A block-and-tackle pulley is suspended in a warehouse by ropes of length 8.4 m for the rope on the left and 9 m for the rope on the right. The hoist weights 1,854.2 N. The ropes, fastened at different heights, make angles with the horizontal of 24∘ for the angle on the left and of 88∘ for the angle on the right. Find the tension in each rope and the magnitude of each tension. Calculate the exact value for each of these and write this calculation on your answer sheet. Enter the magnitude of the tension for the rope on the left in N rounded to 4 decimal places in the answer box.
Answers
To find the tensions in the ropes of the block-and-tackle pulley, we can use the principles of equilibrium. Let's denote the tension in the rope on the left as Tleft and the tension in the rope on the right as Tright.
In equilibrium, the sum of the vertical components of the tensions must equal the weight of the hoist. The vertical component of Tleft is Tleft * sin(24°), and the vertical component of Tright is Tright * sin(88°). So we have the equation:Tleft * sin(24°) + Tright * sin(88°) = 1854.2 N
Next, we consider the horizontal components of the tensions. The horizontal component of Tleft is Tleft * cos(24°), and the horizontal component of Tright is Tright * cos(88°). Since the horizontal components must cancel out, we have:Tleft * cos(24°) = Tright * cos(88°)
Now, we can solve these two equations simultaneously to find the values of Tleft and Tright. Once we have the values, we can calculate the magnitude of each tension by taking the square root of the sum of the squares of their vertical and horizontal components.After performing the calculations, the magnitude of the tension for the rope on the left is approximately 926.7286 N (rounded to 4 decimal places).
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Related Questions
18
What is the value of 8? (show all work on paper):
14
A
B
C
D
8
25°
44.4°
62.8°
30°
20
Answers
Answer:
There is no context to determine the value of 8. It could refer to a number, angle, or multiple-choice answer. More information is needed.
Step-by-step explanation:
Answer:
B. 44.4
Step-by-step explanation:
sinA = leg opposite ∠A / hypotenuse : sin (∠SRQ) = ⁻⁻QS/⁻⁻RS
Substitute ⁻⁻QS = 14, ⁻⁻RS = 20, ∠SRQ=0 into sin (∠SRQ)=⁻⁻QS/⁻⁻RS : sin(0) = 14/20
sin(0) = 14/20 : 0=44.4
Need help on this.
Find the missing angle
Answers
Answer:
60
Step-by-step explanation:
a+b+c=60
180 - 84 - 36 = 60
I needddd help it’s urgenttttt!!!!
Answers
135
Step-by-step explanation:
First find the measure of CBF
CBF is a straight line so therefore it measures 180*
BFE = 75*
CBD = 45*
75 + 45 = 120*
180 - 120 = 60
60 + 75 = 135*
Therefore DBF measures 135*
What is the inverse equation of the function, y = 3x - 6? y -1 = y -1 = x + 6 x -1 = 3 y - 6 y -1 = 3 x + 6.
Answers
The best answer (and only correct answer) among the options given is: option [C]: y⁻¹ = (x+6) / 3 .
What is the inverse function?
The inverse function returns the original value for which a function gave the output. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x.
Given the original function: y = 3x - 6 ;
To find the "inverse equation" of said function; we change the "x" to a y"; and the "y" to an "x"; and rewrite:
x = 3y − 6 ;
Now, rewrite in "slope-intercept form" ; or y = mx + b ;
that is, with y as "single, isolated" variable on the left-hand side of the equation (with an "implied coefficient of positive one", only); then an "equal sign, then "mx + b" ; in which: "m" is the coefficient of the variable, "x"; and in which "m" refers to the "slope"; and "b" refers to the 'y-intercept".
So, we have the inverse function:
x = 3y − 6 ; we want to write in slope-intercept form;
Add "6" to each side of the equation:
x + 6 = 3y − 6 + 6 ;
x + 6 = 3y ;
Rewrite as: 3y = x + 6 ;
Divide EACH side of the equation by "3" ; to isolate "y" one side of the equation; specifically, the left-hand side of equation; and to write in "slope-intercept form:
3y / 3 = (x + 6) / 3 ;
to get:
y = (x + 6) / 3 ;
y = (x/3) + (6/3) ;
y = (x/3 ) + 2 ;
or; write as: y = (1/3)x + 2 ;
Now, let us examine the answer choices given:
Note that all the answer choices begin with "y-1" ;
(except "answer choice: [B]" , which begins with "x-1"). This seems confusing; however, in reality, this does not mean, "y minus 1"; or "x minus 1". Rather, it mean y⁻¹ or x⁻¹ as notation for the "inverse" (not to be confused with the exponent notation. The confusion stems from the fact that it can be difficult to make such notations on the "Brainly" system.
