Help with this math question

The area of the surface generated when the given curve is revolved about the given axis 5x^1/3 is [tex]\frac{\pi }{675} [34\sqrt{34} - 125][/tex].

The curve x = f(y)

The area of the surface around the y-axis from y = a → y = b is:

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

From the given curve:

[tex]y = 5x^{1/3}[/tex] ; assuming the region bounded by the curve is 0 ≤ y ≤ 1

So;

    [tex]y = 5x^{1/3}[/tex]

⇒ 5x = y³

⇒ x = 1/5 y³

The differential of the above equation Is:

   dx/dy = 1/5 (3y²)

⇒ dx/dy = 3/5 (y²)

Now, we have the area of the surface produced around the curve  [tex]y = 5x^{1/3}[/tex] through the y axis from the region y = 0 to y = 1

∴ [tex]\int\limits^1_0 {2\pi \frac{1}{5}y^3\sqrt{1+(\frac{3}{5} y^2)^2} } \, dx[/tex]

= [tex]\frac{2\pi }{5} \int\limits^1_0 {y^3\sqrt{1+(\frac{9}{25} y^4)} } \, dy[/tex]

= [tex]\frac{2\pi }{5} \int\limits^1_0 {y^3\sqrt{\frac{25+9y^4}{25})} } \, dy[/tex]

= [tex]\frac{2\pi }{5} \int\limits^1_0 {y^3\sqrt{25+9} y^{4} )} } \, dy[/tex]

Let make u = [tex]\sqrt{25+9y^{4} }[/tex]

It implies that:

[tex]u^3 = (25+9y^4) \sqrt{25+9y^4}[/tex]

and, [tex]u = \sqrt{25+9y^{4} }[/tex]

⇒ [tex]du = \frac{1}{2\sqrt{25+9y^4} } (36y^3) dy[/tex]

⇒ [tex]y^3dy = \frac{1}{18} \sqrt{25+9y^{4} }du[/tex]

when y = 0 ;

[tex]u = \sqrt{25+9y^{4} }[/tex]

[tex]u = \sqrt{25+9{(0)^4} }[/tex]

[tex]u = \sqrt{25 }[/tex]

u = 5

when y = 1;

[tex]u = \sqrt{25+9{(1)^4} }[/tex]

[tex]u = \sqrt{34} }[/tex]

∴The equation [tex]\frac{2\pi }{5} \int\limits^1_0 {y^3\sqrt{25+9} y^{4} )} } \, dy[/tex]  can be written as:

= [tex]\frac{\pi }{225} [\frac{u^3}{3} ]\left \{ {{y=\sqrt{34} } \atop {x=5}} \right.[/tex]

= [tex]\frac{\pi }{675} [34\sqrt{34} - 125][/tex]

Therefore,

The area of the surface generated when the given curve is revolved about the given axis 5x^1/3 is [tex]\frac{\pi }{675} [34\sqrt{34} - 125][/tex].

Complete Question:

Find The area of the surface generated when the given curve is revolved about the given axis 5x^1/3.

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Answer:4320

Step-by-step explanation:8% interest =108% which is equivalent to x1.08

4000 x 1.08 = 4320

Answer:

h = 9.9

b = 4.6

Step-by-step explanation:

The first triangle is an isosceles right triangle
The base leg = vertical leg = 7

diagonal = 7√2 = 9.9  (rounded to nearest tenth)

h = 9.9

For the 30-60-90 triangle
if the vertical leg is x, the base leg = vertical leg / √3 = 8/√3 = 4.6

b = 4.6

The volume of a cylinder with a diameter of 34 m and a height of 27 m is 24501.42 m³.

A cylinder is a three-dimensional figure that has a rectangular body but is rolled up which gives it a round shape with two circles for its top and bottom. We see a lot of cylinders around us all the time.

Here, we have been told that the diameter of the cylinder is 34 which means that the radius is 34/2 = 17 m.

Furthermore, we have also been told that the height of the cylinder is 27 m.

We already know that the volume of a cylinder can be calculated using

= πr²h

Using the values, we get -

= 3.14 * 17 * 17 * 27

= 24501.42 m³.

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The average rate of change over the interval [9,10] is greater by 6490.

The average rate of change of a polynomial is the slope of the function.

