Answer:
Approximately [tex]4.70 \times 10^{2}\; \rm J[/tex], assuming that [tex]g = 9.81\; \rm m \cdot s^{-2}[/tex].
Step-by-step explanation:
When the force [tex]F[/tex] is constant, moving by [tex]\Delta x[/tex] in the direction of the force would do a work of [tex]F \cdot \Delta x[/tex].
However, in this example, as an increasing portion of the chain gets lifted up, the force lifting the chain would increase in size. Hence, apply the integral form of this equation.
Let [tex]F(x)[/tex] denote the force required to lift the chain when the height above the ground is [tex]x[/tex] meters. At that moment, exactly [tex](x / 10)[/tex] of the chain would be above the ground. The mass of that much of the chain would be [tex](x / 10)\![/tex] the mass of the whole chain.
[tex]\begin{aligned}F(x) &= m(x) \cdot g \\ &= 60 \cdot \frac{x}{10} \cdot g = 6\, g\, x\end{aligned}[/tex].
Integrate with respect to [tex]x[/tex]:
[tex]\begin{aligned}\int \limits_{0}^{4} F(x) \cdot {\rm d} x &= \int \limits_{0}^{4} 6\, g\, x \cdot {\rm d} x \\ &= \left[(3\, g)\, x^{2}\right]_{x=0}^{x=4}\\ &= 48\, g \approx 4.7 \times 10^{2} \end{aligned}[/tex].
In other words, it would take approximately [tex]4.7 \times 10^{2}\; \rm J[/tex] of energy to raise one end of the chain to that height of [tex]4\; \rm m[/tex].
A rectangular piece of tin has an area of 1056 square inches. A square of 3 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 2052 cubic inches, what were the original dimensions of the piece of tin. PLEASE SHOW WORK
Answer:
44 inches and 24 inches
Step-by-step explanation:
Let [tex]l,b[/tex] denotes length and breadth of a rectangle.
[tex]lb=1056[/tex]
A square of 3 inches is cut from each corner, and an open box is made by turning up the ends and sides.
New length [tex]=l-6[/tex] inches
New breadth [tex]=b-6[/tex] inches
Height of box [tex]=3[/tex] inches
Volume of box = length × breadth × height
[tex](l-6)(b-6)3=2052[/tex]
[tex]lb-6l-6b+36=684\\6(l+b)=408\\l+b=68\\b=68-l[/tex]
Put [tex]b=68-l[/tex] in [tex]lb=1056[/tex]
[tex]l(68-l)=1056\\l^2-68l+1056=0\\l^2-44l-24l+1056=0\\l(l-44)-24(l-44)=0\\(l-24)(l-44)=0\\l=24,44[/tex]
At [tex]l=24,b=\frac{1056}{24}=44[/tex] inches
At [tex]l=44,b=\frac{1056}{44}=24[/tex] inches
Can you solve this as soon as possible please
(please answer thank you!)
The cost of a hamburger is $1.15 more than an order of large fries. Bill bought two hamburgers and an order of fries for a total of $8.60. What is the price of each item? Give your answer in full sentences.
Answer:
The order of large fries costs $ 2.10, while each hamburger costs $ 3.25.
Step-by-step explanation:
Given that the cost of a hamburger is $ 1.15 more than an order of large fries, and Bill bought two hamburgers and an order of fries for a total of $ 8.60, to determine what is the price of each item, the following calculation must be performed:
X + X + 1.15 + X + 1.15 = 8.60
3X + 2.30 = 8.60
3X = 8.60 - 2.30
X = 6.30 / 3
X = 2.10
Thus, each order of large fries costs $ 2.10, while each hamburger costs $ 3.25.
Solving linear equations
Answer:
1. P = [tex]\frac{I}{rt}[/tex]
2. y = [tex]\frac{6 - 3x}{11}[/tex] or [tex]\frac{-3x +6}{11}[/tex] (depending on how you want the equation arranged)
3. c = [tex]\frac{a-bd}{b}[/tex]
4 t = [tex]\frac{A - p }{pr}[/tex]
Step-by-step explanation:
1. I =Prt for P:
I = Prt divide both sides by rt to isolate P
P = [tex]\frac{I}{rt}[/tex]
2. 3x + 11y = 6 for y
3x + 11y = 6 subtract 3x from both sides
11y = 6 - 3x divide both sides by 11
y = [tex]\frac{6 - 3x}{11}[/tex] or [tex]\frac{-3x +6}{11}[/tex] depending on how you want the equation arranged
3. a = b(c + d) for c
a = b(c + d) distribute b to (c+d)
a = bc + bd subtract bd from both sides
a - bd = bc divide both sides by b
c = [tex]\frac{a-bd}{b}[/tex]
4. A = p + prt for t
A = p + prt subtract p from both sides
A - p = prt divide both sides by pr
t = [tex]\frac{A - p }{pr}[/tex]
Select the correct answer. What is this expression in simplest form?
