Answers
Answer:
a) A = 3π/16
b) A = ∑₂°° (π/n⁴) = π⁵/90 − π
Step-by-step explanation:
(a) The area between the curve and the x-axis is:
A = ∫ₐᵇ y (dx/dt) dt
x = ½ (1 − cos t) cos t
dx/dt = ½ (1 − cos t) (-sin t) + ½ sin t cos t
dx/dt = -½ sin t + ½ cos t sin t + ½ sin t cos t
dx/dt = -½ sin t + sin t cos t
dx/dt = -½ sin t (1 − 2 cos t)
y dx/dt = -½ sin t (1 − 2 cos t) × ½ (1 − cos t) sin t
y dx/dt = -¼ sin²t (1 − 3 cos t + 2 cos²t)
y dx/dt = -¼ sin²t + ¾ sin²t cos t − ½ sin²t cos²t
y dx/dt = ⅛ (-2 sin²t) + ¾ sin²t cos t − ½ (sin t cos t)²
y dx/dt = ⅛ (-1 + 1 − 2 sin²t) + ¾ sin²t cos t − ½ (½ sin(2t))²
y dx/dt = ⅛ (-1 + cos(2t)) + ¾ sin²t cos t − ⅛ sin²(2t)
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-2 sin²(2t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-1 + 1 − 2 sin²(2t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-1 + cos(4t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t − ¹/₁₆ + ¹/₁₆ cos(4t)
y dx/dt = -³/₁₆ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ cos(4t)
A = ∫₀ᵖⁱ [-³/₁₆ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ cos(4t)] dt
A = -³/₁₆ t + ¹/₁₆ sin(2t) + ¼ sin³t + ¹/₆₄ sin(4t) |₀ᵖⁱ
A = [-³/₁₆ π + ¹/₁₆ sin(2π) + ¼ sin³π + ¹/₆₄ sin(4π)] − [0 + ¹/₁₆ sin(0) + ¼ sin³0 + ¹/₆₄ sin(0)]
A = -³/₁₆ π
We got a negative answer because the graph traces to the left (x decreases as t increases). So the area is simply ³/₁₆ π.
b) Each circle has radius 1/n², so the area is π (1/n)² = π/n⁴.
The sum of the areas from n=2 to n=∞ is:
A = ∑₂°° (π/n⁴)
A = ∑₁°° (π/n⁴) − π
A = π ∑₁°° (1/n⁴) − π
A = π (π⁴/90) − π
A = π⁵/90 − π
Related Questions
Describe the Transformation and CHOOSE ALL THE
CORRECT ANSWERS! (MORE THAN 1 RIGHT
ANSWER).
f(x) = -2(x+3) 3 - 3
Answers
Juanita has fewer than 80 coins in her coin collection. She noticed that she can divide her coins evenly into groups of 3, 5, 15, or 25.
How many coins does she have?
Answers
Find the LCM
3 = 3 times 1
5 = 5 times 1
15 = 5 times 3
25 = 5 times 5
Because they have one 5 and one 3 in common...
5 times 3 times 5 = 75.
She has 75 coins.
in 3 1/2 months John collected a debt of $70.00. What was the average amount of debt John collected per month?
Answers
Answer:
The average amount of debt John collected per month is $20/ month
Step-by-step explanation:
Given;
total debt collected by John, = $70.00
total number of months, = 3 1/2 months = 7/2 months
The average amount of debt John collected per month is given by;
[tex]Average \ amount \ per \ month = \frac{Total \ amount \ of \ debt}{total \ number \ of \ months} \\\\Average \ amount \ per \ month =\frac{70}{1} *(\frac{2}{7} )\\\\Average \ amount \ per \ month = \$20 \ / month[/tex]
Therefore, the average amount of debt John collected per month is $20/ month
=
Drag up the correct symbol to make each statement true.
Answers
Answer:
1. >
2.>
3.<
4. <
Step-by-step explanation:
I am doing it from top to bottom
I hope this helps! :)
Utilizando la equivalencia indicada, resuelve el siguiente ejercicio:
1 galón = 3.785 litros
42 galones = ____ litros
Answers
Answer:
158.97 litros
Step-by-step explanation:
Multiply 42 by 3.785 to get 158.97.
Alright, -3r + 4(-3r + 2) = 53 how do I break it down and solve??
