Calculate the volume of iron needed to create a rectangular prism with a base area of
2250 square cm. The prism has a cylinder missing through the center of the prism. The
radius of the cylinder is 25 cm and the height of the cylinder and the prism are both
100cm. Find the volume to the nearest tenth of a cubic cm.

[tex](x+2)^2=-16\implies x+2=\sqrt{-16}\implies x+2=\sqrt{-1\cdot 16} \\\\\\ x+2=\sqrt{-1}\cdot \sqrt{16}\implies x+2=4i[/tex]

so, whenever you take an "even root" of a "negative value", you'd end up with an imaginary root or value, which is another way to say, such root doesn't really exist or no solution.

now, we can look at it this way, the same equation is really just a parabola like (x+2)² + 16 = 0, notice, the parabola is in vertex form, its vertex is at (-2 , 16), on the II Quadrant 16 units up above the x-axis.  A solution or what's called a solution or root or zero is really nothing but just an x-intercept, well, the parabola's vertex is way up and is opening upwards, so it never touches the x-axis, no zeros, no solution.

Check the picture below.

The value of x is 2 inches, which represents the length of each side of the square.

We can start by setting up the equation using the given expression for the side length and the given area:

(x + 2)² - 16 = 0

Expanding the left side and simplifying, we get:

x² + 4x = 0

Factoring out x, we get:

x(x + 4) = 0

So, either x = 0 or x = -4. However, since x represents a length, it must be positive. Therefore, the only solution is:

x = 0 + 2 = 2

So the value of x is 2 inches.

Learn more about quadratic equations here: brainly.com/question/30098550

#SPJ4

The potato will take approximately 3.1 minutes to reach a temperature of 90 degrees Celsius to the nearest tenth of a minute.

According to Newton's equation, we need to find time taken for the potato to reach 90 degrees Celsius to the nearest tenth of a minute.

Newton's law of cooling equation is used.

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature.

The law of cooling is given as

[tex]T(t) = T_m + (T_0 - T_m)e^{-kt}[/tex]

whereT(t) is the temperature of the object at time t.

[tex]T_0[/tex] is the temperature of the object initially.

[tex]T_m[/tex] is the temperature of the medium in which the object is kept.

k is a positive constant.

The formula is used to solve for the time it will take the baked potato to reach 90 degrees Celsius.

This is given as:

[tex]T(t) = T_m + (T_0 - T_m)e^{-kt}[/tex]

[tex]90 = 20 + (37 - 20)e^{-kt}[/tex]

Let's start by solving for k.

[tex]37 = 20 + (37 - 20)e^{-k(10)}[/tex]

[tex]17 = 17e^{-10k}[/tex]

[tex]ln(1) = -10k[/tex]

[tex]k = 0[/tex]

Substituting k = 0 in the equation,

we have

[tex]90 = 20 + (37 - 20)e^{0(t)}[/tex]

[tex]\frac{70}{17} = e^{(0(t))}[/tex]

Taking the natural log of both sides,

[tex]ln\frac{70}{17}  = lne^{0(t)}[/tex]

[tex]t= 3.0748 minutes[/tex]

Therefore, it will take approximately 3.1 minutes for the potato to reach 90 degrees Celsius to the nearest tenth of a minute.

Learn more about Newton's Law of Cooling here:

https://brainly.com/question/14643865

#SPJ11

The measure of this angle in degrees is 20.52 degrees.

Step by step explanation:Given data is,1/360th of the circumference of the circle is 0.59 cm long Arc length, s = 103.25 cm We need to find the measure of the angle in degrees. Since we know that, the angle subtended by an arc at the center of the circle is 2θ, where θ is the angle subtended by the arc at any point on the circumference of the circle.And the circumference of the circle is 360θ.

