5) Placido pulls a rope attached to a wagon through a pulley at a rate of q m/s. With dimension as in Figure 5:
(a) Find a formula for the speed of the wagon in terms of q and the variable x in the figure.
(b) Find the speed of the wagon when x=0.6 if q=0.5 m/s.
Answers
The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.
[tex](a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]
(b) When x = 0.6 and q = 0.5 m/s, the speed of the wagon is approximately 0.243 m/s.
Reasons:
(a) The distance from the cart to the pulley, r is given by Pythagoras's
theorem as follows;
r = √((3 - 0.6)² + x²) = √(2.4² + x²)
The speed of the wagon = [tex]\mathbf{\dfrac{dx}{dt}}[/tex]
The speed of the rope, q = [tex]\mathbf{\dfrac{dr}{dt}}[/tex]
By chain rule, we have;
[tex]\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}[/tex]
[tex]\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]
Therefore;
[tex]\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}[/tex]
[tex]\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}[/tex]
(b) The speed of the wagon when x = 0.6 if q = 0.5 m/s is given as follows;
[tex]\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243[/tex]
The speed of the wagon when x = 0.6 and q = 0.5 m/s, [tex]\dfrac{dx}{dt}[/tex] ≈ 0.243 m/s
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Related Questions
calculate the Geometric mean for the
distribution 8, 6, 3, 5 and 4
Answers
Answer:
Step-by-step explanation:
The geometric mean is the average of the 5 numbers
8 + 6 + 3 + 5 + 4 Just add.
Total = 26
There are 5 elements, so the average = 26/5 = 5.2
CAN SOME ONE PLS HELP ME THIS IS REALLY HARD
Answers
Answer: 1.25 times as far
Step-by-step explanation:
This problem requires you to find something called the unit rate.
Getting the unit rate for Car A is very simple, and can be found to be 25mi/gal.
To find the unit rate for Car B, simply look at the second row. Because the car can go 60 miles on 3 gallons of gas, divide both these numbers by 3 to get 20mi/gal.
Then, simply multiply both of these numbers by 11 to get 25 * 11 = 275, and 20 * 11 = 220.
Then, by doing 275/220, you get your answer: 1.25.
Hope it helps :) and let me know if you want me to elaborate.
Car A can travel 275 miles and car B can travel 220 miles
Step-by-step explanation:
pls mark as brainliest
60 is the product of Javier's age and 5
Translate this sentence into an equation
Answers
Answer:
J= Javiers age
5J=60
5J/5= 60/5
J= 12
Check:
5(12)= 60
60=6p
Step-by-step explanation:
see answer
hope this helps
Two functions f and g are defined on the set R, of real numbers by f : x 2x 3 and
x g : x 1 3x . Find the inverse of the function f and the domain of gof.
Answers
Answer:8
Step-by-step explanation:
factorize
1) x²-4y²
2) 27-8y³
Answers
you cant factorise both of them as they have nothing in common
What is the base of 4×4×4×4×4?
Answers
Answer:
Step-by-step explanation:
Your base would be the 4
Answer:
4
Step-by-step explanation:
When you have a something raise up to a number this can be represented as:
[tex]b^a = b_1 \cdot b_2 \cdot \cdot \cdot b_a[/tex]
Where [tex]b[/tex] is the base and [tex]a[/tex] the exponent. In this case you have five times four, then you can re-write the expression as:
[tex]4 \times 4 \times 4 \times 4 \times 4 = 4^5[/tex]
Where the [tex]b[/tex] is equal to 4 and [tex]a[/tex] equal to 5
In 2011 online sales were $192 billion and in 2014 they were $243 billion
(a) Find a linear function S that models these data, where S is the sales in billions of dollars and is the year Write S(x) in slope-intercept form
(b) Interpret the slope of the graph of S
(c) Determine when online sales were $226 billion
(a) Write S(x) in slope-intercept form S(x)=
(b) Interpret the slope of the graph of S Choose the correct answer below
A .Sales increased on average by $17 billion/yr B .Sales increased by $17 billion in next 3 years C. Sales decreased an average by $17 billion/y D.Sales decreased by $17 billion in next 3 years
(c) Online sales were 5226 billion in the year ___
Answers
A) S(x) = 18x + -36005
B) 18
C) 2013
b) 18
c) 2013
Work out the area of the parallelogram.
