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January 27, 2015

January 27, 2015

**Recent Homework Questions About Calculus**

Post a New Question | Current Questions

**Calculus**

Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE. sum from 1 to infinity of (5^n+4^n)/20^n It is convergent, but I do not know how to find the sum.
*Thursday, April 3, 2014 at 1:15pm*

**Calculus**

Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE. sum from 1 to infinity of 1/e^2n. It is convergent, but I do not know how to solve for the sum.
*Thursday, April 3, 2014 at 1:13pm*

**Calculus**

If y = y(x), write y’ in Leibniz notation.
*Wednesday, April 2, 2014 at 10:00pm*

**calculus**

revenue function of x^2+3p=675
*Wednesday, April 2, 2014 at 8:37pm*

**calculus**

a farmer wishes to fence off a rectangular plot of land, using an existing wall as one of the sides . the total are enclosed must be 600 square yards. the fence on the side parallel to the wall will cost 20$ per yard, while the fences on the other side will cost 30$ per yard. ...
*Wednesday, April 2, 2014 at 8:36pm*

**Calculus**

If g(x) = a f(x); find g’(x). Is it g'(x)=af?
*Wednesday, April 2, 2014 at 8:13pm*

**calculus**

Let C(t) be the total value of US currency (coins and banknotes) in circulation at time. The table gives values of this function from 1980 to 2000, as of September 30, in billions of dollars. Estimate the value of C(1990) . t 1980 1985 1990 1995 2000 C(t) 129.9 187.3 271.9 409...
*Wednesday, April 2, 2014 at 6:59pm*

**Calculus Help Please!!! Check **

When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round the answers to two decimal place.) (a) What is the temperature of the drink after 60 minutes? (b) When will its ...
*Wednesday, April 2, 2014 at 6:00pm*

**Calculus Help Please**

let f(x)=(x-1)^2, g(x)=e^(-2x), and h(x)=1+ ln(1-2x) find linearization of f, g, and h at a=0 Lf(x)= Lg(x)= Lh(x)= graph f,g, and h, and their linear app. For which function is the linear app. best? for which is the worst? explain. the linear app. appears to be best for the ...
*Wednesday, April 2, 2014 at 5:28pm*

**Calculus Help Please!!!**

When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel: F = kR4 (This is known as Poiseuille's Law.) A partially clogged artery can be ...
*Wednesday, April 2, 2014 at 5:22pm*

**Calculus Help**

A plane flies horizontally at an altitude of 6 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/3 rad/min. How fast is the plane traveling at that time?
*Wednesday, April 2, 2014 at 4:47pm*

**Calculus Help Please!!!**

When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round the answers to two decimal place.) (a) What is the temperature of the drink after 60 minutes? (b) When will its ...
*Wednesday, April 2, 2014 at 4:43pm*

**Calculus Help Please!!! Check **

A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is three times the y-coordinate of P. Find an equation of the curve. dy/dp = 3y or ∫ (3/y) dy = ∫ dp or 3 ln(y) = p + c or @ (0,2) ln(2) = 0 + c or c = ln(2) 3...
*Wednesday, April 2, 2014 at 4:39pm*

**calculus help thanks!**

The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 8.0 atm and is ...
*Wednesday, April 2, 2014 at 4:35pm*

**Calculus Help Please!!!**

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following. after 1 s = after 3 s = after 7 s =
*Wednesday, April 2, 2014 at 4:32pm*

**Calculus Help Please!!!**

Consider the following. f(x) = 8x (square root of (x − x^2)) (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
*Tuesday, April 1, 2014 at 10:27pm*

**Calculus Help Please!!!**

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 2x^2 − 5x + 1, [0, 2] If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list...
*Tuesday, April 1, 2014 at 10:08pm*

**Calculus Help Please!!!**

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe^((−x^2)/98), [−6, 14]
*Tuesday, April 1, 2014 at 9:14pm*

**Calculus Help Please!!!**

Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (t square root of (64 − t^2)) ,[−1,8]
*Tuesday, April 1, 2014 at 9:11pm*

**Calculus Help!**

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe^(−x^(2)/98), [−6, 14]
*Tuesday, April 1, 2014 at 9:09pm*

**Calculus**

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 8 cos t + 4 sin 2t, [0, π/2]
*Tuesday, April 1, 2014 at 5:45pm*