Answer:
[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}\\=\frac{x^2+(2-1)x-2}{x^2(x-1)+2(x-1)}\\=\frac{x^2+2x-x-2}{(x-1)(x^2+2)}\\=\frac{x(x+2)-1(x+2)}{(x-1)(x^2+2)}\\=\frac{(x-1)(x+2)}{(x-1)(x^2+2)} \\=\frac{x+2}{x^2+2}\\So, ~last~option~is~the~correct~answer.[/tex]
The simplest form of the provided expression is (x + 2)/(x² + 2) option (D) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm \dfrac{\left(x^2+x-2\right)}{x^3-x^2+2x-2}[/tex]
[tex]\rm =\dfrac{\left(x-1\right)\left(x+2\right)}{x^3-x^2+2x-2}[/tex]
[tex]\rm =\dfrac{\left(x-1\right)\left(x+2\right)}{\left(x-1\right)\left(x^2+2\right)}[/tex]
= (x + 2)/(x² + 2)
Thus, the simplest form of the provided expression is (x + 2)/(x² + 2) option (D) is correct.
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The width of a rectangle is (5x + 2) inches and the length is (6x − 7) inches. Find the area of the rectangle.
Answer:
30x² − 23x − 14Explanation:
Area = Length · WidthLength: (6x - 7)
Width: (5x + 2)
Create An Equation(6x - 7) (5x + 2)
= (6x + −7)(5x + 2)
(6x)(5x) + (6x)(2) + (−7)(5x) + (−7)(2)
= 30x² + 12x − 35x − 14
30x² − 23x − 14- PNW
i’m kinda confused please help
Answer:
0.8, 0.875, 0.89 or 4/5, 7/8, 0.89
Step-by-step explanation:7/8 is the same as 7 divided by 8 which equals to 0.875.
4/5 is the same as 4 divided by 5 which is 0.8.
Shortest to Longest
0.875
0.89
0.8
reformed into
1. 0.8
2. 0.875
3. 0.89
PLEASE HELP IF YOU CAN, ASAP :)
Answer:
I mean 6
Step-by-step explanation:
That is the answere to you question.
Answer:
$8 originally
Step-by-step explanation:
75%= 3/4
if the price is broke up into 4 pieces we see that 3 pieces where taken off if one piece is $2 then 2+2+2+2= $8 which is the full price.
Graph h(x)=3cos(2x)−1.
Use 3.14 for π.
Step-by-step explanation:
the answer is in the attachment
Answer:
The right answer is in yellow.
Step-by-step explanation:
Took the quiz :)
from the top of a tower 80m high, 2 boats are
seen in a direction due south. The angles of
depression of the boats from the top of the tower
are 30°and 45°respectively, find the distance
between the boat
Step-by-step explanation:
Height of tower - 80m
Distance between foot of tower and boat 1 = x
Distance between boat 1 and boat 2 =y
Tan 45 = 1 = 80/x
x = 80
Tan 30 = 1 / root 3 = 80 / 80 + y
y = 80 root 3 + 80
If 17 ounces of cocoa are needed for 6 cookies, how many ounces of cocoa is needed for 8 cookies?
Answer:
22 and 2/3
Step-by-step explanation:
17/6= 2.8333333
2.8333333333 multiplied by 8= 22.66666666 or 22 and 2/3
Solve the system of equations by graphing. -x+y = -2 y = -1
Answer:
the solution is (9, -1).
Step-by-step explanation:
graph the two equations on a graphing calculator (i use a website called desmos) and the point of intersection is the solution.
i hope this helps! have a great day <3
Travis took out an 80/20 mortgage on a $175,000 home. What is the amount
financed under the first mortgage?
A. $164,000
B. $175,000
C. $35,000
D. $140,000
Answer:
D 140,000
[tex]175000 \div .20 = [/tex]
The answer is D 140,000
Ruby bought two chicken wings for $4 what was the cost of the Wings in dollars per wing?
Answer:
the cost per wing is $2
Step-by-step explanation:
In a survey of 2,700 people who owned a certain type of car, 1,350 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
50%
Step-by-step explanation:
To solve this you would do 1350/2700 which is 50%
the cost of an airplane flight increases from $250 to $295.
what is the increase?
Answer:
Step-by-step explanation:
45 dollars is the answer lol this is 2 ez
Answer: 45 is the increase
Step-by-step explanation:
295-250=45
Name a line segment parallel to DC.
A
B
D
С.
