A cable that weighs 6 lb/ft is used to lift 500 lb of coal up a mine shaft 400 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)
Answers
The work done to lift the coal is 6.8*10^5 ft-lb
Data;
- weight of cable = 6lb/ft
- weight of coal = 500lb
- length of mine shaft = 400ft
Let the distance (ft) below top of the shaft be represented by x
The weight of the coal to be lifted from mine = 500lb
Work Done
The work done to lift the coal is
Taking the summation limit
we can take the integration of both sides where x will the range from 0 to 400.
From the calculations above, the work done is 6.8*10^5 ft-lb
Learn more on work done on a lift here;
Answer:
8.2 *10^5 ft lb
Step-by-step explanation:
Wcoal = 800*500 = 400000 = 4*10^5 ft lb
Using a right Riemann sum
The width of the entireregion to be estimated = 400 - 0 = 400
Considering 8 equal subdivisions, then the width of each rectangular division is 400/8 = 50
F(x) = 6(400-y)
Wrope = 50(2100) + 50(1800) + 50(1500) + 50(1200) + 50(900) + 50(600)
+ 50(300) + 50(0) = 420000 = 4.2 * 10^5 ft lb
Note: Riemann sum is an approximation, so may not give a accurate value
work done = Wcoal + Wrope= 4*10^5+ 4.2 * 10^5 = 8.2 *10^5 ft lb
Related Questions
A bank credit card charges interest at the rate of 24% per year, compounded monthly. If a senior in college charges $1,500 to pay for college expenses, and intends to pay it in one yewhat will he have to pay? (Round your answer to the nearest cent.)$
What is the factors for 14 and 6
4.1 Number Talk: DivisionFind each quotient mentally. 645 divided by 100 645 divided by 50 48.6 divided by 30 48.6 divided by x
Hey can you please help me posted picture of question
6 apples each and the bags with mangoes
contain 3 mangoes each. If David and his
friends ate 2 apples from each bag and 2
mangoes from each bag, what is the total
number of fruits left over?
Answers
Answer:
Step-by-step explanation: the step by step explanation is 6*4=24 so 24 apples then 3*2=6 so 6 mangoes then if 8 apples are ate then 4 mangoes are ate then (24+6)-(8+4)=30-12 so the answer is 18.
6 bags in total
4 bags x 6 apples each = 24 fruits
2 bags with 3 mangoes each= 6 fruits
Total 30 fruits
Friends ate 2 fruits from each of the 6 bags
They ate 12 fruits
30-12 = 18
Answers
Answer:
The sample size 'n' = 576
576 times should you execute the process to get the desired precision
Step-by-step explanation:
Explanation :-
Step(i)
Given data the process can turn 60% of the input compounds into the desired synthesized compound.
Sample proportion ' p' = 60% = 0.60
Given data the estimate within 0.04 of the true proportion that is converted
The margin of error of the true population proportion
M.E = 0.04
Step(ii)
The margin of error of the true population proportion is determined by
on calculation, we get
squaring on both sides ,we get
n = 576
Final answer:-
The sample size 'n' = 576
576 times should you execute the process to get the desired precision
Answers
Answer:
90 degree
Step-by-step explanation:
Three points A, B, and C are added and shown in attached picture.
As the property of inscribed angle in circle:
angle BAC = (1/2) x 88 = 44 deg
As the property of complement angle:
angle ABC = 180 - 89 = 91 deg
As the property of sum of three angles in a triangle:
angle ACB + angle ABC + angle BAC = 180 deg
=> angle ACB = 180 - angle ABC - angle BAC = 180 - 44 - 91 = 45 deg
One more time, we use the property of inscribed angle in circle:
x = 2 x angle ACB = 2 x 45 = 90 deg
Hope this helps!
Answers
Answer:
Wavelengths of all possible photons are;
λ1 = 9.492 × 10^(-8) m
λ2 = 1.28 × 10^(-6) m
λ3 = 1.28 × 10^(-6) m
λ4 = 4.04 × 10^(-6) m
Step-by-step explanation:
We can calculate the wavelength of all the possible photons emitted by the electron during this transition using Rydeberg's equation.
