Describe in words where √30^(3) would be plotted on a number line.
Answers
The cube root of 30 would be between 3 and 4, but closer to 3.
How to find cube root of a number?Cube root is the number that needs to be multiplied three times to get the original number.
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing three same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.
We have to find the cube root of 30.
Prime factorization of 30 = \(2\times3\times5\).
Therefore the cube root of 30 = \(\sqrt[3]{ (2\times3\times5)}= \sqrt[3]{30}\).
As \(\sqrt[3]{30}\) cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.
So here we will use approximation method to find the cube root of 30 using Halley's approach:
Halley’s Cube Root Formula:
\({\sqrt[3]{\text{a}} = \dfrac{\text{x}[(\text{x}^3 + 2\text{a})}{(2\text{x}^3 + \text{a})]}}\)
The letter “a” stands in for the required cube root computation.
Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.
Here we have a = 30
and we will substitute x = 3 because 3³ = 27 < 30 is the nearest perfect cube.
Substituting a and x in Halley's formula,
\(\sqrt[3]{30} = \dfrac{3[(3^3 + 2\times30)}{(2\times3^3 + 30)]}\)
\(= \dfrac{3[(27+60)}{(54+30)]}\)
\(= 3\huge \text(\dfrac{87}{84} \huge \text)\)
\(= 3\times1.0357\)
\(\bold{\sqrt[3]{30} = 3.107}\).
Hence, the cube root of 30 is 3.107.
Therefore, we can conclude that the cube root of 30 would be between 3 and 4, but closer to 3.
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Complete question:
Describe in words where cube root of 30 would be plotted on a number line.
A. Between 3 and 4, but closer to 3
B. Between 3 and 4, but closer to 4
C. Between 2 and 3, but closer to 2
D. Between 2 and 3, but closer to 3
Related Questions
ANSWER FAST!!!
1) which family member ate the most pizza?
2) if the company offered an extra large pizza, how could you find out how much of it a person ate if they cut their own piece with a central angle of M?
Answers
1. Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter
2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M°
How to calculate the valueAndy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter. This means that she ate 100% of the pizza. Andy's wife ate 2/6 of the small pizza, which is 12 inches in diameter. This means that she ate 1/3 of the pizza. Andy's younger daughter ate 1/8 of the medium pizza, which is 14 inches in diameter.
This means that she ate 12.5% of the pizza. Andy cut himself a piece that had a central angle of 180° from the large pizza, which is 16 inches in diameter. This means that he ate 50% of the pizza.
The least amount of pizza was eaten by Andy's younger daughter. She only ate 1/8 of the medium pizza.
2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M° by using the following formula:
Percentage of pizza eaten = (M° / 360°) * 100%
For example, if a person cut themselves a piece of an extra large pizza with a central angle of 180°, they would have eaten 50% of the pizza.
Percentage of pizza eaten = (180° / 360°) * 100% = 50%
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What is the maximum of f(x)=sin(x)
Answers
Answer:
1
Step-by-step explanation:
The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2. If you look at a graph of
y = sin(x) you can see this.
Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.
Step-by-step explanation:
Property of Sine function:
Sin(x)=0 when x=90°,180°,360°The maximum and Minimum value of Sin(x) is 1 and -1 respectively, when and x=270° respectively.The range of values of sin(x) is -1 to 1.Read more on the Sine function:
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2/5 divided by 3 in its simplest form in a fraction is?
Answers
Answer:
2/15
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
The equivalent value of the fraction is A = 2/15
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first fraction be p
Let the second fraction be q
Now , A = p/q
when the value of p = 2/5
And , when the value of q = 3
On simplifying the equation , we get
A = ( 2/5 ) / 3
So , the left hand side of the equation is equated to the right hand side by the value of ( 2/5 ) / 3
A = ( 2/5 ) / 3
A = ( 2/5 ) ( 1/3 )
On simplifying , we get
A = 2/15
A = 0.133333
Therefore , the value of A = 2/15 = 0.133333
Hence , the fraction is A = 2/15
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The number of adults who attend a music festival, measured in hundreds of people, is represented by the function a(d)=−0.3d2+3d+10, where d is the number of days since the festival opened.