The average rate of change over the interval [7, 9] is the slope between  ( 7, f(7) )  and  ( 9, f(9) )

where f(7) and f(9) is the value of the function at 7 and 9.

So, the slope between  ( 7, 1852 )  and  ( 9, 3878 )

= (3878-1852)/(9-7)

= 2026/2

= 1013

Similarly,

The average rate of change over the interval [4, 6]

i.e. slope between  ( 4, f(4) )  and  ( 6, f(6) )

So, the slope between  ( 4, 358 )  and  ( 6, 1178 )

= (1178-358)/(6-4)

= 820/2

= 410

and

1013-410 = 603

So, the polynomial is 603 greater than the average rate of change over the interval [7, 9] than the interval ​ [4, 6]

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Answer:

30 X 4=yhhvvihddthjgyujjnbbbvvvukgdddsxgjooi

The dimensions square must be cut if the volume of the box is to be 189 cubic inches is  9 * 7 * 3.

The mathematical concept of volume represents the amount of three-dimensional space that an object or closed surface takes up. Volume is measured in cubic units like m³, cm³, in³, etc.

The dimension of the box will be:

= L * W* H

=(15-2x)*(13-2x)*x

The volume:

x(15-2x)*(13-2x) = 189

x(195 - 56x + 4x²) = 189

4x³ - 56x² + 195x - 189 = 0

Hopefully it's an integer, we know it's a low value

Try x=3 using synthetic division

we get ,  3 as the solution or or root of the equation.

Check x = 3, the side of the cut out squares

(15-6)(13-6)  3 = 189

9 * 7 * 3 = 189 cu/in

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August is the eighth month of the year. Depending on the region and culture, August is known for a variety of historical and cultural events, as well as natural occurrences.

August is noted in the United States for National Women's Equality Day (August 26th), which honors the enactment of the 19th Amendment to the United States Constitution, which granted women the right to vote.

The Perseid meteor shower, which happens yearly between late July and late August and is visible from many parts of the world, is also celebrated in August.

August is connected with the harvest season in several cultures and is commemorated with numerous festivals and rituals.

August is also a popular month for vacations and travel, particularly in the Northern Hemisphere, where it corresponds with the summer season.

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Equation for 6 halves of pears is 1/2 x 6 = 3

The factor of a number is a number that divides the given number completely without any remainder. The factors of a number can be positive or negative.

Every factor is divisor of that number but every divisor is not a factor of that number.

Given, in the picture,

half of 6 pears

One half of pear can be denoted as = 1/2

Now,

equation of 6 half pears.

= 1/2 x 6

= 4

Hence, equation for 6 half pears can be written as 1/2 × 6 = 3.

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Exponents laws are

[tex]a^n . a^m = a^{n + m}[/tex]

[tex]a^n / a^m[/tex] = [tex]a^{n - m}[/tex]

Exponent laws are important to use because they will help us to simplify complex expressions easier.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Exponents are written in the form [tex]a^n[/tex]

Where n can be any real numbers.

Now,

a = 2

For n = 0, 1, 2, 3, -1, -2, -3

We get,

[tex]2^0[/tex] = 1

2² =  2 x 2 = 4

2³ = 2 x 2 x 2 = 8

[tex]2^{-1}[/tex] = 1/2

[tex]2^{-2}[/tex]  = 1/(2 x 2) = 1/4

[tex]2^{-3}[/tex] = 1/(2 x 2 x 2) = 1/8

Exponents laws are:

[tex]a^n . a^m = a^{n + m}[/tex]

[tex]a^n / a^m[/tex] = [tex]a^{n - m}[/tex]

Thus,

Exponent laws are important to use because they will help us to simplify complex expressions easier.

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For the defined function  f(t)=e^rt and g(t)=e^st where r is not equal to s it was proved that the f and g are linearly independent function in F(r,r).

For the defined function f and g we have,

f(t)=e^rt

g(t)=e^st

Where r is not equal to s.

To prove f and g are linearly independent function we need,

f( t) ± g(t) = 0

Substitute the value of f(t) and g(t) we get,

⇒ e^rt ± e^st  = 0

⇒ e^rt ( 1 ± e^( s - r )t = 0

This implies ,

e^rt = 0 or ( 1 ± e^( s - r )t = 0

But e^rt is always greater than zero for all the values of r and t.

e^rt = 0 is not possible.