**Calculus Help Please!!!**

Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (t square root of (64 − t^2)), [−1, 8]
*Tuesday, April 1, 2014 at 5:27pm*

**Calculus Help Please!!!**

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x^3 − 3x^2 − 72x + 7 , [−4, 5]
*Tuesday, April 1, 2014 at 5:26pm*

**calculus and vectors**

Determine an equation of the line of intersection of the planes 4x − 3y − z = 1 and 2x + 4y + z = 5.
*Tuesday, April 1, 2014 at 4:59pm*

**calculus**

Twenty feet wire is used to make two figures? What is the maximum areas of enclosed figures.
*Tuesday, April 1, 2014 at 11:14am*

**Calculus**

Find the area cut off by x+y=3 from xy=2. I have proceeded as under: y=x/2. Substituting this value we get x+x/2=3 Or x+x/2-3=0 Or x^2-3x+2=0 Or (x-1)(x-2)=0, hence x=1 and x=2 are the points of intersection of the curve xy=2 and the line x+y=3. Area under curve above X axis ...
*Tuesday, April 1, 2014 at 3:07am*

**Calculus**

The circle defined by the equation x^2 + y^2 = 18 has two points where the slope of its tangent line is m=1. Find those points.
*Monday, March 31, 2014 at 11:41am*

**Calculus: Integral**

I don't understand how to do this one integral problem that involves secant. I'm asked to find the integral of sec^4 (4x). I'm not really sure how to go about solving this problem.
*Monday, March 31, 2014 at 3:32am*

**Calculus Help Please!!!**

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) fourth root of (1 + 2x)≈ 1 + (1/2)x
*Sunday, March 30, 2014 at 11:21pm*

**Calculus Help Please!!!**

The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. 1) Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.) 2) What is the relative error? (Round your answer to three decimal ...
*Sunday, March 30, 2014 at 11:17pm*

**Calculus Help**

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 54 m. (Round your answer to two decimal places.)
*Sunday, March 30, 2014 at 11:16pm*

**Calculus Help Please**

Use a linear approximation (or differentials) to estimate the given number. (1.999)^4
*Sunday, March 30, 2014 at 10:14pm*

**Calculus Help Please!!!**

Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.) y = 3x − x^2, x = 3, Δx = −0.6 Δy=???
*Sunday, March 30, 2014 at 9:57pm*

**Calculus Help Please!!!**

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) ln(1 + x) ≈ x xE
*Sunday, March 30, 2014 at 8:28pm*

**Calculus Help Please!!!**

Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 3.5 ft/s. How fast is cart B moving toward Q at...
*Sunday, March 30, 2014 at 7:16pm*

**Calculus Help Please!!!**

A water trough is 5 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.1 m3/min how fast is the water level rising when ...
*Sunday, March 30, 2014 at 6:43pm*

**Calculus**

When dy/dx=(x-6)^½ what does y equal?
*Saturday, March 29, 2014 at 4:11pm*

**Calculus**

Jesse has constructed a huge cylindrical can with a diameter of 60 ft. The can is being filled with water at a rate of 450 ft3/min. How fast is the depth of the water increasing? (Hint: The volume of water in the cylinder is determined by πr2h where r is the radius and h ...
*Friday, March 28, 2014 at 11:39pm*

**Calculus**

At what interval is e^(-5x^2) concave up? I know the second derivative is 100x^2*e^-5x^2-10*e^-5x^2 but I just can not figure this one out. Thank you for your help!
*Friday, March 28, 2014 at 7:38pm*

**Calculus**

Find the area cut off by x=4 from the hyperbola x^2/9-y^2/4=1. Answer is 4.982 in the book. I have proceeded as under: Y=2/3*sqrt(x^2-9) and rhe reqd. area is double of integral 2/3*sqrt(x^2-9) from 3 to 4. Int= 2/3*[xsqrt(x^2-9)/2 – 9/2*log{x+sqrt(x^2-9)}] from 3 to 4 =x...
*Friday, March 28, 2014 at 2:17am*

**Calculus Help Please!!!**

In a murder investigation, the temperature of the corpse was 32.5 C at 1:30pm and 30.3 C an hour later. Normal body temperature is 37.0 C and the temperature of the surrounding was 20.0 C. When did the murder take place? PLEASE SHOW STEP BY STEP
*Thursday, March 27, 2014 at 8:16pm*