13 cm
790
21 cm
Answers
Answer:
Step-by-step explanation:
please try to provide a more accurate information 13cm of what? 790?
Answer:
The area of parallelogram can be found by product of its base and height. The calculations are shown below:
Step-by-step explanation:
We know that,
Area of parallelogram = base × height
assume base to be 21 cm.
Then,
sin 79° = [tex]\frac{height}{13}[/tex]
∴ height = 13 × 0.98 = 12.74
Area of parallelogram = 21 × 12.74
= 267.54 [tex]cm^{2}[/tex]
The area of parallelogram is calculated as 267.54 [tex]cm^{2}[/tex]
Identify the figure and denote it by its appropriate symbol
ОА.
Half Line, AB
OB.
Ray
AB
O C. Line, AB
OD
Line Segment AB
Answers
Rays are a linear formation that start at a point and continue forever in a direction. The photo shows a point on one end, and an arrow on the other indicating that it starts at the point and continues forever past the arrow.
what is the percent of change from 5 to 7
Answers
Answer: 40
Step-by-step explanation:
is -1/8 greater than -1/10
Answers
Answer:
false
Step-by-step explanation:
-1/8 = -0.125
-1/10 = -0.100
as it is negative
-0.125 < -0.1
so it is false
Pls heeellllppppp me pls no links pls no fake answers and pls answer both questions
Answers
Answer:
I think it's True
Step-by-step explanation:
When you multiply a negative and positive, it equals a negative: (-)x(+)=(-)
^-2/5x > -8
Then multiply both sides of the inequality by ^-5/2 and flip the inequality sign
Which gives you:
x < 20
Answer:
Step-by-step explanation:
one would flip the sign on (-2/5)x > -8 because you would be multiplying by a negative number (- 5/2) to get positive x standing alone. It resolves to
x < 20
You would also flip the sign on
-x + ¾ < 10
-x + ¾ - ¾ < 10 - ¾
-x(-1) > 9¼(-1) multiplying by a negative number flips the sign.
x > - 9¼
3x + 3y = 9
-3x + 2y = 1
Answers
Answer:
X=1
Y=2
Step-by-step explanation:
put 1 in for X
3(1)+3(y)=9
-3(1)+2(y)=1
now put 2 for Y
3(2)+3(2)=9
-3(1)+2(2)=1
3•1= 3
3•2=6
3+6=9
-3•1=-3
2•2=4
-3+4=1
Find the slope of the line that passes through:
(5, -10) and (5,-4)
Answers
Answer:
Undefined
Step-by-step explanation:
you use the slope formula
m = y2 - y1 / x2 - x1
substitute
m = -4 - (-10) / 5 - (-5)
subtract 5 from 5
- 4 - (-10) / 0
The expression contains a division by 0. The expression is undefined.
Which statement best explains if the graph correctly represents the proportional relationship y = −2x? A coordinate plane is shown. Points are graphed at negative 2 and 4 and negative 1 and 2. The points are joined by a line. It does not, the points shown would not be part of y = −2x. It does not, proportions cannot be represented on a graph. It does, all proportions can be shown on a graph of this line. It does, the points shown on the line would be part of y = −2x.
Answers
Answer:
d. It does, the points shown on the line would be part of y = −2x.
is the answer let me know if this helped
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
hope i helped
For their group project, Mia and Ichiro researched
hybrid cars that combine gas and an electric motor.
“Awesome, so it consumes less fuel and emits less
CO2 into the environment,” Ichiro said.