E
F
H
G
Answer:
line segment HG
line segment EF
line segment AB
answer quick pls due today
Answer:
B =1/4 s I think, doesn't it mean you multiply when you put a variable next to a fraction? I mean your multiplying his income last year to 1/4
Step-by-step explanation:
I hoped this helped. Wait for more responses if needed too ;)
Write an expression for "12 times 1."
expression for "12 times 1." -> 12*1
A survey was conducted to find the frequency with which people go to the movies. A group of 120 people in a mall were asked about how often they go out for a movie and It was found that 36 people go to movies at least once in a month. Which of these is an example of descriptive statistics
Answer:
30% of the people surveyed in the mall go to movies at least once in a month
Step-by-step explanation:
A descriptive statistic would refer to a summary where it explain in quantitative way from the information collected also it it is used to analyze it. The parameter and descriptive statistics would be the percentage for the surveyed people that goes to the mall for watching out the movies at least for one time in a month
Here 30% come from
= 36 ÷ 120
= 30%
Why is 3 x 1/10 less then 3x 10
Answer:
Beause In the first equation 3 is being multiplied by .1 and the second equation is being multiplied by 10
Step-by-step explanation:
1/10 In decimal for is .1 and .1 times 3 is .3
3 times 10 is 30 so therefore 3 x 1/10 less then 3x 10
Find x.
2x + 40
Зх.
4x
X + 50
x = [?]
Answer:
x=122
Step-by-step explanation:
Recall that an American Roulette wheel has 38 possible outcomes, 18 black, 18 red and 2 green. The numbers go from 1 to 36, and the green outcomes are numbered 0 and 00. Someone places 10 bets on "1st 12", that is, that person wins if the outcome is any number between 1 and 12, included. 1. (2pts) What is the probability of losing a ’1st 12’ bet on a single spin? 2. (3pts) What is the probability of winning 7 out of the 10 total bets?
Answer:
American Roulette
1. The probability of losing a ’1st 12’ bet on a single spin is:
= 0.67
2. The probability of winning 7 out of the 10 total bets is:
= 0.23
Step-by-step explanation:
Possible outcomes in an American Roulette wheel = 38
Make-up of the outcomes = 18 black, 18 red and 2 green
Green outcomes are numbered 0 and 00
Number of wins for this person = 12
Probability of winning = 0.33 (12/36)
Number of possible losses for this person = 24
Probability of losing = 0.67 (24/36)
1. The probability of losing a '1st 12' bet on a single spin is:
= (36 - 12)/36
= 0.67
2. The probability of winning 7 out of the 10 total bets is:
Probability of winning = 12/36 * 7/10
= 0.23
7 more than a number ?
A)n+7
B)7+n
C)7-n
Answer:
B)7+n
Step-by-step explanation:
Answer:
A but see below.
Step-by-step explanation:
A is likely the best answer, although B is also correct. However you should write things in the other they are given.
n + 7 is the very best way to answer.
7 + n is not wrong but maybe not wanted.
PLEASE HELP WILL GIVE BRAINLIST
Two chemical plants, one at Macon and one at Jonestown, produce two types of fertilizer, low phosphorus (LP) and high phosphorus (HP). At each plant, the fertilizer is produced in a single production run, so the two types are produced in fixed proportions. The Macon plant produces 1 ton of LP and 3 tons of HP in a single operation, and it charges $600 for what is produced in one operation, whereas one operation of the Jonestown plant produces 1 ton of LP and 1 ton of HP, and it charges $1,000 for what it produces in one operation. If a customer needs at least 100 tons of LP and 180 tons of HP, how many production runs from each plant should be ordered to minimize the cost.
Answer:500
Step-by-step explanation:
There are 100 production runs from each plant should be ordered to minimize the cost.
What is Production?
The process of making or manufacturing goods and products from raw materials or components is called Production.
The Macon plant produce 1 ton of LP and 3 tons of HP in single operation, and it charge $600 for what is produced in one operation.
And, One operation of Jonestown plant produce 1 ton of LP and 1 ton of HP, and it charges $1,000 for what it produces in one operation.
And, A customer needs at least 100 tons of LP and 180 tons of HP,
Now, A graph of the requirements shows the feasible region is bounded by a polygon with vertices (Macon and Jonestown) as,
= (0, 180), (40, 60), (100, 0).
Hence, By checking costs of these solutions, we find the lowest cost to be obtained when 100 production runs should be ordered from Macon.
So, There are 100 production runs from each plant should be ordered to minimize the cost.
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2/5t=6
Pleaseeeee help
Answer:
t = 1/15
Step-by-step explanation:
[tex]\frac{2}{5t} = 6\\2 = 6 * 5t\\2 = 30t\\\frac{2}{30} = t\\t = \frac{1}{15}[/tex]
Mr. Dylan used 5/12 of a carton of eggs to make breakfast Sunday.
He used 3/12 of the carton on Monday. How many more eggs did
HE USE IN SUNDAY?
2 Eggs
8 Eggs
Answer and I will give you brainiliest
Answer:
2!
Step-by-step explanation:
There's 12 eggs in a carton, 5v3 is 2! :)
Three friends Steve, Jake and Jodie shared a pizza. Steve ate 2/5 of the pizza and Jake ate 1/4
What fraction did Jodie eat?
Answer:
they ate it all together as it all adds to 1
Step-by-step explanation:
1/4+2/5 if you add the missing remainder it totals 1
PLEASE HELP GEOMETRY
Answer:
60
Step-by-step explanation: