a metal block has the following dimensions height 2cm length 10cm width 5cm calculate the volume of the block

​

The two solutions to e² = 6x using Newton's method are x_left = 1.23151 and x_right = 2.157545.

To find the solutions of e² = 6x using Newton's Method, we will follow these steps:

Let f(x) = e² - 6x. Then we want to find the roots of f(x) = 0, which are the solutions to e² = 6x.

We need to choose a starting point x₀. A good choice is x₀ = 1, since it's a reasonable approximation to the solutions.

Apply Newton's Method to find the next approximation x₁:

x₁ = x₀ - f(x₀)/f'(x₀),

where;

Plugging in the values, we get:

x₁ = x₀ - (e² - 6x₀)/(-6) = x₀ + (e²/6 - x₀)

Use x₁ as the new starting point and repeat the process until we achieve the desired level of accuracy.

In this case, we want to find the solutions to six significant figures, so we will repeat the process until the difference between xₙ and xₙ₋₁ is less than 0.000005 (the sixth decimal place).

Using a calculator, we can apply Newton's Method iteratively to find the two solutions:

Iteration 1:

x₁ = x₀ - f(x₀) / f'(x₀)

x₁ = 1 - (e² - 6)/(-6) = 1.231509

Iteration 2:

x₂ = 1.231509 - (e² - 6)/(-6) = 1.463018

Iteration 3:

x₃ = 1.463018 - (e² - 6)/(-6) = 1.694527

Iteration 4:

x₄ = 1.694527 - (e² - 6)/(-6) = 1.926036

Iteration 5:

x₅ = 1.926036 - (e² - 6)/(-6) = 2.157545

The second solution to six significant figures is x_right = 2.157545

Learn more about Newton's method here: https://brainly.com/question/14279052

#SPJ1

Answer:

XYZ = 21.8

Step-by-step explanation:

the missing angle is XYZ

using a calculator:

so XYZ = 21.8

Answer:

p = 22

z = 8

Step-by-step explanation:

Average is sum of the terms divided by number of terms.

Question # 1:

Given that:

\(\displaystyle \frac{p+10}{2} = 16\\\\Multiply\ both\ sides\ by \ 2]]\\ p+10 = 2 \times 16\\\\p+10 = 32\\\\Subtract \ 10\ to \ both \ sides\\\\p = 32-10\\\\p = 22\)

Question # 2:

Given that:

\(\displaystyle \frac{z+12}{2} = 10\\\\Multiply \ both \ sides \ by \ 2\\\\z+12 = 10 \times 2\\\\z+12 = 20\\\\Subtract \ 12\ to \ both \ sides\\\\z = 20-12\\\\z = 8\\\\\rule[224]{225}{2}\)

Hope this helped!

Answer:

DO U PLAY AMONG US WELL I DO

Step-by-step explanation:

WHO LIKES SCHOOL ANYWAYS THATS Y WE R USING THIS APP ADD ME ON SNAP

Using supplementary angles, the measure of angle y is given as follows

y = 140º.

The sum of the internal angles of a triangle is of 180º. For the triangle in this problem, the internal angles are given by:

xº, 20º and 120º.

Hence we can solve for x applying the sum as follows:

x + 20 + 120 = 180

x + 140 = 180

x = 40º.

An angle is supplementary with it's external angle, meaning that the sum of it's measures is also of 180º.

For this problem, y is the external angle of x, hence their measures are related as follows:

y + x = 180º.

From above, we have that x = 40º, hence:

y + 40º = 180º.

y = 140º.

Which is the desired measure for this problem.

More can be learned about supplementary angles at https://brainly.com/question/12919120

#SPJ1

Answer:

C) 240ma

Step-by-step explanation:

The dU/dT at constant P and V is simply nR/P.

According to the ideal gas law, PV = nRT, so we can write P = nRT/V. Using this relationship, we can express the internal energy U as a function of P, V, and T:

U = f(P,V,T) = f(nRT/V, V, T)

To find dU/dP at constant V and T, we can use the chain rule:

dU/dP = (∂U/∂P)V,T + (∂U/∂V)P,T(dP/dP)V,T + (∂U/∂T)P,V(dT/dP)V,T

Since V and T are being held constant, we can simplify the second and third terms to just 0:

dU/dP = (∂U/∂P)V,T

To find (∂U/∂P)V,T, we can differentiate f(nRT/V, V, T) with respect to P, keeping V and T constant:

(∂U/∂P)V,T = (∂f/∂P)nRT/V(-nRT/V²) = -nRT/V²

So, dU/dP at constant V and T is simply -nRT/V².

