Friday

July 25, 2014

July 25, 2014

**Recent Homework Questions About Calculus**

Post a New Question | Current Questions

**calculus**

What is the derivative of y=sin^3(x)+sin(x^3) ?
*Thursday, July 17, 2014 at 9:59pm*

**Calculus**

find the extreme values of the function and where they occur y=1/(sqrt 1-x^2). So far I have y'=x/((1-x^2)(1-x^2)^(1/2)) but I am stuck.
*Thursday, July 17, 2014 at 5:46pm*

**calculus**

N(t) = 120/(1+11e^(−0.4t) D. At what rate is the number of fruit flies increasing after 4 days?
*Wednesday, July 16, 2014 at 10:57pm*

**calculus**

The number of Drosophila fruit flies in a controlled experiment assumes the following growth pattern when the food source is limited: N(t) = 120/(1+11e^(−0.4t)) D. At what rate is the number of fruit flies increasing after 4 days?
*Wednesday, July 16, 2014 at 10:35pm*

**calculus**

Year 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 % having VCR 0.2 0.3 0.7 1.2 2.4 4.6 8.7 15.5 23.9 34.2 45.4 50.6 56.6 61.3 (a) During what year does the point of "diminishing returns" (i.e., the inflection point) appear to take place? ...
*Wednesday, July 16, 2014 at 10:29pm*

**calculus**

The number of Drosophila fruit flies in a controlled experiment assumes the following growth pattern when the food source is limited: N(t) = 120 1+11e−0.4t where t measured in days. A. How many fruit files were there in the beginning? B. What is the limiting number of ...
*Wednesday, July 16, 2014 at 10:10pm*

**calculus**

N(t) = 650 1+649 e−0.5 t . (You may wish to sketch a graph of N(t) to help you understand this situation and answer the questions below.) (a) How many people will have heard the rumor after 2 hours? After 12 hours? (b) When will half the people have heard the rumor? t...
*Wednesday, July 16, 2014 at 10:08pm*

**Calculus Help!**

At a price of $7.5 per ticket, a musical theater group can fill every seat in their 1500 seat performance hall. For every additional dollar charged for admission, the number of tickets sold drops by 95. a) What ticket price maximizes revenue? Round your answer to the nearest ...
*Wednesday, July 16, 2014 at 1:37pm*

**calculus**

C(q) = q3−60q2+1200q+760 for 0 ≤ q ≤ 50 and a price per unit of $551. Round your answers to the nearest whole number. a) What production level maximizes profit? q = b) What is the total cost at this production level? cost = $ c) What is the total revenue at ...
*Wednesday, July 16, 2014 at 1:08pm*

**calculus **

At a price of $7.5 per ticket, a musical theater group can fill every seat in their 1500 seat performance hall. For every additional dollar charged for admission, the number of tickets sold drops by 95. a) What ticket price maximizes revenue? Round your answer to the nearest ...
*Wednesday, July 16, 2014 at 12:52pm*

**Calculus Help**

The deal your assistant signs calls for the sale of a minimum of 260 chairs and up to 410 chairs. The price will be $88 per chair if only 260 chairs are bought, but will be discounted by $0.2 per chair (on the entire order) for every chair ordered in addition to the minimum. ...
*Tuesday, July 15, 2014 at 9:27pm*

**Calculus Help**

At a price of $7.5 per ticket, a musical theater group can fill every seat in their 1500 seat performance hall. For every additional dollar charged for admission, the number of tickets sold drops by 95. a) What ticket price maximizes revenue? Round your answer to the nearest ...
*Tuesday, July 15, 2014 at 9:26pm*

**Calculus Help**

using the cost function C(q) = q3−60q2+1200q+760 for 0 ≤ q ≤ 50 and a price per unit of $551. Round your answers to the nearest whole number. a) What production level maximizes profit? q = b) What is the total cost at this production level? cost = $ c) What ...
*Tuesday, July 15, 2014 at 9:24pm*

**Calculus Help**

Using the revenue function R(q) = 510q and the cost function C(q) = 9400+3q2. Round your answers to the nearest whole number. a) At what quantity is profit maximized? q = b) What is the total profit at this production level? profit = $
*Tuesday, July 15, 2014 at 9:18pm*