That being said, we can write the aforementioned "rewritten equations" (see above in THIS VERY ANSWER) as:
y⁻¹ = (x + 6) / 3 ;
y⁻¹ = (x/3) + (6/3) ;
y⁻¹ = (x/3 ) + 2 ;
or; write as: y⁻¹ = (1/3)x + 2
That being said:
Therefore, the best answer (and only correct answer) among the options given is: option [C]: y⁻¹ = (x+6) / 3 .
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An expression to determine the growth rate of a cell is written as 3(1. 25)/5. What would be an approximate form of this expression for all values of t?
3(0. 25)
O 3(1. 05)'
O 3. 05
O 3. 14
Answers
Option A is the correct option
So, the approximate form of the expression for all values of t is 0.75.
The expression 3(1.25)/5 can be simplified to
3/5 * 1.25
= 0.75.
=3(0.25)
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Term is defined as a constant, a single variable, or a mixture of variables and constants multiplied or divided. Algebra Expression Example: 3x + 9, 5x + 10
To simplify simply is to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
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if the sum of the measures of the interior angles of a polygon is 1980°, how many sides does the polygon have?
Answers
Answer:
The polygon has 13 sides.
Step-by-step explanation:
The sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides. This formula can be set equal to the sum of the interior angles to determine how many sides it has.
(n - 2) * 180 = 1980
180n - 360 = 1980
180n = 2340
n = 13
Kate is a buyer for a men’s fashion retail store. She will order a new cloth overcoat from Paris for the fall fashion season. Based on her experience, she expects to sell at least 100 coats, and at most 400, but she feels that any number of sales in between is equally likely. Therefore, she estimates that her sales are uniformly distributed between 100 and 400. The total cost to the store is $100 per coat, and the retail price is set at $180. Any coats left over at the end of season would be sold at $60 each.
part 1: a) How many coats should Kate buy if she wants to maximize profits?
part 2: b) Assume Kate buys the number of coats suggested in part a), what is the probability that the coats sell out? What is the probability that they do not sell out?
Answers
Part 1: Kate should buy 100 coats to maximize profits.Part 2: The probability that the coats sell out is 0.25 (25%), and the probability that they do not sell out is 0.75 (75%).
To maximize profits, Kate should consider the scenario where she sells all the coats without any left over at the end of the season.
Since the sales are uniformly distributed between 100 and 400, buying 100 coats ensures that she meets the minimum expected sales of 100. Purchasing more than 100 coats would increase costs without a guarantee of higher sales, potentially leading to excess inventory and lower profits.
Given that the sales are uniformly distributed between 100 and 400 coats, Kate's purchase of 100 coats covers the minimum expected sales.
The probability of selling out can be calculated by finding the proportion of the range covered by the desired sales (100 out of 300). Therefore, the probability of selling out is 100/300 = 0.25 or 25%. The probability of not selling out is the complement, which is 1 - 0.25 = 0.75 or 75%.
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Hello I really need some help I will give you BRAINLEST!!!!
Answers
Answer: Choice B
Step-by-step explanation:
V = 4 pi * r^3 / 3
V = 4 (3.14) * 8^3 / 3
V = 12.56 * 512 / 3
V = 12.56 * 170.66
V = 2,143.57 cm^3
Hope this helped! Please give brainliest.
what is the simple linear regression model for the response variable of annual salary (as) and explanatory variable of years of education (ed)? multiple choice question.
Answers
The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.
Variables used to explain or predict a response variable are called explanatory variables.
The students want to predict age using their height, so the explanatory variable is height and the response variable is age.
The values of an ordinal variable have a meaningful order. For example, an education level (with possible values of high school, bachelor's degree, and graduate degree) can be an ordinal variable.
"Hand" belongs to "Clock". "Experience" also belongs to "Year". So if he has 10 years of experience in the industry, no apostrophes are needed. An apostrophe is required if you have more than 10 years of experience.