“While hybrid cars are better for the environment,
I’m seeing that some people are hesitant to buy one
because of the higher purchase price,” Mia noted.
They found the graph to the right, which shows the
miles per gallon (MPG) and the annual tons of GHG
produced by 8 different types of cars. If each gallon
of gasoline burned created 20 pounds of GHG, and
the price of gasoline was $2.454 per gallon, how
much money was saved annually on gas by the car
that got 40 miles per gallon when compared to the
car that got 20 miles per gallon? Provide your answer
to the hundredths place. Note: 1 ton = 2,000 pounds. This is from Pg.2 -7th Grade math problem.
Answers
Hybrid cars have lower operational cost and reduce Green House Gases
GHG when journeys are made on a frequent basis.
The amount saved annually on gas by the car that got 40 miles per gallon when compared to the car that got 20 miles per gallon is $1,076.76.Reasons:
The given parameters are;
The mass of Green House Gases GHG created by each gallon of gasoline burned = 20 pounds
The price per gallon of gasoline = $2.454Let A represent the cars that consume 40 MPG and let B represent the cars that consume 20 MPG.
Amount of GHG produced per year by cars A = 4.4 tons
4.4 US tons = 8,800 lbs
Amount of GHG produced per year by cars A = 8.8 tons
8.8 US tons = 17,600 lbs
[tex]\displaystyle Gasoline \ consumed \ per \ year \ by \ car \ A = \frac{8,800 \ lb}{20 \ lb/ gallon} = \mathbf{440 \ gallons}[/tex]
Cost of gasoline consumed per year by car A per year is therefore;
[tex]Cost_A[/tex] = 440 gallons × $2.454 = $1,079.76
[tex]\displaystyle Gasoline \ consumed \ per \ year \ by \ car\ B = \mathbf{\frac{17,600\ lb}{20 \ lb/ gallon}} = 880 \ gallons[/tex]
Cost of gasoline consumed per year by car B per year is therefore;
[tex]Cost_B[/tex] = 880 gallons × $2.454 = $2,159.52
The amount saved annually by car A compared to car B is therefore;
Fuel cost savings by Car A = $2,159.52 - $1,079.76 = $1,079.76
The amount saved on gas by the 40 MPG car = $1,079.76Learn more here:
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please help me !
• don’t use this for points, or send any gross links.
• if you actually KNOW the answer, please do comment / help me!
this is: KS3 — YEAR 8 ! ❤️
Answers
TICKET MONEY for age 16 and over,
155-49 =106
1 person pays £18.60
106 = 106 × £18.60
=£1,971.6
TICKET MONEY for under 16
1 person pays £12.80
49 people =49 × £12.80
= £627.2
TOTAL NUMBER OF TICKETS
£ 1,971.6 + £6272.2
= £2,598.8
Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is p = 19.00 Mbps. The sample size is n = 21 and the test statistic is t= 1.401
P-value = (Round to three decimal places as needed)
Answers
Using the t-distribution, it is found that the p-value is of 0.177.
At the null hypothesis, it is tested that for a smartphone carrier's data speeds at airports, the mean is 19 Mbps, that is:
[tex]H_0: \mu = 19[/tex]
At the alternative hypothesis, it is tested if the mean is different than 19 Mbps, that is:
[tex]H_1: \mu \neq 19[/tex]
We are testing if the mean is different from a value, hence it is a two-tailed test.The test statistic is t = 1.401.Sample size of n = 21, hence there are 21 - 1 = 20 df.Inputting this information into a calculator, the p-value is of 0.177.
A similar problem is given at https://brainly.com/question/13873630
Solve 2 cot x = csc^2 x symbolically on the interval (0,2pi).