**Calculus 2**

find the arc length of the graph of the function over the indicated interval. x^5/10+1/(6x^3) on the interval (3,6)
*Monday, July 14, 2014 at 9:14am*

**Urgent Calculus Help 2**

Find the equation of the tangent line to the graph of f(x) = 6x ln(x + 4) at x = 2.
*Wednesday, July 9, 2014 at 7:12pm*

**Urgent Calculus Help**

Let H(x)=F(G(x)) and J(x)=F(x)/G(x). Suppose F(7)=4, F′(7)=−8 G(7)=3, G′(7)=−5 G(2)=7, G′(2)=−2 then H′(2)= J′(7)=
*Wednesday, July 9, 2014 at 7:12pm*

**Maths- calculus**

Two ships leave different ports A and B 100 miles apart at 0800 hours, each heading for the opposite port on reciprocal courses. Ship A steams at 20 knots and ship B at 15 knots. calculate: (a) What time are they first 45 miles apart? (b) What time they will pass, and how far ...
*Wednesday, July 9, 2014 at 2:02am*

**Math pre-calculus**

Write an expression for all of the vertical asymptotes of y=-3 csc(pi/4 *x) Can you list step by step to show how to do it , I don't understand this problem !!! Thanks
*Wednesday, July 9, 2014 at 1:27am*

**calculus **

the time required for one complete oscillation of a pendulum is called its period. if the length L of the pendulum is measured in feet and the period P n seconds, then the period is given by P=2¶(L/g)^1/2, where g is constant. use differentials to show the percentage ...
*Tuesday, July 8, 2014 at 9:59pm*

**calculus**

f(t) = − 4 t2 − t− 6 Find the equation of the line tangent to the graph of f(t) at t = 8. Enter the equation of the tangent line here (in terms of the variable t):
*Monday, July 7, 2014 at 9:06pm*

**calculus**

If C′(62) = 120 and R′(62) = 145, approximately how much profit is earned by item number 63?
*Monday, July 7, 2014 at 8:06pm*

**Calculus**

A particle moves with a fixed acceleration of 3 m/s^2. If its initial velocity is v(0)= 2 m/s, and its initial displacement is s(0)= 0 A)Find its velocity function v(t) B)How long does it take for the particle to reach the velocity 14 m/s? C)Find the distance traveled when its...
*Sunday, July 6, 2014 at 11:27pm*

**Statistics**

The mean score on the first calculus exam was 55%. The standard deviation was 7%. Find the smallest interval about the mean that must contain at least 83% of the scores. heeellllppppp
*Friday, July 4, 2014 at 3:50pm*

**Calculus**

A vessel is in the shape of an inverted cone. The radius of the top is 5cm and the height is 8cm. Water is poured into a height of xcm. Show that if the volume of the water is Vcm^3,then V=(25/192)*pi*x^3. (The volume of a cone is given by the formula V=(1/3)*pi*r^2*h)
*Friday, July 4, 2014 at 9:42am*

**Urgent Calculus Help**

Based on the following table of values for the function w(t), answer the questions below. t and w(t) are a table with the following values: (100,2.6), (110,7.3), (120,12.7), (130,19), (140,26.1), (150,34.1) a) Which of the following best describes the derivative of w(t)? A. ...
*Thursday, July 3, 2014 at 7:46pm*

**Calculus Help**

Based on the following table of values for the function w(t), answer the questions below. t= 100 110 120 130 140 150 w(t)= 2.6 7.3 12.7 19 26.1 34.1 a) Which of the following best describes the derivative of w(t)? A. changes sign B. always positive C. always negative b) Which ...
*Thursday, July 3, 2014 at 7:44pm*

**Calculus 1**

A spherical snowball melts in such a way that its surface area decreases at a rate of 1 cm2/min. Find the rate at which its diameter is decreasing when the diameter is 10 cm
*Thursday, July 3, 2014 at 1:46pm*

**Calculus I**

Hello! I am not sure why I am getting this problem wrong, and I keep getting six. Could someone be kind enough to show me how it's done? Thank you very much in advance! Find the limit. Use l'Hospital's Rule if appropriate. lim ((5x − 2)/(5x + 4))^(5x + 1) x&#...
*Monday, June 30, 2014 at 6:51pm*

**Calculus help**

assume that the initial deposit is $20000 and the nominal annual interest rate is 5.7%. Determine the amount in the account in 10 years if the interest is compounded as follows (round your answers to the nearest dollar): (a) Annually: P=20000(1.057)^10 (b) Monthly: (c) Weekly...
*Friday, June 27, 2014 at 10:50pm*

**calculus**

Choice 1: Payments of $ 2600 now, $ 3200 a year from now, and $ 3880 two years from now. Choice 2: Three yearly payments of $ 3200 starting now. Modification: Interest is compounded continuously instead of annually. (a) If the interest rate on savings were 4.86 %, which would ...
*Friday, June 27, 2014 at 2:54pm*

**calculus**

Suppose strontium-90 decays at a rate of 2 percent per year. (a) Write the fraction P of strontium remaining, as function of t, measured in years. (Assume that at time t=0 there is 100 % remaining.) Answer: P(t) = (b) Estimate the half-life of strontium. Answer: Hint: Use your...
*Friday, June 27, 2014 at 2:53pm*

**calculus**

Pretend the world's population in 1989 was 5 billion and that the projection for 2017 is 7.5 billion. What annual rate of growth is assumed in this prediction?
*Friday, June 27, 2014 at 10:48am*

**calculus**

Pretend the world's population in 1989 was 5 billion and that the projection for 2017 is 7.5 billion. What annual rate of growth is assumed in this prediction?
*Friday, June 27, 2014 at 10:47am*

**Calculus I**

Hello! I am taking Calculus I and am in Sec. 4.3 of Stewart's 7th Edition. I ran across a problem that I don't understand the mechanics of, could someone show me? Thanks a bunch! For what values of the numbers a and b does the function f(x)= axe^{b(x^2)} have the ...
*Thursday, June 26, 2014 at 10:47pm*

**Pre calculus**

For the equation 2x^2-5x^3+10=0 find the number the number of complex roots and the possible number of real roots.
*Monday, June 23, 2014 at 11:19pm*

**calculus**

the weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. if a person weighs 180 pounds on the surface of the earth and the radius of the earth is 3900 miles, what will the person ...
*Monday, June 23, 2014 at 7:48pm*

**Calculus**

Given f(x) = cubed root of x^2 (2x+5)^3, find the critical numbers after you identify the domain.
*Monday, June 23, 2014 at 2:15am*

**Calculus**

Given f(x) = csc^4(5x^2-3x+1), find f'(x). Show all work.
*Monday, June 23, 2014 at 2:12am*

**Calculus**

A water tank in the shape of a right circular cylinder has a volume that is increasing at the rate of 300pi cubic centimeters per hour. If the height is decreasing at the rate of 15 centimeters per hour, find the rate at which the radius is changing when the radius is 20 ...
*Monday, June 23, 2014 at 2:11am*

**Calculus**

Water is leaking from the bottom of a tank in the shape of an inverted cone having an altitude of 12 feet and a radius of 2 feet. If the water is leaking at the rate of 0.25 cubic feet per minute, how fast is the water level decreasing when the water is 4 feet deep?
*Monday, June 23, 2014 at 2:05am*

**calculus**

When a hammer thrower spins, the hammer generates a circle with a radius of 5 feet. When thrown, the hammer hits a screen that is 50 feet from the center of the throwing area. Let coordinate axes be introduced. If the hammer is released at (-4, -3) and travels in the tangent ...
*Saturday, June 21, 2014 at 12:04pm*

**Pre-Calculus**

What makes a mathematical induction true? I know how to solve both steps in the proof, but how do you reach this conclusion?
*Friday, June 20, 2014 at 3:04pm*

**Calculus**

The CIA published data about foreign countries on its web page. In particular they show total population as well as population growth. If a student is looking at Russia, they will see that the total population of Russia is declining. When they look at the table that shows ...
*Tuesday, June 17, 2014 at 11:27pm*

**CALCULUS II**

Hi, I needed help with this improper integral. lower limit : 2 upper limit : infinity integral of (lnx)/(x+1) dx Thank You so much :D
*Tuesday, June 17, 2014 at 4:48pm*

**Calculus**

The median value of a home in a particular market is decreasing exponentially. If the value of a home was initially $240,000, then its value two years later is $235,000. a) Write a differential equation that models this situation. Let V represent the value of the home (in ...
*Tuesday, June 17, 2014 at 9:52am*