To find dU/dT at constant P and V, we can again use the chain rule:

dU/dT = (∂U/∂T)P,V + (∂U/∂V)P,T(dV/dT)P,V + (∂U/∂P)V,T(dP/dT)P,V

Since P and V are being held constant, we can simplify the third term to just 0:

dU/dT = (∂U/∂T)P,V + (∂U/∂V)P,T(dV/dT)P,V

To find (∂U/∂T)P,V, we can differentiate f(nRT/V, V, T) with respect to T, keeping P and V constant:

(∂U/∂T)P,V = (∂f/∂T)nRT/V(1) = nR/V

To find (∂U/∂V)P,T, we can differentiate f(nRT/V, V, T) with respect to V, keeping P and T constant:

(∂U/∂V)P,T = (∂f/∂V)nRT/V(-nRT/V²) + (∂f/∂V)V,T = nRT/V² - nRT/V² = 0

Since the ideal gas law shows that PV = nRT, we can write V = nRT/P. Using this relationship, we can simplify the second term of dU/dT to just:

dU/dT = (∂U/∂T)P,V = nR/P

So, dU/dT at constant P and V is simply nR/P.

For more such answers on ideal gas law

https://brainly.com/question/27870704

#SPJ11

a. To find dU/dPv, we need to differentiate U with respect to both P and V while treating T as a constant. Using the chain rule, we have:

dU/dPv = (∂U/∂P)v + (∂U/∂V)p * (dV/dP)v

Since U is a function of P, V, and T, we can express it as U(P,V,T). Using the ideal gas law, we substitute P = nRT/V into U:

U = f(P,V,T) = f(nRT/V, V, T)

Differentiating U with respect to P while treating V and T as constants, we get (∂U/∂P)v = -nRT/V².

Similarly, differentiating U with respect to V while treating P and T as constants, we get (∂U/∂V)p = nRT/V.

Hence, dU/dPv = -nRT/V² + nRT/V * (dV/dP)v.

b. To find dU/dTv, we differentiate U with respect to both T and V while treating P as a constant. Using the chain rule:

dU/dTv = (∂U/∂T)v + (∂U/∂V)t * (dV/dT)v

Differentiating U with respect to T while treating V and P as constants, we get (∂U/∂T)v = (∂f/∂T)v.

Similarly, differentiating U with respect to V while treating T and P as constants, we get (∂U/∂V)t = (∂f/∂V)t.

Hence, dU/dTv = (∂f/∂T)v + (∂f/∂V)t * (dV/dT)v.

Note: The specific form of the function f(P,V,T) is not provided, so we cannot determine the exact values of (∂f/∂T)v, (∂f/∂V)t, and (dV/dT)v without additional information.

Learn more about differentiate here: brainly.com/question/31962094

#SPJ11

Answer

Step-by-step explanation:

Hope it helps you!

Answer:

35 vertices

Explanation:

Given a convex polygon with n-vertices, the number of diagonals in the polygon is given by the formula:

If n is reduced by 20%, the new value of n will be:

Replace n in the formula above with 0.8n:

Next, we are told that the number of its diagonals decreases by 37.5%. Using the original formula for the number of diagonals, we have:

Equate (1) and (2):

We solve the equation for n:

The polygon P has 35 vertices.

\(7\frac{1}{2}\implies 7.5\hspace{5em}1\frac{1}{4}\implies 1.25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Monday through Friday} }{\stackrel{ days }{(5)}\stackrel{ rate }{(10.80)}\stackrel{ hours }{(7.5)}}~~ + ~~\stackrel{ Saturday }{\stackrel{ days }{(1)}\stackrel{ rate }{(10.80)(1.25)}\stackrel{ hours }{(7.5)}} \\\\\\ 405~~ + ~~101.25\implies \text{\LARGE 506.25}\)

The inequality describes a goal of charging more than $1,000 for

yards mowed for the season is, 30x > 1000.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Lenny's Lawn Service has $300 in start-up expenses and charges $30 for each yard mowed.

Assuming the no. of mows to be 'x'.

Therefore, The inequality 30x > 1000 expresses an aim of charging more than $1,000 for each season's worth of yards mowed.

learn more about inequalities here :

https://brainly.com/question/28823603

#SPJ1

Answer:

x=0.885622

Step-by-step explanation:

Dont forget to round

Answer:

0.77

Step-by-step explanation:

7=9x

9x/9

7=x

7/9=0.77777777777

Answer:

The total amount of spiders needed to have the same mass as spider man would be 84,571.