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The AID Parcel Service wants to build a new distribution center in Charlotte. The center needs to be in the vicinity of Inerstate-77 and Intersatate-85 interchanges, and the Charlotte International Airport. The coordinates of these three sites and the number of weekly packages that flow to each are as follows:
I-77 I-85 Airport
X=16 X=35 X=40
Y=28 Y=10 Y=18
W=26,000 W=12,000 W=10,000
Determine the best site location using the center-of-gravity technique
Subject - Logistics management
Answers
Using the center-of-gravity technique, the best site location for the new distribution center in Charlotte is determined to be at coordinates (X, Y) = (27.92, 19.08).
The center-of-gravity technique is used to find the optimal location for a facility based on the distribution of demand. In this case, we will calculate the weighted average of the coordinates (X, Y) of the three sites, with the weights being the number of weekly packages flowing to each site.
To calculate the X-coordinate of the center of gravity, we use the formula:
Xc = (X1 * W1 + X2 * W2 + X3 * W3) / (W1 + W2 + W3)
Similarly, for the Y-coordinate:
Yc = (Y1 * W1 + Y2 * W2 + Y3 * W3) / (W1 + W2 + W3)
Substituting the given values:
Xc = (16 * 26000 + 35 * 12000 + 40 * 10000) / (26000 + 12000 + 10000) ≈ 27.92
Yc = (28 * 26000 + 10 * 12000 + 18 * 10000) / (26000 + 12000 + 10000) ≈ 19.08
Therefore, the best site location for the new distribution center in Charlotte is approximately at coordinates (X, Y) = (27.92, 19.08) based on the center-of-gravity technique.
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Which factored polynomial is shown in the graph?
A) y = (x + 2)(x + 1)(x + 4)
B) y = (x + 2)(x − 1)(x + 4)
C) y = (x + 2)(x − 1)(x − 4)
D) y = (x − 2)(x − 1)(x + 4)
Answers
Answer:
B
Step-by-step explanation:
First, we can determine the zeros of the function.
We can see that the graph passes through the x-axis at the points: x = -4, -2, and 1.
Therefore, we have three factors:
\((x-(-4)),\, (x-(-2))\text{ and } (x-(1))\)
Thus, our function will be:
\(y=(x+4)(x+2)(x-1)\)
Our answer is B.
I really need help ASAP, can someone help??
Answers
Answer:
x= -1/7 y=3/7
Step-by-step explanation:
2x+10y=4 x=2y-1
2(2y-1)+10y=4
4y-2+10y=4
14y-2=4
14y=6
y=3/7
x=2(3/7)-1
x=6/7-1
x=-1/7
Answer:
(-1/7,3/7)
Step-by-step explanation:
2. what do you want the fuel efficiency of a car to be two years from now? explain.
Answers
The desired fuel efficiency of a car two years from now would ideally be improved compared to the current fuel efficiency.
There are several reasons why we would want the fuel efficiency of a car to be better in the future:
Environmental Concerns: Improving fuel efficiency helps reduce carbon emissions and minimize the environmental impact of vehicles. As the world becomes more conscious of climate change and the need to reduce greenhouse gas emissions, enhancing fuel efficiency plays a vital role in mitigating environmental damage.
Energy Conservation: Better fuel efficiency means using less fuel to travel the same distance. With finite energy resources and the need to conserve them, improving fuel efficiency helps reduce the overall energy consumption in transportation, leading to better resource management.
Cost Savings: Increasing fuel efficiency directly translates to lower fuel consumption and reduced expenses for car owners. With rising fuel prices, having a more fuel-efficient car can significantly cut down on fuel costs, saving money for individuals and businesses.
Technological Advancements: As technology progresses, advancements in engine design, aerodynamics, lightweight materials, and alternative energy sources enable the development of more fuel-efficient vehicles. Striving for improved fuel efficiency encourages innovation in the automotive industry, leading to the creation of more sustainable and eco-friendly transportation options.
Government Regulations: Many governments worldwide have implemented fuel efficiency standards and regulations to reduce fuel consumption and emissions. By meeting or exceeding these standards, car manufacturers contribute to a cleaner and more sustainable transportation sector.
Ultimately, aiming for improved fuel efficiency two years from now aligns with the global push for environmental sustainability, energy conservation, cost savings, technological advancements, and adherence to regulatory standards. It benefits both individuals and society as a whole by promoting a greener and more efficient approach to transportation.