If ( 1 ± e^( s - r )t = 0

This is possible if and only if r = s .

Which is against the given condition.

Therefore, f(t) and g(t) are linearly independent function in f( r , r).

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The above question is incomplete, the complete question is:

Let f, g, element F(r,r) be the function defined by f(t)=e^rt and g(t)=e^st, where r cannot equal s. prove that f and g are linearly independent in F(r,r).

The correct interpretation of the given confidence interval is: We are 90% confident that the interval from 0.397 to 0.503 captures the true proportion (p) of all US doctors who are satisfied with the current state of US health care.

In statistics, a confidence interval is a range of values that is likely to contain an unknown population parameter, such as a population mean or proportion, based on a sample from that population. A confidence interval is constructed with a particular level of confidence, which represents the probability that the interval will contain the true population parameter. The confidence level is typically expressed as a percentage, such as 90%, 95%, or 99%.

Here,

This means that if we were to repeat the process of taking a random sample of 240 US doctors and calculating a 90% confidence interval for the proportion of doctors who are satisfied with the current state of US health care, 90% of those intervals would contain the true proportion.

It is not correct to say that 90% of all doctors are satisfied with the current state of US health care, because the confidence interval only provides information about the range of plausible values for the true proportion, not the exact value.

It is also not correct to say that a majority of the doctors in the sample are satisfied with the current state of US health care, because the confidence interval includes values both above and below 0.5, which means that we cannot conclude whether a majority or a minority of doctors are satisfied with the current state of US health care.

Therefore, the correct answer is: We are 90% confident that the interval from 0.397 to 0.503 captures the true proportion of all US doctors who are satisfied with the current state of US health care.

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Answer:

Step-by-step explanation:

The total amount of yards are 4(1/8).

To find the total amount of fabric Tanya used, we need to add the amount of fabric she used for the dress and the amount of fabric she used for the jacket.

Tanya used 3(3/8) yards of fabric for the dress and 1(1/3) yards of fabric for the jacket. We can add these two amounts by finding a common denominator for the fractions and adding the whole numbers:

3(3/8) + 1(1/3) = 3(9/24) + 1(8/24)

=> 3(17/24)

Therefore, Tanya used a total of 3(17/24) yards of fabric. This can be simplified to:

=> 3(17/24) = 4(1/8)

So the answer is A. 4(1/8).

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The value of millimeter in inches can be calculated by simply dividing the millimeter by 25.4 so 125 mm is 4.921 inches.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

Converting from millimetres to inches

Between millimetres (mm) and inches (in)

Calculation of Inches (dec) in Inches (frac) in Feet plus Inches ft mm to inches

* The value is rounded to the nearest 1/64 fraction for the inches fraction.

How to change metric units to inches

Inches are equal to 0.03937007874 millimetres in length:

1mm = (1/25.4)″ = 0.03937007874″

The distance d in millimetres (mm) divided by 25.4 gives the distance d in inches (′′):

d(″) = d(mm) / 25.4

Example of 20 mm converted to inches:

d(″) = 125mm / 25.4 = 4.92126″

How many millimetres are in one inch

0.03937 inches are equal to one millimetre:

1mm is equal to 1mm / 25.4mm/in = 0.03937in.

What is the millimetre to inch conversion

25.4 millimetres make up one inch.

1 inch Equals 25.4 millimetres per inch.

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The correct answer to this question is option D: (0.60 minus 0.70) plus-or-minus 1.96 StartRoot StartFraction 0.60 (1 minus 0.60) Over 50 EndFraction + StartFraction 0.70 (1 minus 0.70) Over 50 EndFraction EndRoot.

To find the 95% confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups, we need to use the formula:

CI = (p1 - p2) ± z*√[(p1(1-p1)/n1) + (p2(1-p2)/n2)]

Where p1 and p2 are the proportions of patients experiencing stress relief in the yoga and meditation groups, respectively, n1 and n2 are the sample sizes of the yoga and meditation groups, respectively, and z is the critical value from the z-table corresponding to the 95% confidence level.