**Calculus**

A weight oscillates in a vertical motion according to the position function y(t)=-5 cos(t). Assuming t≥0, when will the acceleration if the weight be zero for the first time?
*Thursday, March 27, 2014 at 2:51pm*

**Calculus**

An object in free fall has its distance from the ground measured by the function d(t)=-4.9t^2 +50, where d is in meters and t is in seconds. If gravity is the only acceleration affecting the object, what is gravity's constant value?
*Thursday, March 27, 2014 at 2:37pm*

**Calculus**

If y=cos x, what is y^(6) (x)?
*Thursday, March 27, 2014 at 11:18am*

**CALCULUS problem**

There are four parts to this one question, and would really appreciate if you could show and explain how you get to the answer, because I tried looking up how to find the answer myself, but nothing made sense. Thank you! 11. The region R is bounded by the x-axis, x = 1, x = 3...
*Thursday, March 27, 2014 at 8:51am*

**Calculus**

Posted by MG on Wednesday, March 26, 2014 at 6:54pm. The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at ...
*Thursday, March 27, 2014 at 3:36am*

**Calculus**

If e^x = 243 and e^y = 32 then e^((3x + 4y)/5) =? The answer is 432, but I don't understand why.
*Thursday, March 27, 2014 at 3:34am*

**pre calculus**

A taxi company charges $2.00 for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 < x < 2
*Thursday, March 27, 2014 at 12:07am*

**Calculus**

The height in feet above the ground of a ball thrown upwards from the top of a building is given by s=-16t^2 + 160t + 200, where t is the time in seconds. If the maximum height is 600 feet, what is v^-1(32)? The answer is supposed to be 4 seconds, but I don't understand ...
*Wednesday, March 26, 2014 at 11:07pm*

**Calculus **

You are given a piece of sheet metal that is twice as long as it is wide an has an area of 800m^2. Find the dimensions of the rectangular box that would contain a max volume if it were constructed from this piece of metal by cutting out squares of equal area at all four ...
*Wednesday, March 26, 2014 at 9:49pm*

**Calculus**

Use a tangent line approximation at x=0 to estimate the value of sin(-0.1). I got 0.1
*Wednesday, March 26, 2014 at 8:56pm*

**Calculus**

The vertical position of an object is modeled by the function h(t)=-16t^2 +5t+7, where h is measured in feet and t is measured in seconds. Find the object's initial velocity (that is, the velocity at t=0). Is it 5 feet per second?
*Wednesday, March 26, 2014 at 8:46pm*

**Pre calculus**

For the most part, will a law of cosines always be one triangle? As in one triangle to solve?
*Wednesday, March 26, 2014 at 8:35pm*

**College Calculus**

The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at a rate of _______ m/hr at 9:00? I tried several times...
*Wednesday, March 26, 2014 at 6:54pm*

**Calculus**

If position is given by p(t)=t^2 +1, find the velocity v(t) at t = 2. I'm completely lost as to where to even start with this problem.
*Wednesday, March 26, 2014 at 4:25pm*

**Calculus**

The amount of carbon-14 still present in a sample after t years is given by the function where C0 is the initial amount. Estimate the age of a sample of wood discovered by an archeologist if the carbon level in the sample is only 18% of its original carbon-14 level.
*Wednesday, March 26, 2014 at 10:31am*

**Calculus**

If 40 milligrams of strontium-90 radioactively decays to 12 milligrams in 30 years, find its half-life (the number of years it takes until half of it remains). Use the formula A = p ⋅ e−kt, where p is the amount and A the (smaller) final amount.
*Wednesday, March 26, 2014 at 10:29am*

**pre calculus**

Find the exact values: tan(7pi/4) - tan (pi/6)
*Wednesday, March 26, 2014 at 1:42am*

**Calculus**

Find a positive number such that the sum of the square of the number and its reciprocal is a minimum.
*Tuesday, March 25, 2014 at 9:25pm*

**Grade 12 Calculus**

For an outdoor concert, a ticket price of $30 typically attracts 5000 people. For each $1 increase in the ticket price, 100 fewer people will attend. The revenue, R, is the product of the number of people attending and the price per ticket. a) Let x represent the number of $1 ...
*Tuesday, March 25, 2014 at 8:46pm*

**Calculus**

There are 50 apple trees in an orchard, and each tree produces an average of 200 apples each year. For each additional tree planted within the orchard, the average number of apples produced drops by 5. What is the optimal number of trees to plant in the orchard? I mostly need ...
*Tuesday, March 25, 2014 at 8:09pm*