The number of teenagers who attend the same music festival, measured in hundreds of people, is represented by the function t(d)=−0.2d2+4d+12, where d is the number of days since the festival opened.
What function, f(d) , can be used to determine how many more teenagers than adults attend the festival on any day?
f(d)=−0.1d2+d+22
f(d)=0.1d2+d+2
f(d)=−0.1d2+7d+2
f(d)=0.1d2+7d+2
Answers
Answer:
f(d)=0.1d^2+d+2
Step-by-step explanation:
t(d)=−0.2d2+4d+12
a(d)=−0.3d2+3d+10
how many more teenagers than adults attend the festival on any day?
==>
f(d) = t(d) - a(d)
=0.1d^2+d+2
The midpoint of AB is M(1,4). If the coordinates of A are (8,7), what are thecoordinates of B?
Answers
First you have to draw points A and M and the line between them. Add two lines, one paralel to X and one paralel to Y to form a triangle.
Since M is the midpoint between A and B, this means that the distance between A and M, is equal to the distance between M and B.
Following the same inclination of the line, you have to draw another triangle starting from M with the same heigth and base as the one drawn under segment AM. The hypotenuse of this second triangle will be segment MB.
Now that you know were point B stand in the cartesian system, you can read the coordinates from the graphic.
X-coordinate is -6
Y-coordinate is 1
The coordinates for B are (-6,1)
Pineapples are on sale for $2 each, but customers can buy no more than 5 at
this price.
For pineapples bought at the sale price, the total cost, y, is directly
proportional to the number bought, x. This function can be modeled by y = 2x.
What is the domain of the function in this situation?
A. {0, 2, 4, 6, 8, 10)
B. All positive numbers, x > 0
O C. {0, 1,2,3,4,5)
D. {0, 1, 2, 3, 4, ...}
Answers
9514 1404 393
Answer:
C. {0,1,2,3,4,5)
Step-by-step explanation:
The domain of the function is the possible numbers of pineapples that could be bought at the indicated price. That will be a non-negative integer less than or equal to 5:
{0, 1, 2, 3, 4, 5)
Hi can someone please help me solve the following system of inequalities and state the coordinates in the solution setz
Answers
The graph of the system of the inequalities is attached.
To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.
Let's begin with the equation y = -x - 4:
Choose a range of x-values to plot.
For simplicity, let's use x-values from -10 to 10.
Substitute different x-values into the equation to find corresponding y-values.
For example:
When x = -10, y = -(-10) - 4 = 10 - 4 = 6.
When x = 0, y = -(0) - 4 = -4.
When x = 10, y = -(10) - 4 = -10 - 4 = -14.
Plot these points on the coordinate plane and draw a straight line passing through them.
This line represents the equation y = -x - 4.
Next, let's graph the equation y = (3/5)x + 4:
Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.
Substitute different x-values into the equation to find corresponding y-values. For example:
When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.
When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.
When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.
Plot these points on the coordinate plane and draw a straight line passing through them.
This line represents the equation y = (3/5)x + 4.
Now, let's shade the regions based on the inequalities:
For y < -x - 4, we need to shade the region below the line y = -x - 4.
For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.
Hence, the region where the shaded regions overlap represents the solution to both inequalities.
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Situation 1. ROCKET RIDE.
The Rocket Coaster has 10 cars, some that
hold 4 people and some that hold 8 people.
There is room for 56 people altogether.
How many 4-passenger cars are there?
How many 8-passenger cars are there?
Let x= number of 4-passenger cars
Let y = number of 8-passenger cars
equation #1:
equation #2:
Solution:
Answers
What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
Answers
An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).
The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.
In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.
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10/27 x (3/8 divided by 5/24) =
Evaluate the expression
I will crown if right any weird answers reported
Answers
I hope this helps you!