**Calculus**

dy/dx = 4ye^(5x) a) Separate the differential equation, then integrate both sides. b) Write the general solution as a function y(x). For the second part, I got y(x)=e^((5e^(5x))/(5)) + C but I don't understand how to separate differential equations and/or integrate both ...
*Monday, June 16, 2014 at 9:41pm*

**Calculus **

∫1/(x2 − 2x + 8)3/2 dx
*Monday, June 16, 2014 at 3:42pm*

**Calculus**

Q: If y=sinx/(1+tanx), find value of x not greater than pi, corresponding to maxima or minima value of y. I have proceeded thus- Equating dy/dx=0 we get{ (1+tanx)cosx-sinx.sec^2 x}/(1+tanx)^2=0……..(A) Or cosx+sinx=sinx.sec^2 x or cosx= sinx.sec^2-sinx Or cosx=sinx....
*Monday, June 16, 2014 at 2:29am*

**Precalc**

Are exponential equations the same as exponential functions? I am writing a summary of this year's Pre-Calculus lessons and one of the topics on the outline is "Exponential Equations", but on the lesson Power Points on my teacher's website there is only one ...
*Sunday, June 15, 2014 at 5:35pm*

**calculus**

Eric is standing on the ground, a distance of 70 ft from the bottom of Ferris wheel that has a 20 ft radius. His arm is at the same height as the bottom of the Ferris wheel. Janice is on Ferris wheel which makes one revolution counter clock wise every 16 secs. At the instant ...
*Sunday, June 15, 2014 at 10:25am*

**calculus**

An electron, travelling at 2000 m/s, is suddenly influenced by an extreme deceleration of 3000 m/s2. How fast is it going 0.03 s later?
*Wednesday, June 11, 2014 at 1:55pm*

**calculus**

A parabola ,f, intersect the x axis at A and B and the y axis at C. The axis of symmetry of the parabola has the equation x=-3.The line through A and C has the equation g(x)=x+7. Determine the coordinates of A,B and C
*Tuesday, June 10, 2014 at 10:03am*

**Calculus**

Assume v(t) = 6t - 18 on the interval [0, 6]. Find the total distance that the object traveled on [0, 6].
*Monday, June 9, 2014 at 6:11pm*

**Calculus**

What is the total change of f(x), if f'(x) = 2x - 3x^2, over the interval [0, 3]?
*Monday, June 9, 2014 at 4:54pm*

**Calculus**

A rock is dropped from the top of a 400-foot-tall building. Its distance s (in feet) from the top of the building after t seconds is s(t) = 16t^2. How many seconds will it take the rock to hit the ground?
*Sunday, June 8, 2014 at 6:34pm*

**Calculus**

The rate of change in the volume of a tank is known to be dV/dt=0.6t*cos(0.08t^2 -1), where V(t) is in gallons per minute and 0<=t<=10 (0 is less than or equal to t which is less than or equal to 10). If the tank has a volume of 14 gallons initially, what is its volume ...
*Sunday, June 8, 2014 at 4:49pm*

**Calculus**

An object with an initial position of x(0) = 3 has a velocity of v(t) =sin(t). Find its position at t =2.
*Saturday, June 7, 2014 at 12:00pm*

**calculus**

The Audubon Society at Enormous State University (ESU) is planning its annual fund-raising "Eat-a-thon." The society will charge students 90¢ per serving of pasta. The only expenses the society will incur are the cost of the pasta, estimated at 20¢ per ...
*Saturday, June 7, 2014 at 1:07am*

**Calculus**

Given the area of a rectangle is A = LW. If three sides of the rectangle are fixed, I.e. 2W + L = 40, find L and W such that you maximize the area of the rectangle. Is it L=10, W=20?
*Friday, June 6, 2014 at 12:11pm*

**Calculus**

A square with side x cm, is changing with time where x(t) = 3t + 1. What is the rate of change of the area of the square when t = 2 seconds?
*Friday, June 6, 2014 at 11:01am*

**Calculus**

A rectangular box has a square base whose edge has length at least one centimeter, and its total surface area is 600 cm2. What is the largest possible volume that such a box can have? V = 500 in3 V = 750 in3 V = 900 in3 V = 1,000 in3
*Tuesday, June 3, 2014 at 11:53am*