**Grade 12 Calculus**

A rectangular piece of paper with perimeter 100 cm is to be rolled to form a cylindrical tube. Find the dimensions of the paper that will produce a tube with maximum volume. I have made it up to getting an equation for V(w).
*Tuesday, March 25, 2014 at 7:49pm*

**Calculus Rate of Change**

Find the average rate of change h(x)=2x^2-4 from x=2 to x=6 Simplify your answer as much as possible
*Tuesday, March 25, 2014 at 10:27am*

**calculus**

Recall that the volume of a sphere of radius r is V(r) =4\, \pi\, r^3 /3. Find L, the linearisation of V(r) at r=50
*Tuesday, March 25, 2014 at 2:05am*

**Calculus A **

Find all relative extrema and points of inflection for the function; h(x)=(x^2+5x+4)/(x-1)
*Monday, March 24, 2014 at 11:20pm*

**Calculus **

Find dy/dx implicitly in terms of x and y only for the following function; x+ 4xy=y^2
*Monday, March 24, 2014 at 11:17pm*

**Calculus A **

Find all relative extrema and points of inflection for the following function... h(X)= X^2+5X+4/ X-1 min= max= inflection points=
*Monday, March 24, 2014 at 7:16pm*

**calculus**

Suppose that a particle moves along a line so that its velocity v at time t is given by this piecewise function: v(t)=5t if 0≤t<1 v(t)=6((t)^(1/2))-(1/t) if 1≤t where t is in seconds and v is in centimeters per second (cm/s). Estimate the time(s) at which the ...
*Sunday, March 23, 2014 at 8:17pm*

**Calculus**

Find the slope of the tangent line to the ellipse x^2/4 + y^2/16= 1 at the point (x,y)
*Sunday, March 23, 2014 at 8:11pm*

**Calculus**

Suppose you have a hot cup of coffee in a room where the temp is 45 Celcius. Let y(t) represent the temp. of coffee as a function of the number of minutes t that have passed since the coffee was poured a) write a differential equation that applies to newtons law of cooling. ...
*Sunday, March 23, 2014 at 6:16pm*

**Calculus Help Please!!! **

find y' and y” by implicit differentiation. 2x^3 + 3y^3 = 8
*Saturday, March 22, 2014 at 3:53pm*

**Calculus **

A rancher wants to build a rectangular fence next to a river, using 100 yd of fencing. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the rancher should not fence the side next to the river.)
*Saturday, March 22, 2014 at 5:45am*

**Calculus**

A ball is thrown vertically upward with an initial velocity of 135 feet per second, the ball’s height after t second is s(t) = 135t – 22t How to calculate average velocity from 1 to 3 seconds?
*Saturday, March 22, 2014 at 12:34am*

**Calculus**

Evaluate the improper integral or state that it diverges: integral from -inf to inf (2xe^-x) dx. Please help!
*Thursday, March 20, 2014 at 8:39pm*

**Calculus Help STEVE**

find y'' by implicit differentiation. 2x^3 + 3y^3 = 8 I got the first derivative as you but the problem was asking for second derivative by implicit diff. this is where i got confused. Thank you!!!
*Thursday, March 20, 2014 at 5:51pm*

**Calculus Help**

find y'' by implicit differentiation. 2x^3 + 3y^3 = 8
*Thursday, March 20, 2014 at 3:28pm*

**Calculus Help Please!!! **

find the derivative of the function. Simplify where possible. F(theta)=arcsin(square root of (sin9(theta)))
*Thursday, March 20, 2014 at 2:42pm*

**CALCULUS HELP**

Let r(x)= f(g(h(x))), where h(1)=4, g(4)=5, h'(1)=3 , g'(4)=5 and f'(5)=7. find r'(1).
*Thursday, March 20, 2014 at 2:04pm*

**Calculus Help Please!!! **

Find an equation of the tangent line to the curve at the given point. ((pi/6),(2 square root of (3)/3)) y = sec (x)
*Thursday, March 20, 2014 at 1:54pm*

**Calculus :(**

Differentiate with respect to (t). y = d cos(t) + (t^2)sin(t)
*Thursday, March 20, 2014 at 1:52pm*

**calculus**

Evaluate the improper integral or state that it diverges: integral from 6 to infinity (1/t^2-5t)dt. I need help on solving this and what does it mean by converges and diverges?
*Thursday, March 20, 2014 at 2:10am*