Step-by-step explanation:

16 ounces = 1 pound

1. divide 16 by 0.035 to get the total number of spiders that weigh 1 pound together (which is 457.142857143 or rounded up to 457)

2. multiply 457.142857143 by 185 to get the total number of spiders that together weigh 185 pounds (which gets you 84571.4285714 or rounded up to 84,571)

3. Check your work

(only trust me if it's a multiple choice question)

the work done in pumping the tank of water up to ground level is approximately 166320π joules.

To find the work done in pumping a cylindrical tank of water up to ground level, we can follow these steps:

1. Calculate the volume of the tank using the formula for the volume of a cylinder: V = πr²h, where r is the radius of the tank and h is the height. Given that the radius is 2 meters and the height is 6 meters, we have V = π(2²)(6) = 24π cubic meters.

2. Determine the mass of the water in the tank by multiplying the volume by the density of water. The density of water is approximately 1000 kilograms per cubic meter. So, the mass (m) of the water is m = V * density = 24π * 1000 = 24000π kilograms.

3. Calculate the height difference between the top of the tank and ground level. Since the top of the tank is 1 meter below ground level, the height difference (h) is 6 + 1 = 7 meters.

4. Determine the potential energy (PE) of the water using the formula PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s²). Substituting the values, we have PE = (24000π) * 9.8 * 7 = 166320π joules.

Therefore, the work done in pumping the tank of water up to ground level is approximately 166320π joules.

To know more about cylindrical tank related question visit:

https://brainly.com/question/25562559

#SPJ11

The differential dv allows us to quantify how the volume of the cylinder changes as we make infinitesimally small adjustments to both the radius and the height.

To find the differential dv, we need to take the derivative of the volume function v(r, h) with respect to both variables, r and h.

dv = (∂v/∂r) dr + (∂v/∂h) dh

Taking the partial derivatives, we have:

∂v/∂r = 2πrh
∂v/∂h = πr^2

Substituting these values back into the differential equation, we get:

dv = (2πrh) dr + (πr^2) dh

Now let's interpret the formula geometrically. The volume of a right circular cylinder, given by v(r, h) = πr^2h, represents the amount of space enclosed within the cylinder.

The differential dv, which is given by (2πrh) dr + (πr^2) dh, represents the small change in volume that occurs when there is a small change in both the radius (dr) and the height (dh) of the cylinder.

Geometrically, the term (2πrh) dr represents the contribution to the volume due to a small change in the radius of the cylinder, while the term (πr^2) dh represents the contribution to the volume due to a small change in the height of the cylinder.

The overall differential dv captures the combined effect of these small changes in both variables.

To learn more about differential go to:

https://brainly.com/question/31539041

#SPJ11

Answer:220

Step-by-step explanation:88/4=22 x 10= 220

After adding (-7) to each value in the given data set, the mean is 38.25, the median is 38, the mode does not exist, the range is 24, and the standard deviation is approximately 8.85.

To find the mean of the data set, add all the values together (49, 30, 34, 43, 31, 37, 25, 47) and divide the sum by the total number of values (8). The mean is the average value of the data set.

To determine the median, arrange the values in ascending order (25, 30, 31, 34, 37, 43, 47, 49) and find the middle value. In this case, the median is the average of the two middle values (34 and 37).

The mode refers to the value(s) that appear most frequently in the data set. In this case, there is no mode since no value appears more than once.

The range is calculated by subtracting the smallest value (25) from the largest value (49). Thus, the range is 24.

To calculate the standard deviation, subtract the mean from each value, square the differences, calculate the mean of those squared differences, and finally take the square root of the resulting value. This provides a measure of the dispersion or spread of the data around the mean.

Learn more about Standard Deviation

brainly.com/question/13498201

#SPJ11

True. Line graphs are not suitable for representing central tendencies and variation between categorical data.They are effective in showing changes and patterns in numerical data.

Line graphs are typically used to display trends over time or the relationship between two continuous variables. However, when it comes to categorical data, which consists of distinct categories or groups, line graphs are not appropriate for representing central tendencies and variation.

Central tendencies, such as the mean or median, are measures that describe the average or typical value within a set of data. Variation refers to the spread or dispersion of the data points. Categorical data does not have a natural numerical scale or order, making it difficult to determine central tendencies and variation using line graphs.

For categorical data, alternative graphical representations like bar charts, pie charts, or stacked column charts are more suitable. These graphs provide a visual representation of the frequencies or proportions of different categories, allowing for a better understanding of the distribution and comparison between categories. Such graphs are effective in capturing the central tendencies and variation in categorical data.

To learn more about central tendencies click here : brainly.com/question/30218735

#SPJ11

Answer:

Option A

Step-by-step explanation:

The answer is Option A because \(- \frac{2}{3} j + \frac{1}{5}k\) can be writen as \(\frac{1}{5}k - \frac{2}{3}j\).