Answers
Answer:
r = -3
Step-by-step explanation:
-3r + 4(-3r +2) = 53
-3r + -12r + 8 = 53
-8 -8
-3r + -12r = 45
-15r = 45
Divide both sides by -15 to get
r = -3
Answer:
r = -3
Step-by-step explanation:
expand 4(-3r+2)
= -12r+8
add similar variables
= -15r+8=53
subtract 8 from both sides
= -15r+8-8=53-8
simplify
= -15r=45
divide 45 by -15
= -3
what is Hola, soy el chico nuevo de la clase y me gustan los coches, in english, and what is 100x100x38
Answers
Answer:380000
Step-by-step explanation:
Answer:
Hi, I'm the new kid in class and I like cars AND 380000
Step-by-step explanation:
NOBODY IS ANSWERING THIS PLEASE PLEASE PLEASE ANSWER ILL LOVE YOU FOREVER
Car A is traveling east at a steady speed of 60 miles per hour after 2 hours, it is 130 miles east of Johnstown. car B is traveling east on the same road. its distance east of Johnstown is represented by the graph.
PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE HELP
Answers
Answer:
D
Step-by-step explanation:
It looks right
sorry if it’s wrong
The value of 2 in 724,638, is 20,00p?
Answers
Step-by-step explanation:
total value would be 20,000
place value is hundreds of thousands
that's my opinion cuz I didn't fully understand it but I tried thanks
Check all of the irrational numbers.
Answers
Answer:
√36, √17, 0.33333...., 1.2874....
Step-by-step explanation:
irrational numbers - a number that cannot be exactly expressed as a ratio of two integers.
Select each transformation that carries a square onto itself.
Answers
Answer:
b,c,d
Step-by-step explanation:
cus I said so and it's right
Find the product.
(36 + 4) (262 – 6 + 4)
Answers
Answer:
10,400
Step-by-step explanation:
(36+4)= 40
(262-6+4)= 260
(40)(260)= 10,400
Answer:
10,400
Step-by-step explanation:
Add 36 + 4
40
Now we do the second parentheses.
262 - 6 = 256
256 + 4 = 260
Now we multiply.
40 multiplied by 260 = 10,400
Hope I helped :)
Please consider Brainliest :)
describe how you can
identify if two lines are coinciding using substitution, elimination, and/or
graphing methods? *
Answers
To use substitution to identify if two lines intersect,
1. Rearrange one of the two given equations so that only one variable is on one side of the equation with all other values on the other side of the equation. (if needed)
2. Plug this new equation into the other (in place of a variable)
3. Solve the equation to get the answer of one of the variables
4. Plug this variable into one of the two original equations and solve for the second variable (if needed)
5. Plug both variables back into one of the original equations. If both sides of the equation are equal, the two lines do coincide.
Example:Equation 1: 2x+3y=9
Equation 2: x+8=3
1. Rearrange equation 2
x+8=3
x=3-8
x=-5
2. Plug -5 into the first equation as x
2x+3y=9
2(-5)+3y=9
3. Solve this equation
-10+3y=9
3y=9+10
3y=19
y=[tex]\frac{19}{3}[/tex]
4. Plug x and y back into the first equation
2x+3y=9
2(-5)+3([tex]\frac{19}{3}[/tex])=9
-10+19=9
9=9
Therefore, these two lines do coincide. The point of intersection is (-5,[tex]\frac{19}{3}[/tex]).
Using Elimination:To use elimination to identify if two lines intersect:
1. Multiply one or both of the equations by a factor so both equations have either an x or y coefficient that are equal or opposite of each other (if needed)
2. Add or subtract the two equations to get rid of one variable
3. Solve this new equation for a variable
4. Substitute this variable into one of the two equations to solve for the other
5. Plug both variables back into one of the equations. If both sides are equal, the two lines do coincide.
Example:Equation 1: 2x+3y=4
Equation 2: 4x+2y=3
1. For this specific system of equations, we would multiply the first equation by 2.
2x+3y=4
4x+6y=8
Notice how now, both equations have 4x in them, so we can subtract them:
2. Subtract the new equation from the second original equation
4x+6y=8
- 4x+2y=3
4y=5
3. Solve
4y=5
y=[tex]\frac{5}{4}[/tex]
3. Substitute y back into the first equations (any of the two equations will work) to solve for x
2x+3y=4
2x+3([tex]\frac{5}{4}[/tex])=4
2x+[tex]\frac{15}{4}[/tex]=4
2x=4-[tex]\frac{15}{4}[/tex]
2x=[tex]\frac{16}{4}[/tex]-[tex]\frac{15}{4}[/tex]
2x=[tex]\frac{1}{4}[/tex]
x=[tex]\frac{\frac{1}{4} }{2}[/tex]
x=[tex]\frac{1}{4}*\frac{1}{2}[/tex]
x=[tex]\frac{1}{8}[/tex]
4. Plug both variables back into the first equation (either equation works)
2x+3y=4
2([tex]\frac{1}{8}[/tex])+3([tex]\frac{5}{4}[/tex])=4
[tex]\frac{1}{4}[/tex]+[tex]\frac{15}{4}[/tex]=4
[tex]\frac{16}{4}[/tex]=4
4=4
Since the left side equals the right side, the two lines are coinciding.
Using Graphing Methods:To use graphing methods to identify if two lines coincide, we would just have to graph the line and identify if the two lines meet at a point of intersection/overlap each other.
I hope this helps!
y-intercept of (-2,2) and (-5,-4)
Answers
Answer:
-8
Step-by-step explanation:
An object is moving at a speed of 6 miles per month. Express this speed in feet per hour
Answers
Answer:
44 feet/hour
Step-by-step explanation:
6mi/month(5280ft/1mi)(1month/30days)(1day/24hrs)
Assuming the month has 30 days, object moves at 44 feet/hour. You want all the units to cancel till you get the ones you need, in this case feet/hr.
16. Solve the equation by factoring.
2² - 62-27=0
a. z = 3 or z = 9
b. z = 3 or z = -9
c. z = -3 or z = -9
d. z = -3 or z = 9
Answers
Answer:
Step-by-step explanation:
B
Two consecutive vertices of a regular octagon are located at (1, 4) and (4,8). This octagon's perimeter is.....?
Answers
Answer:
40 units
Step-by-step explanation:
An octagon is a polygon with 8 sides. A regular octagon is an octagon in which all their sides and angles are equal to each other.
Since the vertices of a regular octagon are located at (1, 4) and (4,8), hence the length of the side is gotten using the formula for calculating the distance between two points [tex]X(x_1,y_1)\ and\ Y (x_2,y_2)[/tex].
[tex]|XY|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence:
[tex]Length=\sqrt{(4-1)^2+(8-4)^2}=5\ units[/tex]
Since all the sides of a regular octagon are equal, therefore:
Perimeter = 8 × length = 8 × 5 = 40 units
Sarah is 1 1/2 meters tall. Which of the following is equivalent to 1 1/2 meters?
A. 150 millimeters
B. 1,500 millimeters
C. 100 millimeters
D. 1,000 millimeters
Answers
Answer:
B. 1,500 millimeters
Make w the subject of the relation p=2 (k+w)
Answers
Answer:
hope that will help you
w = ( p - 2k )/2
Step-by-step explanation:Hi there !
p = 2(k + w)
2k + 2w = p
2w = p - 2k
w = ( p - 2k )/2
Good luck !
quotient of Fraction 3 over 4 divided byFraction 3 over 4 .
Answers
Answer:
1
Step-by-step explanation:
The equation would look like this: ¾ ÷ ¾
When dividing fractions, you always flip the second one to receive the reciprocal, so the equation now looks like this: ¾ ÷ 4/3
If you cross simplify, the answer will end up being 1.
Need help!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
9514 1404 393
Answer:
a) GH or HG
b) KL
c) YZ or ZY
d) EF
Step-by-step explanation:
A segment or line can be named by naming two points on it in any order. The points naming a line segment are its end points.
A ray is named by first naming its end point, then any other point on the ray.
a) GH or HG
b) KL
c) YZ or ZY
d) EF
Please help me solve this I will give u brainlst :)
Answers
Answer: 3 pencils
For each of the following questions, say whether the random process is a binomial process or not, and explain your answer. As part of your explanation, you will want to comment on the potential validity of each of the four things that must be true for a process to be a binomial process.
a. One basketball player attempts 10 free throws and the number of successful attempts is totalled.
b. Ten different basketball players each attempt 1 free throw and the total number of successful attempts is totalled.
Answers
Answer:
a
This process follows is a binomial process
b
This process is not a binomial process
Step-by-step explanation:
Considering the first statement
One basketball player attempts 10 free throws and the number of successful attempts is totaled.