**Calculus Help**

use logarithmic diff. to find the derivative of the function. Show steps please! so I can see how it is done. Thank you so much! y=(e^(-x)cos^(2)(x))/(x^(2)+x+1)
*Tuesday, March 18, 2014 at 10:47pm*

**AP Calculus**

Approximating the integral from 0 to 6 of (e^x dx) by 3 circumscribed rectangles of equal width on the x-axis yields ____. a) 2e^2 + 4e^4 + 6e^6 b) 2(e^2 + e^4 + e^6) c) 2(e + e^3 + e^5) d) e + 3e^3 + 5e^5 e) e^2 + 3e^4 + 5e^6
*Monday, March 17, 2014 at 4:40pm*

**Calculus Help**

Use logarithmic differentiation to find the derivative of the function. y = (tan x)^(7/x)
*Sunday, March 16, 2014 at 7:43pm*

**Calculus**

Solve the initial-value problem. y'' - 2y' + y = 0 , y(2) = 0 , y'(2) = 1
*Sunday, March 16, 2014 at 6:40pm*

**Calculus**

Solve the boundary-value problem. y'' + 5y' - 6y = 0 , y(0) = 0 , y(2) = 1
*Sunday, March 16, 2014 at 6:39pm*

**AP Calculus**

The average area of all squares with sides between a inches and b inches (b>a) is ____ in^2.
*Sunday, March 16, 2014 at 6:14pm*

**AP Calculus**

The base of a solid is bounded by y =|x|+a, 0<a<3, and the line y=3. find in cu. units in terms of a, the volume of the solid if every cross section perpendicular to the y-axis is an equilateral triangle.
*Sunday, March 16, 2014 at 6:13pm*

**Calculus Help**

Use logarithmic differentiation to find the derivative of the function. show steps please! y=(e^-xcos^2(x))/(x^2+x+1)
*Sunday, March 16, 2014 at 4:12pm*

**Calculus Help Please!!! **

Use implicit diff. to find dy/dx of each of the following. In the following x,y and (a) are all variables. Show step by step please! Thank you! 1) y^2 = x^2+a^2 2) y^2+ay = x^2+ax+a^2
*Sunday, March 16, 2014 at 3:54pm*

**calculus**

using the method of shells, set up, but dont evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1
*Sunday, March 16, 2014 at 2:30pm*

**Pre-Calculus**

Express the complex number in polar form. 5-12i
*Saturday, March 15, 2014 at 6:51pm*

**Pre-Calculus**

Find this quotient. Express the result in rectangular form. 9(cos3π/2 + isin3π/2) ÷ 3(cosπ/4 + isinπ/4)
*Saturday, March 15, 2014 at 6:49pm*

**Pre-Calculus**

Express the number in rectangular form. 3(cosπ/3+isinπ/3)
*Saturday, March 15, 2014 at 6:40pm*

**Pre Calculus**

Find each product or quotient. Express the result in rectangular form. 2(cosπ/6+isinπ/6) X 4(cos2π/3 +i2π/3)
*Saturday, March 15, 2014 at 6:39pm*

**Calculus**

Find equations of both the tangent lines to the ellipse x^2 + 4y^2 = 36 that pass through the point (12, 3). smaller slope y= larger slope y=
*Friday, March 14, 2014 at 5:24pm*

**Calculus Help and Check **

Find dy/dx by implicit differentiation. x^5(x + y) = y^2(9x − y) this is what i've got so far but I dont think it is the right answer. y'= 9y^2-6x^5-5x^3y/x^5+9y^2-18xy
*Friday, March 14, 2014 at 3:53pm*

**Calculus**

Find four other forms of the point (4, 105°) Two of the four must include a negative r value.
*Friday, March 14, 2014 at 12:02am*

**Calculus Help **

In the following x,y and (a) are all variables. Show steps please! Thank you! 1) y^2 = x^2+a^2 2) y^2+ay = x^2+ax+a^2
*Thursday, March 13, 2014 at 8:19pm*

**CALCULUS ECONOMICS**

Consider the problem of a competitive firm which has fixed costs of $1000, semi-fixed-costs of $1000, and variable costs given by q^2. QUESTION: What is the maximum market price at which the firm decides to supply zero?
*Thursday, March 13, 2014 at 4:10pm*

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