You wish to test the following claim H^Ц at a significance level of а=0.10. For the context of this problem. Ц₄=Ц₂-Ц₁ where the first data set represents a pre-test and the second data set represents a post-test.
Hₐ² Ц =0
Ha² Ц ≠0
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-4est simples for n=25 subjects. The average difference (post - pre) is d=-34.3 with a standard deviation of the differences of sd=42.9.
What is the critical value for this test? (Report answer accurate to three decimal places.) critical value . ± ____
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
fest statistic = ____
Answers
We have a two-tailed test, as we are testing if the mean is different of a value.
The t-distribution is used, as we have the standard deviation for the sample, and the parameters are given as follows:
25 - 1 = 24 degrees of freedom.Significance level of 0.10.Using a t-distribution calculator, the critical value is of:
t = ± 1.7109.
How to obtain the test statistic?The equation for the test statistic is defined as follows:
\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)
The parameters are:
\(\overline{x}\) is the sample mean.\(\mu\) is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In the context of this problem, the values of these parameters are of:
\(\overline{x} = -34.3, \mu = 0, s = 42.9, n = 25\)
Hence the value of the test statistic is of:
\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)
\(t = \frac{-34.3 - 0}{\frac{42.9}{\sqrt{25}}}\)
t = -4.
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Write the standard form of the equation of the circle with radius 6 and center (−3,3)
Answers
Answer:
(x+3)^2+(y-3)^2=36
Step-by-step explanation:
Standard equation of circle is (x-a)^2+(y-b)^2=r^2
jen's total assets are $8,794. Her liabilities are $2,670 in credit card debt and $3,622 for a student loan. What is her net worth?
Answers
Answer:
2502
Step-by-step explanation:
8,794-2,670-3,622=
Work out the perimeter of a semicircle with radius 3cm.
give your answer in terms of pi
Answers
Answer:
(6 + 6π) cm
Step-by-step explanation:
2π(3) / 2 + 3x2
= (6 + 6π) cm
PLEASE HELP ASAPPPP !!! WILL GIVE BRAINLIEST !!!
1. Find the equation of the line through point (4,−7) and parallel to y=−2/3x+3/2.
2. Find the equation of the line through point (−1,4) and parallel to 5x+y=4
3. Find the equation of the line through point (5,4) and perpendicular to y=−4/3x−2
4. Find the equation of the line through point (8,−9) and perpendicular to 3x+8y=4
Answers
Answer:
Step-by-step explanation:
Slope of parallel lines are equal.
1) m = -2/3
(4,-7)
\(y-y_{1}=m(x-x_{1})\\\\y-[-7]=\frac{-2}{3}(x-4)\\\\y+7=\frac{-2}{3}*x-\frac{-2}{3}*4\\\\y+7=\frac{-2}{3}x+\frac{8}{3}\\\\y=\frac{-2}{3}x+\frac{8}{3}-7\\\\y=\frac{-2}{3}x+\frac{8}{3}-\frac{7*3}{1*3}\\\\y=\frac{-2}{3}x+\frac{8}{3}-\frac{21}{3}\\\\y=\frac{-2}{3}x-\frac{13}{3}\)
2) 5x + y = 4
y = -5x + 4
slope m = -5
(-1,4)
y - 4 = -5(x -[-1])
y- 4 = -5(x+1)
y - 4 = -5x - 5
y = -5x - 5 + 4
y = -5x -1
If two lines are perpendicular, m2 = -1/m1
m1 = -4/3
\(m_{2}=\frac{-1}{\frac{-4}{3}}=-1*\frac{-3}{4}=\frac{3}{4}\\\)
(5,4)
\(y-4=\frac{3}{4}(x - 5)\\\\y-4=\frac{3}{4}x-\frac{3}{4}*5\\\\y-4=\frac{3}{4}x-\frac{15}{4}\\\\y=\frac{3}{4}x-\frac{15}{4}+4\\\\y=\frac{3}{4}x-\frac{15}{4}+\frac{4*4}{1*4}\\\\y=\frac{3}{4}x-\frac{15}{4}+\frac{16}{4}\\\\y=\frac{3}{4}x+\frac{1}{4}\)
Answer:
3.) is y=3/4x+1/4 That's what i got but i hope this helps.