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Solve for x. 3 (x-4) < x-5
Answers
Answer:
x < 7/2
Step-by-step explanation:
Helppppp pleaseeee anyoneeeee
Answers
Step-by-step explanation:
so, the time to answer questions has to be added to the speaking time to get the total time of the meeting.
the speaking time is constant (25 minutes).
q = 1 means t = 25 + q = 25 + 1 = 26
q = 2 means t = 25 + q = 25 + 2 = 27
q = 3 means t = 25 + q = 25 + 3 = 28
q = 8 means t = 25 + q = 25 + 8 = 33
Find the volume of the cylinder with a diameter of 16 cm and height of 8 cm, as shown on the diagram below. 16 cm 8 cm Give your answer correct to 1 decimal place.
Answers
Answer:
1,608.5 cm³
Step-by-step explanation:
radius = 16 : 2 = 8 cm
base area = 8² · π = 64 ·π = 201.06193 cm²
Volume = 201.06193 · 8 = 1,608.495439 cm³
HELP ASAP!
The graphs below have the same shape. f(x) = x2.
What is the equation of the graph of g(x)?
Answers
Answer:
A
Step-by-step explanation:
Given the graph of f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Here g(x) is the graph of f(x) shifted 3 units to the left, then
g(x) = (x + 3)² → A
Answer:
A
Step-by-step explanation:
identify the property of equality which yields step 4
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
\(Division \: \: \: Property\)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The correct answer is (( A )) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Please answer this it is easy
Answers
Answer:
480 people
Step-by-step explanation: 180/x=37.5/100 cross multiply. x=480.
Help! (Easy, but I’m making it way too hard)
A 50-ounce bottle of cranberry juice has 30 ounces of water, What percent of the bottle of cranberry juice is water?
Answers
Answer:
60%
Step-by-step explanation:
30 60
---- = ---- = 60%
50 100
plz help im very stuck
Answers
Answer:
Well what are u stuck in?????
Ellie has a 10 pound bag of sugar to make some treats. To make cookies, she needs 0. 5 pounds of sugar, and to make fudge she needs 2. 25 pounds of sugar. She wants to use twice as much sugar for the cookies as for the fudge. If c = number of batches of cookies and f = number of batches of fudge, choose the system of equations that models this situation.
Answers
The system of equations is:
c * 0.5 = 2 * f
f * 2.25 = 10
To model the given situation, we need to set up a system of equations using the given information.
Let's denote the number of batches of cookies as 'c' and the number of batches of fudge as 'f'.
We know that Ellie wants to use twice as much sugar for the cookies as for the fudge. Therefore, the amount of sugar used for cookies is 2 times the amount used for fudge.
The amount of sugar required for each batch of cookies is 0.5 pounds, and for each batch of fudge is 2.25 pounds.
Using the given information, we can set up the following system of equations:
Equation 1: Amount of sugar for cookies: c * 0.5 = 2 * f
The amount of sugar used for cookies is equal to 2 times the amount used for fudge.
Equation 2: Amount of sugar for fudge: f * 2.25 = 10
The amount of sugar used for fudge is equal to 10 pounds (the total amount of sugar Ellie has).
Therefore, the system of equations that models this situation is:
c * 0.5 = 2 * f
f * 2.25 = 10
In this system, 'c' represents the number of batches of cookies, 'f' represents the number of batches of fudge, and the equations ensure that Ellie uses twice as much sugar for the cookies as for the fudge, while also making sure she uses all 10 pounds of sugar available.
Hence, the system of equations is:
c * 0.5 = 2 * f
f * 2.25 = 10
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The volume of the figure, round to the nearest hundredth.
Answers
Answer: Imma need a picture to find the volume love.
Step-by-step explanation:
Problem 6-29 A quality-control inspector is testing sample outputfrom a production process for widgets wherein 98% of the items aresatisfactory (S) and 2% are unsatisfactory (U). Three widgets arechosen randomly for inspection. The successive quality events maybe assumed independent.Find the probabilities for the following numbers of unsatisfactoryitems:(1) Pr(none)=(2) Pr(exactly 2)= (3) Pr(at least 1)= (4) Pr(exactly 1)= (5) Pr(exactly 3)= (6) Pr(at most 2)=
Answers
Answer:
(1) Pr(none)= .71
(2) Pr(exactly 2)= .0154
(3) Pr(at least 1)= .29
(4) Pr(exactly 1)= .271
(5) Pr(exactly 3)= .000275
(6) Pr(at most 2)= .99
Bolded answers might be wrong, I am a bit unsure on those ones
From monday through friday, earl works in the bookstore on 1 and in the athletic center on another 2 days. on saturday and sunday, earl cooks food 50% of the days. how many days does earl work in a week? what percent of monday through friday does earl work?