It's given by;
1/λ = R(1/(n_f)² - 1/(n_i)²)
Where;
λ is wavelength
R is Rydberg's constant = 1.0974 × 10^(7) /m
n_f is the final energy level = 1,2,3,4
n_i is the initial energy level = 5
At n_f = 1,.we have;
1/λ = (1.0974 × 10^(7))(1/(1)² - 1/(5)²)
1/λ = 10535040
λ = 1/10535040
λ = 9.492 × 10^(-8) m
At n_f = 2,.we have;
1/λ = (1.0974 × 10^(7))(1/(2)² - 1/(5)²)
1/λ = (1.0974 × 10^(7))(0.21)
1/λ = 2304540
λ = 1/2304540
λ = 4.34 × 10^(-7) m
At n_f = 3, we have;
1/λ = (1.0974 × 10^(7))(1/(3)² - 1/(5)²)
1/λ = (1.0974 × 10^(7))(0.07111)
1/λ = 780373.3333333334
λ = 1/780373.3333333334
λ = 1.28 × 10^(-6) m
At n_f = 4, we have;
1/λ = (1.0974 × 10^(7))(1/(4)² - 1/(5)²)
1/λ = (1.0974 × 10^(7))(0.0225)
1/λ = 246915
λ = 1/246915
λ = 4.04 × 10^(-6) m
Answers
9514 1404 393
Answer:
(a) k = –2.5
Step-by-step explanation:
When the function f(x) is transformed to f(x -h) +k, the graph is translated h units right and k units up.
If the absolute value function has its original vertex of (0, 0) moved to (1, -2.5), then (h, k) = (1, -2.5).
The value of k is -2.5.
_____
Additional comment
The above answer applies to the given problem statement. The question asked in the comment has a vertex of (0, 2.5), so (h, k) = (0, 2.5) for that question.
If you're going to copy the answer, make sure it is the answer to the question you're looking at.
In an absolute value function expressed as f(x) = |x – h| + k, the value of k corresponds to the y-coordinate of the function's vertex. In this case, as the vertex is at the point (1, -2.5), the value of k is -2.5.
The student's question relates to the concepts of Two-Dimensional (x-y). Graphing and the graphing of the absolute value function. It is vital to remember that the vertex of an absolute value graph in the form f(x) = |x – h| + k corresponds to the point (h, k) on the Cartesian coordinate plane. The student states that the vertex is at the point (1, -2.5), so based on our function analysis, the value of k, which represents the y-coordinate of the vertex, is -2.5. Therefore, the correct answer is k = -2.5.
For more about Absolute Value Graph here:
#SPJ3
Answers
(a) The length of time it takes to fill up your gas tank - Continuous
(b) The number of students applying to graduate schools - Continuous
(c) The number of voters who vote Democratic - Discrete
(d) The number of customers waiting at the grocery store-Discrete
What is the difference between continuous and discrete data?
Continuous data can have an infinite range of values while Discrete data can take some certain values only.
Let us consider the given examples
a) The length of time it takes to fill up your gas tank.
In this case, the time duration can be of a wide range. Time taken while filling up a gas tank can take many values. So it is an example of continuous data.
b) The number of students applying to graduate schools.
In this case, the number of students applying to graduate schools can be of a wide range. it can be n number of values. So it is an example of continuous data.
c)The number of voters who vote Democratic.
The number of voters who vote can be of a certain value. Hence, this is an example of discrete data.
d)The number of customers waiting in line at the grocery store.
The number of customers waiting in line at the grocery store can be of a certain value. Hence, this is an example of discrete data.
Therefore, we can say that
(a) The length of time it takes to fill up your gas tank - Continuous
(b) The number of students applying to graduate schools - Continuous
(c) The number of voters who vote Democratic - Discrete
(d) The number of customers waiting at the grocery store-Discrete
To get more about continuous and discrete data refer to the link,
Answer:
(a) The length of time it takes to fill up your gas tank - CONTINUOUS
(b) The number of students applying to graduate schools - CONTINUOUS
(c) The number of voters who vote Democratic - DISCRETE
(d) The number of customers waiting in line at the grocery store - DISCRETE
Step-by-step explanation:
To determine either the set of data are discrete or continuous, let consider their characteristics.
CONTINUOUS
continuous data is quantitative data, It can be measured, it has an infinite values within selected range.
DISCRETE
Discrete data is counted, it can only take certain values.