inequality becomes -

= 4200 + x ≤ 8500 pounds

So, if we solve this we will find that the weight of stuff to be carried is going to be -

= x ≤ 8500 - 4200

= x ≤  4300

It should be no more than 4300 pounds.

We can still classify it as a passenger vehicle by carrying only 1.4655 pounds of sand because -

= 2.6875 *1600 = 4300 pounds

This means that by carrying 2.6875 pounds we maintain the rules to remain a passenger vehicle.

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The total price is 40.8, which can be represented by the coordinates (15, 40.8).

The equation y = 2.72x can be used to calculate the price of gasoline in terms of the number of gallons purchased.

The equation y = 2.72x can be used to calculate the total price of any number of gallons of gasoline. In this equation, y represents the total price and x represents the number of gallons of gasoline. In this equation, y represents the total price and x represents the number of gallons. If we input 15 gallons into the equation, we can calculate the total price of gasoline. To do this, we must substitute 15 for x in the equation, giving us y = 2.72(15). We can then calculate the total price by multiplying 2.72 and 15, which yields 40.8. Thus, for 15 gallons of gasoline, the total price is 40.8, which can be represented by the coordinates (15, 40.8).

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Contrapositive: If not isosceles, then not two equal sides or angles. Converse: If two equal sides or angles, then isosceles. Inverse: If not isosceles, then not two equal sides or angles.

What is triangle ?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C.

Contrapositive: If a triangle is not an isosceles triangle, then it does not have either two equal sides or two equal angles.

Converse: If a triangle has either two equal sides or two equal angles, then it is an isosceles triangle.

Inverse: If a triangle is not an isosceles triangle, then it does not have either two equal sides or two equal angles.

Contrapositive: If not isosceles, then not two equal sides or angles. Converse: If two equal sides or angles, then isosceles. Inverse: If not isosceles, then not two equal sides or angles.

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The rule for the transformation above include the following: B. (x' , y') = (x - 6 , -y + 1).

In Geometry, a reflection over the x-axis is given by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive:

(x, y)                               →              (x, -y)

This ultimately implies that, the parallelogram was reflected over the x-axis and then translated by 6 units to the left, and followed by a vertical translation downward by 1 unit.

(x' , y') = (x - 6 , -y + 1)

(x' , y') = (1 - 6 , -2 + 1)

(x' , y') = (-5, -1)

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Functions that take a positive integer n as input and return a real number are F(n) = 100n log n and g(n) = n (log n)2. A different algorithm's time complexity is represented by g(n), whereas another algorithm's time complexity is represented by F(n).

As n approaches infinity, F(n) and g(n) both expand as O(n log n), which indicates that the growth rate of the two functions is proportional to n log n as n gets very big. However, because the coefficient 100 in F(n) is smaller than the coefficient 1 in g, it develops more slowly than g(n) (n).

Hence, functions that take a positive integer n as input and return a real number are F(n) = 100n log n and g(n) = n (log n)2.

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The normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a small variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the values deviate from the mean. The most popular way to assess dispersion is standard deviation, which is based on all values.

From the given samples of 9oz of chips we have the following values:

Mean = 9.12 ounces

SD = 0.05 ounces

The normal distribution of the chart below will have the following values:

The mean or the center value of the graph with the highest peak is:

Mean = 9.12

The value to the right of the mean value will be:

Mean + SD = 9.12 + 0.05 = 9.17

Mean + 2(SD) = 9.12 + 2(0.05) = 9.22

Similarly, the value to the left of the mean value will be:

Mean - SD = 9.12 - 0.05 = 9.07

Mean - 2(SD) = 9.12 - 2(SD) = 9.02

Hence, the normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.

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