Hence, we can find the length of the circumference of the circle. Circumference of the circle = 360 × 0.59Circumference of the circle = 212.4 cmNow, we can find the radius of the circle.r = s/2πr = 103.25/(2 × π) = 16.441 cmDiameter of the circle = 2 × rDiameter of the circle = 32.882 cmThe circumference of the circle = πdCircumference of the circle = π × 32.882Circumference of the circle = 103.26 cm Now, we can find the angle of the circle. Angle of the circle = 360θ103.26 = 360θθ = 103.26/360θ = 0.286 degrees So, the measure of this angle in degrees is 20.52 degrees.

See more about angle at: https://brainly.com/question/25716982

#SPJ11

This selection process is referred to as "systematic sampling"

Systematic sampling is the sampling method where samples are selected based on a systematic interval in a population. It is a type of probability sampling, where every kth element in the population is selected as a sample, where k is a constant value.

The interval k is calculated by dividing the population size N by the sample size n; hence, k = N/n. In this case, the sample size is 100, and the population size is 100,000, so the interval is k = 1000. The selection process involved in this question is an example of systematic sampling because the selection of the 100 sales invoices is based on a systematic interval of 1000. Starting at a random point, every, 1000th sale invoice is selected until 100 are chosen.

See more about systematic sampling at: https://brainly.com/question/28505229

#SPJ11

Answer:

Step-by-step explanation:

120

Answer:

If the store marks up the price of the diving board by 45%, the selling price will be 100% + 45% = 145% of the cost price.

Let's calculate the selling price:

Selling price = Cost price + Mark-up

Mark-up = Selling price - Cost price

Mark-up = (145% of cost price) - cost price

Mark-up = 0.45 * cost price

We know that the store paid $261 for the diving board, so:

Mark-up = 0.45 * $261 = $117.45

Therefore, the amount of the mark-up is $117.45.

well, what's 45% of 261?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{45\% of 261}}{\left( \cfrac{45}{100} \right)261}\implies \text{\LARGE 117.45}[/tex]

The probability that exactly 3 homes will be sold tomorrow is A) 0.1809.

To solve this problem, we can use the Poisson distribution formula, which is:

P(x; μ) = (e^-μ) (μ^x) / x!

where P(x; μ) is the probability of x events happening in a given time period, μ is the mean number of events in that time period, e is the mathematical constant approximately equal to 2.71828, and x! is the factorial of x.

In this case, we want to find the probability of exactly 3 homes being sold tomorrow, given that the average number of homes sold is 2 per day. So, we plug in μ = 2 and x = 3 into the formula:

P(3; 2) = (e^-2) (2^3) / 3! = 0.1809

Therefore, the probability that exactly 3 homes will be sold tomorrow is 0.1809 or approximately 18.09%. This means that out of every 100 days, we can expect that around 18 of those days will have exactly 3 homes sold by Acme Realty Company.

For more questions like Probability visit the link below:

https://brainly.com/question/28945832

#SPJ11

The expression that is equivalent to 6(w + 7) is 6w + 42.

An expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that are grouped together to represent a mathematical quantity or relationship.

The distributive property is a property of multiplication that allows us to multiply a single term by a sum or difference of terms. It states that:

a(b + c) = ab + ac and a(b - c) = ab - ac.

In other words, we can distribute the factor a to each term within the parentheses by multiplying it by each term, and then add or subtract the resulting products.

In the given question,

To simplify the expression 6(w + 7), we can use the distributive property of multiplication over addition, which states that:

a(b + c) = ab + ac

Using this property, we can expand the expression 6(w + 7) as:

6w + 6(7)

Simplifying the second term by multiplying, we get:

6w + 42

Therefore, the expression that is equivalent to 6(w + 7) is 6w + 42.

To know more about distributive property, visit:

https://brainly.com/question/6276874

#SPJ1

Measure of last angle of triangle is 117°

The triangle's characteristics include:

The angle sum property states that the sum of a triangle's three interior angles is always 180 degrees.

Angle of Triangle are

28° and 35°

Let the third angle be x

According to angle sum property

28°+35°+x=180°

x=117°

Measure of last angle of triangle is 117°

To know more about degrees, visit:

https://brainly.com/question/364572

#SPJ1

The complete question is;

Find the measure of the last angle of the triangle below.