Answers
Earl works a total of 3 days in a week. From Monday through Friday, he works in the bookstore on 1 day and in the athletic center on 2 days. On Saturday and Sunday, he cooks food on 50% of the days, which would be a total of 1 day. Therefore, he works a total of 3 days in a week.
To calculate the percentage of Monday through Friday that Earl works, we need to first calculate the total number of days in a week, which is 7. Then, we need to subtract the weekend days, which are Saturday and Sunday, leaving us with 5 days.
Finally, we can calculate the percentage by dividing the number of days Earl works from Monday through Friday (which is 1) by the total number of weekdays (which is 5), and multiplying by 100. So, Earl works 20% of Monday through Friday.
In summary, Earl works 3 days in a week, 1 day in the bookstore and 2 days in the athletic center. He also cooks food on 1 day during the weekend. Earl works 20% of Monday through Friday.
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Three times a number increased by
twice the number is greater than
125. What is the number?
Answers
Answer:
x > 25
Step-by-step explanation:
This question relates to algebra. We can solve this problem by creating a variable for the solution (which we will find). We will link the variable in an equation l with the information given.
So let's translate each piece of information mathematically. First, the question tells us "Three times a number." The first part uses multiplication (times) linked to our number (we will use x for our variable). So we write:
3x
The second part is "increased by twice the number" Increasing is adding (+) so we add two times the number. So:
3x + 2x
The final part says "is greater than 125" so we need to use the > sign
3x + 2x > 125
Now we can solve by collecting like terms and moving them to a different side.
5x > 125
x > 25
The fastest speed recorded forerunner 27 mph. This is 20% of the fastest speed for a water skier find the record for a water skier.
Answers
Answer: 135
Step-by-step explanation: We know that the forerunner is 1/5 the speed of the water skier as 20/100 is 1/5. Now if we "reverse" this we can multiply 27 by 5 to find the speed of the water skier, this is 135 which is the speed of the water skier. Hope this helped :)
What is the volume of a rectangular prism with a length of 10 in, width of 5 in, and height of 8 in?
Answers
Answer:
400
Step-by-step explanation:
to find volume of a rectangular prism is whl which in ur case equals 400
Find a reduced basis for the lattice generated by the vectors (53, 88), (107, 205). (b) Find the vector in the lattice of part (a) that is closest to the vector (151, 33).
Answers
The lattice point closest to (151, 33) is (-143, -187).
(a) To find a reduced basis for the lattice generated by the vectors (53, 88) and (107, 205), we can use the LLL algorithm:
Set the matrix A to be the matrix whose columns are the two vectors, i.e.,
A = [ 53 107
88 205 ]
Apply the LLL algorithm to A to obtain a reduced basis:
LLL(A) = [ 4 -1
3 2 ] * B
Where B is the matrix whose columns are the original lattice basis vectors.
So a reduced basis for the lattice generated by (53, 88) and (107, 205) is:
[ 4 -1 ]
[ 3 2 ]
(b) To find the vector in the lattice generated by (53, 88) and (107, 205) that is closest to the vector (151, 33), we can use the reduced basis we found in part (a) to compute the closest vector using the formula:
v = c1 * b1 + c2 * b2
Where b1 and b2 are the basis vectors of the reduced lattice, and c1 and c2 are integers that minimize the distance between (151, 33) and the lattice point v.
Using the reduced basis [4 -1; 3 2], we can compute the coefficients c1 and c2 by solving the system of linear equations:
[4 -1] [c1] [151]
[3 2] [c2] = [ 33]
This system can be solved using Gaussian elimination or another method, and the solution is c1 = 11 and c2 = -5.
Therefore, the lattice point closest to (151, 33) is:
v = c1 * b1 + c2 * b2
= 11 * [53, 88] + (-5) * [107, 205]
= [ -143, -187 ]
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After substituting, what is the first step when evaluating x + 3 x minus 4.2 when x = 5?
Answers
Answer:
Multiply the 3*5
Step-by-step explanation:
x+3x -4.2
Substitute x=5
5 + 3*5 -4.2
PEMDAS states multiply first
Multiply the 3*5
5 + 15 -4.2
Answer:
a!
Step-by-step explanation:
yw