Step-by-step explanation:
Describe how p(x)=-f(x)-3 transforms the graph of the parent function f(x)=x^2
.
Answers
The transformation of f(x) to p(x) is that (a) the graph is reflected and shifted down
Describing the transformation of f(x) to p(x).From the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
In the function equations, we can see that
f(x) = x²
p(x) = -f(x) - 3
So, we have
Vertical Difference = 0 - 3
Evaluate
Vertical Difference = - 3
This means that the transformation of f(x) to p(x) is that f(x) is reflected and shifted down 3 units to p(x).
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Addison has x pennies and y nickels. She has a minimum of 16 coins worth no more
than $0.40 combined. Solve this system of inequalities graphically and determine
one possible solution.
Answers
What is the mean of the following data set?
82, 100, 92, 66, 72, 96, 70, 88.
Answers
Answer:
83.25
Step-by-step explanation:
add all the numbers and divide by 8. 666/8 = 83.25
Answer:
83.25
Step-by-step explanation:
Mean = sum of all terms / number of terms
82+100+92+66+72+96+70+88 = 666
666 / 8 = 83.25
it is 4.5 miles from moulton to filby via Burnham and denton how far is it between denton and filby
Answers
Answer: I think that the answer is 3/4 miles
Step-by-step explanation:
graph of function f(x)=1/x+7-14
Answers
Vertical Asymptotes: x=0
Horizontal Asymptotes: y= -7
No Oblique Asymptotes
10) The temperature recorded at 12 noon was 15°C above zero. If it decreases at the rateof 3°C per hour until midnight, at what time would the temperature be 9°C below zero? Whatwould be the temperature at midnight?
Answers
Answer:
at 8 pm the temperature will be -9 degrees. and at midnight the temperature will be negitive twenty one(-21) degrees
Step-by-step explanation:
the start time is 12 pm and finish is 12 am and every hour your going to subtract 3 from the given degree so 15-3= 12 , 12-3=9 ect.
Jennie makes quilts. She can make 7 quilts with 21 yards of material. How many yards of material would be required to make 14 quilts? also someone need help asap
Answers
Answer:
42 yards
Step-by-step explanation:
Given that Jennie could mkae 7 quilts out of 21 yards of material:
We could establish a proportion to find the value of x yards of material required to make 14 quilts:
21 yards/7 quilts = x yards / 14 quilts
\(\frac{21}{7} = \frac{x}{14}\) ⇒ Perform cross-multiplication:
7x = 21 × 14
7x = 294
Divide both sides by 7 to solve for x:
\(\frac{7x}{7} = \frac{294}{7}\)
x = 42 yards
Therefore, Jennie needs 42 yards of material in order to make 14 quilts.
PLEASE HELP AS FAST AS YOU CAN ASAP DUE IN 30 MINUTES!!!!
the prism is made up of unit cubes. the side length of the unit cube is 1/4 inch
what us the volume of the prism
A. 3/8
B. 8
C. 24
D. 1/64
please explain as well
Answers
Answer:
C
<$&#&#;#;#;#;#
Step-by-step explanation:
1/4= 4x6=24
Answer:
C
Step-by-step explanation:
The weights of 7000 boxes of corn flakes filled by a machine are normally distributed, with an average weight of 15 ounces and standard deviation of 0.4 ounce.
(a) What percentage of boxes weight less than 15.4 ounces?
(b) What percentage of boxes weight more than 15.4 ounces?
(c) What percentage of boxes weight less than 14 ounces?
(d) What percentage of boxes weight between 14 and 15.4 ounces?
Answers
(a) The percentage of boxes that weigh less than 15.4 ounces is approximately 84.13%.
(b) Approximately 15.87% of boxes weigh more than 15.4 ounces.