**pre calculus**

Find a cubic function with the given zeros. -2, 5, -6 help me please
*Tuesday, June 3, 2014 at 10:01am*

**calculus**

Multiple choice: An airplane flying due east at 539 mph in still air, encounters a 61-mph tail wind acting in the direction 45 degrees north of east. The airplane holds its compass heading but because of the wind acquires a new ground speed and direction. What is its new ...
*Tuesday, June 3, 2014 at 2:00am*

**Calculus**

find the area of the region inside the limacon r= 8 + 4sin(theta) HElp!! if you can show steps, i'd be greatful
*Monday, June 2, 2014 at 11:17pm*

**Calculus Help**

I am given this data table: Time After Consumption (min): 30, 60, 90, 120, 150, 180 Amount of Codeine in Blood (mg): 27.0, 23.5, 21.2, 18.7, 16.6, 14.5 Question: I created a scatter plot of the data. How would I determine an equation to model the amount of codeine in the ...
*Monday, June 2, 2014 at 7:41pm*

**Calculus **

Compute the absolute and relative errors in using c to approximate x. x=e;c=2.68
*Sunday, June 1, 2014 at 10:47pm*

**Pre-Calculus**

if cos theta =7/13, where 0<theta<pi/2, fin the value of cos2theta
*Saturday, May 31, 2014 at 6:56pm*

**calculus**

Identify the open intervals) where the function f of F(x)= x√10-x^2 is increasing.
*Wednesday, May 28, 2014 at 2:21pm*

**calculus**

A golf ball is hit off the top of a cliff that is 75 feet tall at an angle of 45° to the horizontal with an initial velocity of 80 feet per second. The quadratic equation shown below models the height, h(x), of the ball when it is x feet from the cliff’s edge. How far...
*Wednesday, May 28, 2014 at 12:14pm*

**Calculus**

Find all values for c in the intercal (1,4) so that the slope of the tangent line at (c,f(c)) equals the slope of the secant line through (1,1/3) and (4,2/3) where f(x) = x/(x+2) 1 </ x </ 4 (<-- that is suppose to be the less than or equal to sign) I'm not sure ...
*Tuesday, May 27, 2014 at 11:21pm*

**Calculus**

Please help I am stuck evaluate the following intergral x cos 15x dx.
*Tuesday, May 27, 2014 at 11:17pm*

**calculus**

Evaluate the following integrals using the given substitutions. (a) (3x^2 + 10x)dx/(x^3 + 5x^2 + 18 , substitution u = x3 + 5x2 + 18; (b)(14x + 4)cos(7x^2 + 4x)dx,substitution u = 7x^2 + 4x.
*Tuesday, May 27, 2014 at 4:37pm*

**Calculus**

Let t be some ﬁxed real number. Find the volume of the region bounded by y =1/x and the y = 0 on the interval [1, t] rotated about the x-axis. What happens as t → ∞?
*Tuesday, May 27, 2014 at 3:10pm*

**Calculus**

inding vertex and focus of parabola y^2 +4y +8x - 12 =0
*Tuesday, May 27, 2014 at 2:21pm*

**Calculus**

How do you solve the equation log(x+6)-log(2x+1)=log4
*Monday, May 26, 2014 at 2:06pm*

**Calculus**

A cable is suspended from two towers with a distance of 100m between them. The 1st tower has a height of 50m and the 2nd tower has a height of 70m from the ground. The lowest part of the cable has a distance of 47m from the ground. Find the length of the cable
*Sunday, May 25, 2014 at 4:37am*

**calculus**

A region is bounded in the second quadrant by the curve y = ln(1–x), the line y=3, and the y-axis. Find the area of the region.
*Thursday, May 22, 2014 at 6:50pm*

**college calculus**

the amount of carbon-14 in a mammoth's bone is 45% of the amount found in a living organism. How long ago did the mammoth die? the half-life of carbon-14 is about 5,730 years.
*Thursday, May 22, 2014 at 4:44pm*

**Calculus**

Jill burns 100 calories per hour while sleep and 300 calories per hour while walking and 200 calories per hour at work. If in a typical day Jill spends 7 hours sleeping, 2 hours walking and 6 hours working, what is her average calories burned for those hours? 166.67 cal/hr 200...
*Thursday, May 22, 2014 at 12:58pm*