Answers
Answer:
x=pi/4, 5pi/4
Step-by-step explanation:
cot x = cos x / sin x, csc x = 1/sin x, so we have 2 cos x / sin x = 1/ sin^2 x. multiply both sides by sin^2 x to get 2 cos x * sin x = 1, divide both sides by 2 to get cos x sin x = 1/2, this would work for angles pi/4 and 5pi/4 (3pi/4 and 7pi/4 would make cos x sin x = -1/2) since cos x = sin x = sqrt(2)/2
i rlly need help ill give u brainliest
Answers
Answer:
1728 for A
7290000 for B
Step-by-step explanation:
Here’s a freebie for the lucky people who answer this
79 - 10 =
A. 70
B. 7
C. 69
D. 6.9
430 - 10 =
A. 469
B. 421
C. 4.2.0
D. 420
Answers
Answer:
The answer is C.
The answer is D.
Step-by-step explanation:
Thank you:)
Azad wants to Buy a book he has 25,000 dinars which is 9000 dinars less than she needs does the book cost 34,000 Dinars or 16,000 dinars
Answers
Answer: 34,000 Dinars
Step-by-step explanation: As 25,000 + 9000 is 34,000
how do I do 2÷834
Fourth grade
Answers
Answer:
I honestly don't know why you are on this if your in 4th grade because this is for middle, high, and college school kids.
The answer is anyways 417
Answer:
2 divided by 834 is 1/417 or 417
Step By Step Explanation:
Why is a fourth-grader even on a website for middle, high school, and college...
Order the following numbers from least to greatest.
|-1 1⁄2|, 1 3⁄4, |-1 1⁄5|, 1 2⁄5
Answers
Answer:
|- 1 1/5|, 1 2/5, |-1 1/2|, 1 3/4
Step-by-step explanation:
A number n is a prime factor of 28 and 63
Answers
Answer:
7
Step-by-step explanation:
The factors of 28 and 63 are
28 : 1, 2, 4, 7, 14, 28
63 : 1, 3, 7, 9, 21, 63
The common factors are 1 and 7
7 is a prime factor of both 28 and 63
Sử dụng phép tính mệnh đề (các luật logic) để chứng minh các biểu thức sau là hằng
đúng:
[p -> (q ∨ r)] ->[(p -> q) ∨ (p ->r)]
Answers
Answer: “P hay Q” là một mệnh đề được
Step-by-step explanation: Các quy tắc tương đương logic: ... Chứng minh biểu thức mệnh đề (¬((r ∨ q) ∧ q) ∨. ¬p)∧ ((¬p
the area of a square is 36 centimeters. how long is each side of the square?
Answers
Answer:
6cm
Step-by-step explanation:
square root of 36 because the area of a square is base x height and a square has equal sides
5 div by 4=25 div by y
Answers
[tex]\dfrac 54 = \dfrac{25} y\\\\\\\implies \dfrac 14 = \dfrac 5y\\\\\implies y = 4 \times 5 =20[/tex]
Three friends each create 4 bags of starter bread dough. After ten
days, each of those four bags is then divided into four more bags of
dough. How many days pass before 192 of dough are created?
1.20
2.40
3.30
Answers
Answer:
20
Step-by-step explanation:
4x3=12
12x4=48 after 10
48x4=192 after another 10
Write the equation of the line that passes through the given points.
(1,2.5) and (0,6.5)
Answers
let's change the decials first off to fractions and get the slope and line
[tex]2.\underline{5}\implies \cfrac{25}{1\underline{0}}\implies \cfrac{5}{2}~\hfill 6.\underline{5}\implies \cfrac{65}{1\underline{0}}\implies \cfrac{13}{2} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{5}{2}})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{\frac{13}{2}})[/tex]
[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{13}{2}}-\stackrel{y1}{\frac{5}{2}}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{1}}}\implies \cfrac{~~ \frac{8}{2}~~}{-1}\implies \cfrac{4}{-1}\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{-4}(x-\stackrel{x_1}{1})[/tex]
[tex]y-\cfrac{5}{2}=-4x+4\implies y=-4x+4+\cfrac{5}{2}\implies y = -4x+\cfrac{13}{2}[/tex]