28⁰

35°

Image is attached below.

Answer:

1/12

Step-by-step explanation:

Each row would be 1/8 of the whole pan. Now multiply 1/8 by 2/3.

Multiply the numerators: 1*2=2

Multiply the denominators: 8*3=24

Your answer: 2/24 or 1/12 simplified (dividing both top and bottom by 2)

Hope this helps. :)

Answer:

[tex]\frac{1}{11}[/tex]

Step-by-step explanation:

[tex]\frac{2}{22}[/tex] = [tex]\frac{1}{11}[/tex]

I drew a pan when I divided into 8 rows.  Then I divided that up inot 2/3.  In the first row that is divided into 3 parts, I want one of those 2 parts.  The total parts are 22.  2/22

So the correct answer is option A) m=5, LO=14, NO-12 for the indicated variables and measures for the figure below.

A triangle is a closed two-dimensional geometric figure with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides and the measures of its angles. The sum of the interior angles of a triangle is always 180 degrees, and the length of each side is less than the sum of the lengths of the other two sides. Triangles have many properties and are used in various mathematical and real-world applications, including trigonometry, geometry, and engineering.

Here,

Since all the angles are equal, we can set up the following proportion:

LO/NO = 7/2

Multiplying both sides by NO, we get:

LO = (7/2)NO

We can also use the fact that the angles are equal to set up an equation involving m:

m + (1/2)LO + (1/2)NO = 180

Substituting LO = (7/2)NO, we get:

m + (7/4)NO = 180

Now we can substitute the given values for LO and NO:

m + (7/4)(14) = 180

m + 49 = 180

m = 131

Therefore, the answer is: m = 131, LO = 49, NO = 14

To know more about triangle,

https://brainly.com/question/28600396

#SPJ1

Yes, it can be proved that the driver had been speeding.

The driver had been speeding since the distance traveled during the 19-second skid is greater than the distance the car would have traveled at 60 mph in the same time. This implies that the driver was traveling at a higher speed than the speed limit before braking.

To explain further, we can calculate the distance a car traveling at 60 mph would cover in 19 seconds, which is 1,672 feet (60 mph = 88 fps, 19 seconds x 88 fps = 1,672 feet). However, the car in question skidded for 1700 feet before coming to a complete stop, which is greater than the distance it would have traveled at 60 mph in the same time. This implies that the driver was traveling at a higher speed than the speed limit before braking. Therefore, it can be concluded that the driver was speeding.

For more questions like Speed visit the link below:

https://brainly.com/question/3100499

#SPJ11

Answer:

12b (1-2) -n (u-8) this is the answer

The solution set of the equation x/3 = 8/(x + 2) when calculated is x = -6 or x = 4

Given the following equation

x/3 = 8/(x + 2)

Cross multiply

x(x + 2) = 24

To find the solution set of x(x + 2) = 24, we need to solve for x by simplifying the left-hand side of the equation and then factoring it.

x(x + 2) = 24

Expanding the left-hand side, we get:

x² + 2x = 24

Subtracting 24 from both sides, we get:

x² + 2x - 24 = 0

Now we can factor the quadratic expression on the left-hand side:

(x + 6)(x - 4) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.

Therefore, we can set each factor equal to zero and solve for x:

x + 6 = 0 or x - 4 = 0

Solving for x, we get:

x = -6 or x = 4

So, the solution set is { -6, 4 }.

These are the values of x that make the equation true when plugged in.

Read more about equation at

https://brainly.com/question/2972832

#SPJ1

The area of the cylinder's base is 25π square units. The volume of the cylinder is 100π cubic units.

a. The base of a cylinder is a circle. We can shade the circle at the bottom of the cylinder to represent the cylinder's base.

b. The diameter of the cylinder is 10 units, which means the radius of the base is half of that or 5 units. The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius.

Therefore, the area of the cylinder's base is:

A = πr^2 = π(5^2) = 25π

So the area of the cylinder's base is 25π square units.

c. The volume of a cylinder is calculated using the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

Substituting the values given, we get:

V = πr^2h = π(5^2)(4) = 100π

So the volume of the cylinder is 100π cubic units.