**Calculus**

2x -------- (x-2)(x+2) using partial fractions That's supposed to be a division sign of some sort
*Thursday, May 22, 2014 at 5:33am*

**Calculus**

Consider the function f (x) = 2x^3 - 3x^2 - 72x + 7 Find and classify the critical points. Identify the intervals of increase and decrease, and state the intervals of concavity.
*Thursday, May 22, 2014 at 1:04am*

**Calculus**

find the co-ordinates y=x(2-x) where the gradient is 2
*Wednesday, May 21, 2014 at 1:23pm*

**Calculus**

1/X by first principles
*Wednesday, May 21, 2014 at 12:43pm*

**Calculus**

A fragment of bone is discovered to contain 20% of the usual carbon-14 concentration. Estimate the age of the bone to the nearest hundred years, given that Carbon-1 is radioactive with half-life of 5730 years and the rate of decay is given by the following differential ...
*Wednesday, May 21, 2014 at 2:20am*

**Calculus**

Find the volume of the solid generated by rotating about the y axis the area in the first quadrant bounded by the following curve and lines. y=x^2, x=0, y=2.
*Wednesday, May 21, 2014 at 2:17am*

**Calculus**

Find the area of the region enclosed by the parabolas y=x^2 and y+2x-x^2
*Wednesday, May 21, 2014 at 2:15am*

**Calculus**

2x -------- (x-2)(x+2) using partial fractions That's supposed to be a division sign of some sort
*Wednesday, May 21, 2014 at 2:14am*

**Calculus**

xe^x using integration by parts
*Wednesday, May 21, 2014 at 2:12am*

**Calculus**

x(x^2-1)^3 using change of variable
*Wednesday, May 21, 2014 at 2:09am*

**Calculus**

a rectangular storage area is to be constructed along the sides of a tall building. A security fence is required along the three remaining sides of the area. What is the maximum area that can be enclosed with 1000m fencing?
*Wednesday, May 21, 2014 at 12:21am*

**Calculus**

a meteorite slams into the earths crust and penetrates d=(1200t-36000t^2)m in t seconds after impact. What is the maximum depth of penetration?
*Wednesday, May 21, 2014 at 12:21am*

**Calculus **

An inverted conical tank is 3m tall and 1m in diameter at its widest point. The water is being pumped out of a spout 2m above the top of the tank. Recall that the density of water is ρ = 1000kg/m^3 (a) Find the work needed to empty the tank if it is full. Include units. (...
*Tuesday, May 20, 2014 at 11:28pm*

**Calculus **

I did an experiment where I had to measure how fast water flowed out of a container at different times and with different volumes (from 0mL-1000mL in increments of 50). I also had to record the values into a table and graph them. (I got an exponential function). I got a slope ...
*Tuesday, May 20, 2014 at 11:24pm*

**Calculus**

I have a data table and I graphed the data. I have to find the slope of a tangent at t=0. Would the slope just be zero?
*Tuesday, May 20, 2014 at 6:41pm*

**Calculus**

In First principles there is usually a part that states as lim approaches 0. Now I came across a question where the limit was as 1 approaches 3. what should I do?
*Tuesday, May 20, 2014 at 4:13pm*

**calculus**

Consider the motion of a particle of mass m falling vertically under the earth’s gravitational field, and suppose the downward motion is opposed by a frictional force p(v) dependent on the velocity v(t) of the particle. Then the velocity satisfies the equation mv0(t) = &#...
*Tuesday, May 20, 2014 at 2:59pm*

**Calculus**

A circular oilspill is spreading such that the radius is increasing at 0.5 metres per minute. Find the rate of increase of the are of the oil spill when the radius is 10m.
*Tuesday, May 20, 2014 at 1:22pm*

**Calculus**

a meteorite slams into the earths crust and penetrates d=(1200t-36000t^2)m in t seconds after impact. What is the maximum depth of penetration?
*Tuesday, May 20, 2014 at 1:13pm*

**Calculus**

a rectangular storage area is to be constructed along the sides of a tall building. A security fence is required along the three remaining sides of the area. What is the maximum area that can be enclosed with 1000m fencing?
*Tuesday, May 20, 2014 at 1:12pm*

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