Answer:

n = -6

x = -7

n = 27

Step-by-step explanation:

Question 1

-3n - n + 12 = 36

First we get all the variables to one side using subtraction property of equality.

-3n - n + 12 (-12) = 36 (-12)

-4n = 24

divide by the coefficient of n to isolate the variable

-4n/-4 = 24/-4

n = -6

Question 2

-2x - 3x - 15 = 20

-5x - 15 = 20

-5x = 35

x = -7

Question 3

3 + n/9 = 6

Isolate the n variable

n/9 = 6 - 3

multiply by 9

n = 27

Answer:

1. n = -6

2. x = -7

3. n = 27

The quadratic equation exists \($x^{2}+3 x+2=0$\).

If a quadratic equation exists \($a x^{2}+b x+c=0$\), the utilizing the quadratic equation the solutions for x will be given by

\($x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$\)

The solution for x exists

\($x=\frac{-3 \pm \sqrt{3^{2}-4(1)(2)}}{2(1)}\)

Comparing equations (1) and (2) we get, a = 1, b = 3 and c = 2.

Therefore, the quadratic equation exists \($x^{2}+3 x+2=0$\).

To learn more about quadratic equations refer to:

https://brainly.com/question/1214333

#SPJ4

Answer:

One guy said it was B. but I'm going with A.

Step-by-step explanation:

Ramiya is using the quadratic formula to solve a quadratic equation. her equation is x = startfraction negative 3 plus or minus startroot 3 squared minus 4(1)(2) endroot over 2(1) endfraction after substituting the values of a, b, and c into the formula. which is ramiya’s quadratic equation?

The risk of owning a home in Randolph County based on the given sample can be calculated as:

Risk of owning a home = Number of residents who own a home / Total number of residents in the sample

Risk of owning a home = 59 / 90

Therefore, the risk of owning a home in Randolph County based on the given sample is approximately 0.656 or 65.6%.

Answer:

\( \sf \: x = 6\)

Step-by-step explanation:

Given equation,

\( \sf \rightarrow \: x + x + ( \frac{1}{6} )x = 13\)

Now the value of x will be,

\( \sf \rightarrow \: x + x + ( \frac{1}{6} )x = 13\)

\( \sf \rightarrow \: 2x + ( \frac{1}{6} )x = 13\)

\( \sf \rightarrow \: ( \frac{12}{6} )x + ( \frac{1}{6} )x = 13\)

\( \sf \rightarrow \: \frac{13}{ 6} x = 13\)

\( \sf \rightarrow \: 13x = 13 \times 6\)

\( \sf \rightarrow \: x = \frac{78}{13} \)

\( \sf \rightarrow \boxed{ \sf x = 6}\)

Hence, the value of x is 6.

Answer:$89.00

Step-by-step explanation:22 times 2 is 44.

15 times 3 is 45.

44 plus 45 is 89

Answer:

$89.00

Step-by-step explanation:

2 adults = $22 x 2 = $44

3 children = $15 x 3 = $45

$44 + $45 = $89.00

Hope this helps!

Statistical guidance should perform well in situations such as clinical trials and market research where rigorous data analysis and inference are necessary. Statistical methods provide a systematic approach to control biases, handle variability, and draw reliable conclusions, ensuring accurate decision-making and predictions based on the data.

Statistical methods are crucial in determining sample sizes, designing the study, and analyzing the data to draw valid conclusions about the effectiveness and safety of the treatment.

In this situation, statistical guidance should do well because it provides a systematic framework to control for biases, random variability, and confounding factors, ensuring robust and reliable results that can be generalized to a larger population.

One example where statistical guidance should perform well is in clinical trials for new drugs or treatments.

Another example is in market research and opinion polling. Statistical techniques can be used to collect and analyze data from a representative sample of the target population, allowing for accurate estimation and prediction of consumer preferences, market trends, or election outcomes.

Statistical guidance should do well in this situation because it provides methods for random sampling, hypothesis testing, and confidence interval estimation, which help minimize sampling errors and increase the reliability of the findings.

Additionally, statistical models can capture complex relationships and make accurate predictions based on the observed data.

To know more about statistical guidance refer here:

https://brainly.com/question/33175276#

#SPJ11

Solve the system of Equations:

Using the graphical method, plot the system of equations on the same graph as shown below:

The solution to the system of equations is the point of intersection of the graphs.

From the graph, the solution is:

The solution set to the inequality is w > 3

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

w+ 4<4 (w - 2)

Open the bracket

So, we have the following representation

w+ 4 < 4w - 8

Evaluate the like terms

So, we have the following representation

12 < 3w

Divide by 3

4 < w

So, we have

w > 4

See attachment for number line

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1