A cylinder is a three-dimensional object with a circular base and straight sides that rise to a circular top. The area of a cylinder is the total amount of space on the surface of the cylinder. It can be calculated by finding the sum of the areas of the two circular bases and the curved surface area in between.

The formula for finding the surface area of a cylinder is A = 2πr² + 2πrh, where "r" is the radius of the circular base, "h" is the height of the cylinder, and "π" is a constant value of approximately 3.14159. To calculate the area of a cylinder with a radius of "r" and height of "h", we first find the area of the circular base by using the formula for the area of a circle: A_base = πr².

To learn more about Area of the cylinder's visit here:

brainly.com/question/28575608

#SPJ4

Complete Question: -

Here is a cylinder with height 4 units and diameter 10 units. a. Shade the cylinder’s base. b. What is the area of the cylinder’s base? Express your answer in terms of π. c. What is the volume of this cylinder? Express your answer in terms of π.

The value of the x is equal to 7 using the secant tangent angle formula.

The secant tangent angle is the angle formed by a tangent and a secant that intersect outside of a circle. The measure of the secant tangent angle can be found using the following formula:

θ = 1/2 (arc EB - arc BD)

where arc EB and arc BD are the measures of the arcs intercepted by the secant and tangent, respectively.

From the question,

θ = m∠NXK = 4x + 6

arc EB = 8x - 13

arc BD = 70° + (6x - 1) = 69 + 6x

4x + 6 = 1/2[69 + 6x - (8x - 13)]

4x + 6 = 1/2(69 + 6x - 8x + 13)

4x + 6 = 1/2(82 - 2x)

4x + 6 = 41 - x

4x + x = 41 - 6 {collect like terms}

5x = 35

x = 35/5 {divide through by 5}

x = 7

Therefore, the value of the x is equal to 7 using the secant tangent angle formula.

Know more about secant tangent here:https://brainly.com/question/9132922

#SPJ1

2.75  is the decimal of fraction .

In math, what is a fraction? 

The amount is represented mathematically as a quotient, where the numerator and denominator are split. In a simple fraction, both are integers. A complicated fraction includes a fraction, either in the denominator or the numerator.

                                    The numerator and denominator must be smaller in a proper fraction. A fraction is a number that is a component of a whole. A whole is appraised by dissecting it into many sections. Half of a whole number or item, for instance, is represented by the number 12.

= [tex]2\frac{75}{100}[/tex]

 = [tex]2\frac{3}{4}[/tex]

  = 11/4

  =  2.75

Learn more about fraction

brainly.com/question/10354322

#SPJ1

Answer:

あたしの最後はあなたがいい (いい)

あなたとこのままおサラバするより

死ぬのがいいわ

死ぬのがいいわ

三度の飯よりあんたがええのよ

あんたとこのままおサラバするよか

死ぬのがいいわ

死ぬのがいいわ

それでも時々 浮つく

Step-by-step explanation:

The equation representing total fraction strip is  ³/₃ + ¹/₃ = ⁴/₃.

option B.

A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.

For this case, 1 is divided into, and 1 divide into 3.

To obtain the total fractions, we will add the individual fractions as shown below;

For this first fraction = ¹/₃ + ¹/₃ + ¹/₃

For the second fraction = ¹/₃

Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃

Total fraction = ³/₃ + ¹/₃ = ⁴/₃

Learn more about total fraction here: https://brainly.com/question/28699958

#SPJ1

The z value when making 98% confidence interval for p will be 2.33.

When making a confidence interval for a proportion, we use the standard normal distribution, and the value of z depends on the level of confidence we want to achieve.

In this case, we want to make a 98% confidence interval, which means that we want to be 98% confident that the true proportion falls within our interval.

To determine the value of z, we can use a z-table or a calculator. The z-value corresponding to a 98% confidence level is 2.33. Therefore, we use 2.33 as our value of z when making a 98% confidence interval for p.