Plugging in the given values:

p1 = 30/50 = 0.60
p2 = 35/50 = 0.70
n1 = 50
n2 = 50
z = 1.96 (from the z-table for a 95% confidence level)

CI = (0.60 - 0.70) ± 1.96*√[(0.60(1-0.60)/50) + (0.70(1-0.70)/50)]
CI = (-0.10) ± 1.96*√[(0.24/50) + (0.21/50)]
CI = (-0.10) ± 1.96*√[0.009]
CI = (-0.10) ± 1.96*(0.095)
CI = (-0.10) ± 0.186

Therefore, the 95% confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups is (-0.286, 0.086).

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Answer:

Step-by-step explanation:

5 seconds later acceleration of the car is 6m/h^2

We know that the initial velocity of a car is 50 mph.

In the end, the final velocity of a car is 80 mph.

The time difference is 5 seconds.

For the calculation of the acceleration, we have this formula,

α = δv/t

so here, according to our data, velocity and time are,

u = 50 mph

v = 80 mph

t = 5 s

Finally, the acceleration of the car can be calculated by,

α = (80 - 50) / 5

α = 30 / 5

α = 6 m/h^2

From the above calculations, the car's acceleration is 6 m/h^2.

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To eliminate the x-variable term from an equation, we need to multiply that equation by the opposite of the coefficient of the x-variable. If the first equation is of the form ax + by = c, then we need to multiply it by -a to eliminate the x-variable. Therefore, the number we should multiply the first equation by to eliminate the x-variable term is -3 if the first equation is of the form 3x + 2y = 7.

Area is calculated using length measurements, specifically measurements of two dimensions of a flat or planar shape, such as length and width. The resulting value represents the amount of space occupied by the shape on a flat surface.

Area is commonly measured in square units such as square metres ([tex]m^{2}[/tex]), square feet ([tex]ft^{2}[/tex]), square inches ([tex]in^{2}[/tex]), and so on.

To calculate the area of a flat shape, multiply its length and width by the appropriate unit of measurement.

Area = Length x Width

Similarly, to find the area of a circular surface, we would use the formula for the area of a circle:

Area = π x (Radius)^2

[tex]Area = \pi . (r)^2[/tex]

where π is the mathematical constant pi, and the radius is half the diameter:

So, area is a measure of the amount of space occupied by a flat or planar shape and is calculated using length measurements.

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The value of weight of 67 kg when converted to pounds is   147.70954 pounds.

kilogram is the standard unit of mass in the International System of Units (SI), while pounds are a common unit of mass used in the United States and other countries.

To Know how to convert between different units of measurement is essential for accurate calculations and comparisons. convert 67kg to pounds, you can use the formula: 1 kilogram is equal to 2.20462 pounds.

Therefore, to convert 67kg to pounds, you would multiply 64 by 2.20462.

67 x 2.20462 =  147.70954 pounds

So, weight of 64kg is equivalent to  141.09568 pounds.

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Answer:

[tex]2\pi[/tex] inches

Option B

Step-by-step explanation:

The arc length is proportional to the central angle
If L is the arc length and θ is the central angle in degrees
[tex]L = \dfrac{\theta}{360} \times C[/tex]

where C is the circumference of the circle

Given radius r = 6 inches, C = 2πr = 2π·6 = 12π
θ = 60°

So
[tex]L = \dfrac{60}{360} \times 12\pi\\\\= \dfrac{1}{6} \times 12\pi\\\\= 2\pi\;inches[/tex]

The probability that at most three records will be incomplete is approximately 0.650 (rounded to three decimal places).

What is Binomial Distribution ?

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment.

This is a binomial distribution problem with n=10 and p=0.156. Let X be the number of incomplete records. We need to find P(X ≤ 3).

Using a TI-83, TI-83 Plus, or TI-84 calculator, we can use the binomial cumulative distribution function (binomcdf) to find this probability:

binomcdf(10, 0.156, 3) ≈ 0.650

Therefore, the probability that at most three records will be incomplete is approximately 0.650 (rounded to three decimal places).

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The price for 5 pounds of honey is $13.32.

Unitary method is a mathematical technique used to solve problems related to proportions and ratios.

To find the price for 5 pounds of honey, we can use a proportion:

Price of 3 pounds of honey / 3 = Price of 1 pound of honey

We can use this equation to find the price of 1 pound of honey, and then multiply by 5 to find the price of 5 pounds of honey.