This process is a binomial process because
The number of trials is finite Each trial is independent of the other There is only two possible outcome (make a basket and make no basket The probability of making a basket and not making a basket is constant throughout the trialsOne basketball player attempts 10 free throws and the number of successful attempts is totaled.
This process is not a binomial process because chance that is the probability of success and failure will remain constant throughout the trial is not equal (what this means is that given the number of player is more than on their probability of success and failure will differ.)
scale factor of 2 to 3.5 inches
Answers
when conducting a perpendicular line through point of a line, how can you verify that the line contested is perpendicular?
Answers
Answer:
C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right
Step-by-step explanation:
Two shooters, Rodney and Philip, practice at a shooting range. They fire rounds each at separate targets. The targets are marked with circles and each bullet hitting a particular circle gets them a particular number of points. rounds are selected at random. The sample mean scores of Rodney and Philip are and , respectively. And, their variances are and , respectively. The standard error of the difference between their mean scores is . 13. (Round your answer to two decimal places.) The 95% confidence interval for the difference between the mean scores of Rodney and Philip is
Answers
Complete Question
Answer:
a
[tex]SE = 0.66}[/tex]
b
[tex] -3.29 < \mu_1 - \mu_2 < -0.70[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 60
The first sample mean is [tex]\= x _1 = 8[/tex]
The second sample mean is [tex]\= x _2 = 10[/tex]
The first variance is [tex]v_1 = 0.25[/tex]
The first variance is [tex]v_2 = 0.55[/tex]
Given that the confidence level is 95% then the level of significance is 5% = 0.05
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the first standard deviation is
[tex]\sigma_1 = \sqrt{v_1}[/tex]
=> [tex]\sigma_1 = \sqrt{0.25}[/tex]
=> [tex]\sigma_1 = 0.5[/tex]
Generally the second standard deviation is
[tex]\sigma_2 = \sqrt{v_2}[/tex]
=> [tex]\sigma_2 = \sqrt{0.55}[/tex]
=> [tex]\sigma_2 = 0.742 [/tex]
Generally the first standard error is
[tex]SE_1 = \frac{\sigma_1}{\sqrt{n} }[/tex]
[tex]SE_1 = \frac{0.5}{\sqrt{60} }[/tex]
[tex]SE_1 = 0.06[/tex]
Generally the second standard error is
[tex]SE_2 = \frac{\sigma_2}{\sqrt{n} }[/tex]
[tex]SE_2 = \frac{0.742}{\sqrt{60} }[/tex]
[tex]SE_2 = 0.09[/tex]
Generally the standard error of the difference between their mean scores is mathematically represented as
[tex]SE = \sqrt{SE_1^2 + SE_2^2 }[/tex]
=> [tex]SE = \sqrt{0.06^2 +0.09^2 }[/tex]
=> [tex]SE = 0.66}[/tex]
Generally 95% confidence interval is mathematically represented as
[tex](\= x_1 -\= x_2) -(Z_{\frac{\alpha }{2} } * SE) < \mu_1 - \mu_2 < (\= x_1 -\= x_2) +(Z_{\frac{\alpha }{2} } * SE)[/tex]
=> [tex](8 -10) -(1.96 * 0.66) < \mu_1 - \mu_2 < (8-10) +(Z_{\frac{\alpha }{2} } * 0.66)[/tex]
=> [tex] -3.29 < \mu_1 - \mu_2 < -0.70[/tex]
Correct pair
3x+5y=6
4x+2y=-6
Answers
Answer:
Step-by-step explanation:
6x + 10y = 12
-20x - 10y = 30
-14x = 42
x = -3
4(-3) + 2y = -6
-12 + 2y = -6
2y = 6
y = 3
(-3, 3)
HELP QUICK WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
How do you do this question?
Answers
Answer: Choice A
Explanation:
The sequence converges to a nonzero value, so as n gets very large, the partial sums will grow forever (since we're effectively adding at least 1 to each term regardless how large n gets)
The reason why [tex]s_n[/tex] approaches 1 is because the 1/n term goes to 0 when n gets very large.
First, rewrite 17/25 and 7/10
so that they have a common denominator.
Answers
Answer:
85/50. 35/50
You would times 17/25 by 5 and you would get 85/50 which would simplify to 1 35/50
you would multiply 7/10 by 5 to get 35/50