It is not impossible to make a 98% confidence interval, and the value of z is not 2.88. The z-value of 2.88 corresponds to a much higher confidence level of approximately 99.5%. Using a higher confidence level means we can be more confident that our interval contains the true proportion, but it also means that our interval will be wider, which reduces its precision.

Learn more about confidence here:

https://brainly.com/question/13242669

#SPJ4

Jen has 54 pages left to read to meet her assignment requirement.

The inequality that represents this situation is p ≥ 85 - 31

To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.

The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:

p = 85 - 31

p = 54

Therefore, Jen has 54 pages left to read.

To represent this situation with an inequality, we can use:

p ≥ 85 - 31

This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).

Solving for p:

p ≥ 85 - 31

p ≥ 54

This means that Jen must read at least 54 more pages to meet her assignment requirement.

To learn more about inequality Click here:
brainly.com/question/30228778

#SPJ4

The for the values of the variables x = 7 and y = 10, the given must be a parallelogram.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base and height of the parallelogram determine its area.

For the given quadrilateral to be parallelogram the opposite sides need to be parallel and equal.

For the given quadrilateral we have:

2y - 16 = y - 6

2y - y = -6 + 16

y = 10

Also,

2x + 2 = y + 6

Substitute the value of y = 10:

2x + 2 = 10 + 6

2x = 16- 2

2x = 14

x = 7

Hence, the for the values of the variables x = 7 and y = 10, the given must be a parallelogram.

Learn more about parallelogram here:

https://brainly.com/question/11220936

#SPJ1

In order to expect a return on $400 from across all policies of a similar nature, the insurance firm should charge the policy for about $501.88.

Return[expr] leaves control structures that are present during a function's definition and returns the value expression for the entire function. Even if it comes inside other functions, yield takes effect as quickly as it is evaluated. Functions like Scan can use Return inside of them.

Since p is the chance that the 28-year-old woman survives the year and is given as 0.99962, we can enter this number into the equation for n as follows: n = 400(0.99962)/500,400 n 0.799

In light of this, the insurance provider should impose a premium of: Premium = 400/n

$501.88 is the premium ($Premium = 400/0.799)

To know more about return visit:

https://brainly.com/question/28562900

#SPJ1

The measurement of  of angle c is (4x-24. 6) and measure of angle d is (x+11. 3). If the angles are supplementary, the value of x is 38.66.

The measure of angle c is (4x-24. 6)

The measure of angle d is (x+11. 3)

If both angles are supplementary angles then,

angle c + angle d = 180

(4x-24. 6) + (x+11. 3) = 180

5x - 13.3 = 180

5x = 180 + 13.3

5x = 193.3

x = 193.3/5

x = 38.66

So, the value of x is 38.66

What distinguishes complimentary from supplementary angles?

Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.

To know more about supplementary angles, click the below link

https://brainly.com/question/13045673

#SPJ4

As per the given percentage, Sandesh should aim to sell his apples at 250rs per kg in order to gain 20% profit.

Let C be the cost of the 15kgs of apples. Sandesh gained 12%, so his profit is 0.12C. We know that Sandesh sold the apples for 2100rs, so we can write an equation:

C + 0.12C = 2100

Simplifying this equation gives:

1.12C = 2100

Dividing both sides by 1.12 gives:

C = 1875

So Sandesh's cost for 15kgs of apples was 1875rs.

Now, we need to find the selling price per kg of apples that Sandesh should aim for in order to gain 20% profit. Let P be the selling price per kg of apples.

Since Sandesh wants to gain 20% profit, his selling price per kg of apples needs to be his cost plus 20% of his cost, or 1.2 times his cost.

So we can write another equation:

1.2C = 15P

Substituting the value of C we found earlier, we get:

1.2(1875) = 15P

Simplifying gives:

P = 250

To know more about percentage here

https://brainly.com/question/13729841

#SPJ4

The instantaneous velocity of the object at t = 6 is 2.

Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56

Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2

Therefore, the instantaneous velocity of the object at t = 6 is 2.