Price of 3 pounds of honey / 3 = 7.99 / 3

Price of 1 pound of honey = 2.6633 (rounded to 4 decimal places)

Price of 5 pounds of honey = 2.6633 x 5 = $13.32 (rounded to 2 decimal places)

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The scale factor of the drawing is 5:36.The scale factor is the amount by which a shape is increased or shrunk.

Scale factor is the proportion of an original object's scale to a new one that is an representation of it that is a different size (bigger or smaller). For instance, by increasing each side by, say, 2, we can expand overall size of the a rectangle having lengths of 4 cm and 8 cm. The scale discrepancy between two things is contrasted by a scale factor, which is a ratio. You can figure out the scale factor by selecting two comparable or related components on the two items you are comparing. By comparing every one of these two elements, you may determine a ratio.

When we find the scale factor , we obtain:

5 inches = 1 yard

1 inches=[tex]\frac{1}{5}[/tex] yard.

actual , 1 inche = [tex]\frac{1}{36}[/tex] yard

Scale factor= [tex]\frac{\frac{1}{36} }{\frac{1}{5} }[/tex]= [tex]\frac{5}{36}[/tex].

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Answer:

Below

Step-by-step explanation:

Volume of a cone = 1/3  pi  r^2 h

      4125 pi             = 1/3 pi r^2 h

                       4125  = 1/3 r^2 h  <===if diameter =30  then radius = 15 units

                         4125 = 1/3 (15)^2 h

                            4125 / (1/3 * 15^2) = h = 55 units

Answer:

Measuring Spoon

Step-by-step explanation:

The tool you would use is a measuring spoon.

Answer:

Measuring spoon

Step-by-step explanation:

Answer:

+x+=+3+

+y+=+-.9%2A%28+3+%2B+3+%29%2A%28+3+-+3+%29+

+y+=+-.9%2A6%2A0+

+y+=+0+

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

The distance between ( -3, 0 ) and ( 3, 0 )

is +3+-%28-3%29+=+6+

The width of the arch at ground level is 6 ft

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

Here's the plot of the equation:

Step-by-step explanation:

The solution set for this equation is {4}, since 4 is the only value that makes the equation true.

You have done a great job of explaining how to check if the numbers 3 and 2 are part of the solution set for the equation 13 = 2x + 5. You correctly substituted each number in for x and simplified the equation to see if it was true or false. You found that both numbers resulted in a false equation, so they are not part of the solution set.

One thing to note is that the solution set for an equation is the set of all values that make the equation true. So, in order to find the solution set for this equation, you would need to solve for x. Here is how you would do that:

13 = 2x + 5

Subtract 5 from both sides of the equation:

8 = 2x

Divide both sides of the equation by 2:

4 = x

So, the solution set for this equation is {4}, since 4 is the only value that makes the equation true.

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Answer:

x = 14°

z = 74°

Step-by-step explanation:

10x - 34° = 106° ( A.I.A )

x = 72°

106° + z = 180° ( linear pair axiom )

z = 74°

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Answer:

x=14°

z= 74°

Step-by-step explanation:

Here

(10x-34)°= 106°

since the Vertically Opposite Angle are equal.

so solving for it.

First, we can add 34° to both sides of the equation to get:

10x° - 34°+ 34° = 106° + 34°

Simplifying the left side gives:

10x° = 140°

Then we can divide both sides of the equation by 10 to get:

x = 14°

Again

z+106°=180°

since the sum of angle in the linear pair is equal to 180°

solving for it

we can subtract 106° from both sides of the equation to get:

z + 106° - 106° = 180° - 106°

Simplifying the left side gives:

z = 74°

According to the Empirical Rule, approximately 68% of the data in a normal distribution will fall within ±1 standard deviation of the mean. The correct option is (d) 68%

The Empirical Rule is a statistical rule of thumb that describes the approximate proportions of data that fall within a certain number of standard deviations from the mean in a normal distribution.

The Empirical Rule states that for a normal distribution:

About 68% of the data will fall within 1 standard deviation of the mean

About 95% of the data will fall within 2 standard deviations of the mean

About 99.7% of the data will fall within 3 standard deviations of the mean

Therefore, option (b) 68 is the correct answer.

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