(c) The percentage of boxes that weigh less than 14 ounces is approximately 0.62%.
(d) Approximately 83.51% of boxes weigh between 14 and 15.4 ounces.
The percentage of boxes that weigh less than 15.4 ounces, we need to calculate the z-score for this value:
z = (15.4 - 15) / 0.4 = 1
A standard normal distribution table or a calculator with a normal distribution function, we can find that the percentage of boxes that weigh less than 15.4 ounces is approximately 84.13%.
The percentage of boxes that weigh more than 15.4 ounces, we can subtract the percentage from part (a) from 100%:
100% - 84.13% = 15.87%
Approximately 15.87% of boxes weigh more than 15.4 ounces.
The percentage of boxes that weigh less than 14 ounces, we need to calculate the z-score for this value:
z = (14 - 15) / 0.4 = -2.5
A standard normal distribution table or a calculator with a normal distribution function, we can find that the percentage of boxes that weigh less than 14 ounces is approximately 0.62%.
The percentage of boxes that weigh between 14 and 15.4 ounces, we need to calculate the area under the curve between these two values.
The z-scores for these values and subtracting the area to the left of the lower z-score from the area to the left of the higher z-score:
z1 = (14 - 15) / 0.4
= -2.5
z2 = (15.4 - 15) / 0.4
= 1
A standard normal distribution table or a calculator with a normal distribution function, we can find that the area to the left of z1 is approximately 0.62% (as found in part (c)) and the area to the left of z2 is approximately 84.13% (as found in part (a)).
The area between these two z-scores is:
84.13% - 0.62% = 83.51%
Approximately 83.51% of boxes weigh between 14 and 15.4 ounces.
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A line passes through the points (-3, 7) and (6, 4). Which shows the graph of this line?
Answers
Answer:
y= -1/3x + 6
Step-by-step explanation:
To find slope use y2-y1/x2-x1. I used y2=4 x2=6 y1=7 x1=-3
It doesn't matter which one is y2 or y1 etc. As long as they match up with each other.
You end up with -1/3 as your slope.
To find y intercept we use y=mx+b with m being the slope we just found and plugin in y and x with either point that was given.
I used (6,4)
4= -1/3(6) + b then you solve for b and get 6. Equation should be -1/3x+ 6.
The graph have a negative 1 over 3 slope with a y intercept at 6.
Hope this helps!
Answer:
A
Step-by-step explanation:
got it right on edg
1.A car is traveling down a highway at a constant speed, described by the equation ca st waveleng topres his tay istance, in miles, that the car travels at this speed in
d = 65t, where d represents the distance, in miles, that the car travels at this speed in
1 hours.
a. What does the 65 tell us in this situation?
b. How many miles does the car travel in 1.5 hours?
c. How long does it take the car to travel 26 miles at this speed?
Answers
a) The 65 in the equation, d = 65t, where d is the distance in miles and t is the time, is the speed of the car.
b) In 1.5 hours, the car will cover a distance of 97.5 miles.
c) At the speed of 65 miles per hour, the car will take 24 minutes to travel 26 miles.
What is the distance?The distance represents the length covered based on speed and time.
We compute distance as the product of speed and time.
On the other, speed or time is the quotient of distance and time or speed.
Distance in miles in 1 hour, d = 65t
t = time
a) The formula for distance = speed x time
Since t is the time, 65 is the driving speed of the car.
b) Distance in 1.5 hours = 65(1.5) = 97.5 miles
c) At 65 miles per hour, the car will take 24 minutes to travel 26 miles (26/65 x 60).
Thus, there is a ratio relationship between distance, time, and speed.
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If Melinda wanted to build a patio in her backyard that was 14 feet long, 6 feet wide
and 4 inches deep using pervious concrete mix that is 4 parts aggregate to 4.5 parts
loose cement, with some water added then how many cubic feet of aggregate would
she need to build the walkway?