Learn more about Instantaneous velocity

brainly.com/question/28837697

#SPJ11

If r(x) is a rational function in simplest form where the degree of the numerator is 3 and the degree of the denominator is 1, a)then r(x) has a horizontal asymptote at y=0.

This is because the degree of the denominator is greater than the degree of the numerator, which means that as x gets very large or very small, the denominator will dominate the behavior of the function.

As a result, the function will approach zero, and thus, there is a horizontal asymptote at y=0. If the degree of the numerator were greater than or equal to the degree of the denominator, then the function could have a horizontal asymptote at a nonzero value or no horizontal asymptote at all.

For more questions like Function click the link below:

https://brainly.com/question/12431044

#SPJ11

Answer:

When the determinant of a matrix is almost 0, it means that the matrix is close to being singular, which means that its inverse does not exist or is very close to not existing. This has important implications for the solution of systems of linear equations represented by the matrix.

Specifically, if the determinant of a matrix is almost 0, then the matrix is almost singular, which means that its columns are almost linearly dependent. This, in turn, means that the system of equations represented by the matrix has almost linearly dependent equations, which can lead to multiple solutions or no solutions at all.

In terms of the sensitivity of the solution to changes in the constants of the system, a small change in the constants can lead to a large change in the solution when the determinant of the matrix is almost 0. This is because the inverse of the matrix is very sensitive to changes in its entries when the determinant is almost 0.

For example, consider a system of linear equations represented by a matrix A with determinant very close to 0, and let b be the vector of constants on the right-hand side of the equations. Then, the solution to the system can be approximated by the product of the inverse of A (if it exists) and b, that is:

x = A^(-1) b

However, if A is almost singular, then its inverse is very sensitive to changes in its entries, and a small change in b can lead to a large change in x. This can make the solution to the system unreliable and unstable, and can be a source of numerical errors in computations.

Step-by-step explanation:

The shown that v= √8 RT/ πM.

To show that v= √8 RT/ πM, we will first rewrite the given integral. It is:

$$\left(\dfrac{-u}{4}\right)=\dfrac{1}{\sqrt\pi}\left(\dfrac{M}{2RT}\right)^{\frac{3}{2}}\int_{0}^{\infty}v^{3}e^{\frac{-Mv^{2}}{2RT}}dv$$Let's solve the integral first. We'll use the integral rule:

$$\int xe^{ax^{2}}dx=\dfrac{1}{2a}e^{ax^{2}}+C$$

So, the integral from the given formula can be re-written as:

$$\begin{aligned}&\int_{0}^{\infty}v^{3}e^{\frac{-Mv^{2}}{2RT}}dv \\ &\quad =-\dfrac{2RT}{M}\int_{0}^{\infty}\left(-\dfrac{Mv^{2}}{2RT}\right)\cdot v\cdot e^{\frac{-Mv^{2}}{2RT}}dv \\ &\quad =-\dfrac{2RT}{M}\int_{0}^{\infty}vde^{\frac{-Mv^{2}}{2RT}} \\ &\quad =-\dfrac{2RT}{M}\left[ve^{\frac{-Mv^{2}}{2RT}}\right]_{0}^{\infty} \\ &\quad =\dfrac{2RT}{M}\cdot 0+ \dfrac{2RT}{M}\cdot \infty \\ &\quad =\infty\end{aligned}$$This means that the integral of the formula is infinity. Therefore, to make the equation equal to the given answer, the given formula for the average speed of molecules in an ideal gas must be equated with the most probable speed. The most probable speed of the gas is the speed at which the likelihood of finding molecules is the highest. It is given by the following formula:

$$v_{mp}=\sqrt{\dfrac{2RT}{M}}$$Therefore,

$$v_{mp}=\sqrt{\dfrac{2RT}{M}}=\sqrt{\dfrac{8RT}{4M}}=\sqrt{\dfrac{8RT}{\pi M}}$$Hence, we have shown that v= √8 RT/ πM.

Learn more about Shown

brainly.com/question/17022472

#SPJ11