Round the final answer to the hundredths place. If you answer doesn't have a
hundredths place include zeros so that it does
Answers
The volume of aggregate that she needs to build the patio is 13.18 ft^3
How many cubic feet of aggregate would she need to build the walkway?
We know that the backyard is 14ft long, 6 feet wide and 4 inches deep.
Rememeber that:
1ft = 12 in
Then:
4 in = (4/12) ft = (1/3) ft
Then the volume of the backyard is:
V = (14ft)*(6ft)*(1/3 ft) = 28ft^3
Now we know that we have a mix of 4 parts aggregate to 4.5 parts loose cement that need to fill these 28 cubic feet.
Note that:
4 + 4.5 = 8.5
How many times we have 8.5 in 28?
28/8.5 = 3.294
Now for each of these we have 4 parts of aggregate, then the volume of aggregate that we need is:
4*3.294 ft^3 = 13.18 ft^3
The volume of aggregate that she needs to build the patio is 13.18 ft^3
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solve the PDE using separation of variables method Uxx = 1/2 Ut 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Answers
The general solution of the partial differential equation is:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
How to solve Partial Differential Equations?The partial differential equation (PDE) is given as:
Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Assume that the solution can be written as a product of two functions:
U(x, t) = X(x)T(t)
Substituting this into the PDE, we have:
X''(x)T(t) = (1/2)X(x)T'(t)
Dividing both sides by X(x)T(t), we get:
(X''(x))/X(x) = (1/2)(T'(t))/T(t)
Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:
(X''(x))/X(x) = -λ²
(1/2)(T'(t))/T(t) = -λ²
Simplifying the second equation, we have:
T'(t)/T(t) = -2λ²
Solving the second equation, we find:
T(t) = Ce^(-2λ²t)
Applying the boundary condition U(0, t) = 0, we have:
U(0, t) = X(0)T(t) = 0
Since T(t) ≠ 0, we must have X(0) = 0.
Applying the boundary condition U(3, t) = 0, we have:
U(3, t) = X(3)T(t) = 0
Again, since T(t) ≠ 0, we must have X(3) = 0.
Therefore, we can conclude that X(x) must satisfy the following boundary value problem:
X''(x)/X(x) = -λ²
X(0) = 0
X(3) = 0
The general solution to this ordinary differential equation is given by:
X(x) = Asin(λx) + Bcos(λx)
Applying the initial condition U(x, 0) = 5*sin(4πx), we have:
U(x, 0) = X(x)T(0) = X(x)C
Comparing this with the given initial condition, we can conclude that T(0) = C = 5.
Therefore, the complete solution for U(x, t) is given by:
U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)
where:
Σ represents the summation over all values of n
λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).
To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):
X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0
X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0
From the first equation, we have Bₙ = 0.
From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.
This implies that 3λₙ = nπ, where n is an integer.
Therefore, λₙ = (nπ)/3.
Substituting the eigenvalues into the general solution, we have:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
where Aₙ are the coefficients that can be determined from the initial condition.
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Answers
A wiring job requires 4 electricians to work for 6 hours to finish the job.
On the day of the job, one electrician does not report. How long would it
take to complete the same job by the remaining electricians?
Answers
if we are talking about 24hrs. 24/4=6 so 24/3=8 (3 bc there is one less)!
The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.
How are number of people to time needed to complete a task related?More people to do a task means less time it will take.
Less people to do a task means more time it will take.
Thus, they are inversely related.
If x men take y time for a work,
We can define a constant as "Manpower" needed for doing that specific work.
Let we define:
Manpower needed for a work = y + y + y + .. + y = Time per man × count of men
Manpower needed for a work = xy
We are given that;
Number of electricians= 4
Number of hours= 6
Now,
We can use the formula:
workers × time = work
where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.
In this case, we know that 4 electricians can complete the job in 6 hours. So:
4 × 6 = work
work = 24
This means that the total amount of work required to complete the job is 24 "units".
Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".
So we have:
3 × t = 24
Dividing both sides by 3, we get:
t = 8
Therefore, by work and time answer will be 3 electricians and 8 hours.
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