Wednesday

December 7, 2016
**calculus**

A wooden artifact recovered from a tomb contains 29% of the carbon-14 that is present in living trees. The half life of carbon-14 is 5730 years. How long ago was the artifact made?

*Friday, December 18, 2015 by jeremy*

**Pre-calculus/ trig**

Given the vectors a= (-1,9) and b= (4,2) explain the difference between a-b and b-a. Thank you for your help! :)

*Thursday, December 17, 2015 by Rachel*

**Pre-calculus**

A square of size x inches is cut out of each corner of an 8in by 12in piece of cardboard, and the sides are folded up to form an open-topped box. Determine the dimensions of the cut-out squares that will produce the box of maximum volume.

*Wednesday, December 16, 2015 by jul*

**Pre-calculus: Logarithms**

ln56/ln7=ln8. Is this true or is this false? How can I find this out?

*Wednesday, December 16, 2015 by jenny*

**calculus**

A person can row at a constant speed of 6 miles per hour. If the rower wants to row directly across a river with a current of 2 mph, at what angle should they row? How fast does the boat actually cross the river?

*Tuesday, December 15, 2015 by teddy *

**Calculus **

Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the exposed surface area of the water changing when the radius is 2 feet?

*Monday, December 14, 2015 by Lacy*

**Calculus**

Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the radius of the water in the tank increasing when the radius is 2 feet?

*Monday, December 14, 2015 by Lacy*

**Calculus**

The curve y = 11x - 24 - x^2 cuts the x-axis at points A and B, and PN is the greatest positive value of the y coordinate. Show that 2 PN • AB equals three times the area bounded by that portion of the curve which lies in the first quadrant. Kinda confused on how to do this

*Monday, December 14, 2015 by Pip Paladins*

**Calculus, Physics**

The curve y = 11x - 24 - x^2 cuts the x-axis at points A and B, and PN is the greatest positive value of the y coordinate. Show that 2 PN • AB equals three times the area bounded by that portion of the curve which lies in the first quadrant. Kinda confused on how to do this

*Monday, December 14, 2015 by Pip Paladins*

**calculus**

Let Y = 7x sin-1(2x)+^3 square root 1+4x2. Find Y'. I don't know how to do the square root part. I have done y'= (7x)' (Sin^-1(2x)) + (7x)(sin^-1)'+...... y'= 7 sin^-1 + (7x)sq(2x)'/square root (1-(2x))^2 + .....

*Sunday, December 13, 2015 by Jason*

**Calculus**

A spherical balloon is being inflated so that, at the time when the radius is 5m, the radius is increasing at the rate of 0.15m/s. (A) Find the rate of increase of the volume at this time. (B) If the rate of increase of volume thereafter remains constant, find the rate at ...

*Sunday, December 13, 2015 by John*

**Calculus**

Consider the curve below. x = (cos(t))^2 y = cos(t) 0 ≤ t ≤ 6π (a) Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. (b) What is the length of the curve? I have no idea on how to evaluate this integral. I ...

*Saturday, December 12, 2015 by Jed*

**calculus**

Anti-Derivatives 2x^6-x^3/x^2

*Friday, December 11, 2015 by Jason*

**Calulus**

Fundamental Theorem of Calculus 1. (4e^x-3)dx plus the number in x (6,1)

*Friday, December 11, 2015 by Daniel*

**Calculus**

As an ice cube melts its surface area in decreasing at a rate of 6 cm^2 / sec. Find the rate at which the length of each side is decreasing at the moment when each side has length 2 cm.

*Friday, December 11, 2015 by Daniel*

**Pre-calculus**

A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 34.53 units of niacin and 25,430 units of retinol. She uses two types of commercial pellet foods. Food A ...

*Thursday, December 10, 2015 by Gift*

**Calculus**

A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The concentration C(x), in parts per million,is approximately given by the function: C(x)= 0.5/x^2, where x is the distance away from the plant in miles. The instantaneous rate of change ...

*Wednesday, December 9, 2015 by Anonymous*

**Calculus**

The area of a square with a side s is A(s)=s^2.What is the rate of the change of the area of a square in respect to its side?

*Wednesday, December 9, 2015 by Anonymous*

**Calculus**

Determine the values of x for which the function is continuous: f(x)= 10x^2-10

*Wednesday, December 9, 2015 by Anonymous*

**calculus**

find the area of the region: y=4 y=2sqrt(x) y=3-x

*Wednesday, December 9, 2015 by georges*

**Calculus**

A parabolic arch bridge has a 60ft base and a height of 24ft. Find the height of the arch at a distance of 5, 10, and 20 ft from the center

*Tuesday, December 8, 2015 by Net*

**Calculus**

I am standing on the roof of a building with a pea shooter, and I shoot a pea up into the air from a height of 80 feet. The pea reaches its maximum height 2 seconds after I shoot, then falls to the ground. Give the position of the pea as a function of time

*Tuesday, December 8, 2015 by Jose*

**Calculus AB**

If f(x) is continuous on the interval [4, 7], how many of the following statements are true? A. f(x) has a maximum value on [4, 7]. B. f(x) has a minimum value on [4, 7]. C. f(7) > f(4) D. lim f(x) = f(6) ᵡ¨6

*Tuesday, December 8, 2015 by Billy*

**Calculus**

Find the sum of the squared errors for the linear model f(x) and the quadratic model g(x) using the given points. f(x) = 2.0x − 3, g(x) = 0.09x^2 + 1.6x − 3 (−1, −4), (1, −2), (2, 0), (4, 6), (6, 9) linear model-? quadratic model- ?

*Tuesday, December 8, 2015 by Calculus Help *

**Calculus**

Find the sum of the squared errors for the linear model f(x) and the quadratic model g(x) using the given points. f(x) = −0.7x+3, g(x)=0.06x^2−0.6x+2 (−3, 5), (−1, 3), (1, 2), (3, 1) linear model-? quadratic model -?

*Tuesday, December 8, 2015 by Calculus Help *

**Mulitvariable Calculus**

How to proof tangential and normal components of a vector Thank you

*Tuesday, December 8, 2015 by cal*

**Calculus**

A spotlight on the ground is shining on a wall 24\text{m} away. If a woman 2\text{m} tall walks from the spotlight toward the building at a speed of 0.6\text{m/s}, how fast is the length of her shadow on the building decreasing when she is 2\text{m} from the building?

*Tuesday, December 8, 2015 by Spencer*

**Calculus **

A home owner wants to fence in his yard of 600 sq. feet. Three sides are to be constructed with chain link fence at a cost of 3.25 per linear feet. The fourth side is to be constructed with a wood stockade fence at a cost of $5.45 per linear foot. A) what is a complete model ...

*Monday, December 7, 2015 by Jen*

**calculus**

Find the critical numbers x1 and x2 of y=(9x^2+3)/4x.

*Monday, December 7, 2015 by beth*

**calculus**

Use implicit differentiation to find the slope of the tangent line to the graph of 18*x^(1/2)+5y^(1/2)+14 at(81/324,1)

*Monday, December 7, 2015 by beth*

**calculus**

Find the derivative of y=(7x^(1/3))/(x^2+9)

*Monday, December 7, 2015 by beth*

**calculus**

Find the derivative of 4sinx(6cosx+9sinx) at x=¦Ð/6.

*Monday, December 7, 2015 by beth*

**Calculus**

Compute the surface area of revolution about the x-axis over the interval. y = x^2, [0, 4] Is it (pi/12)(65^2 - 65)^(3/2)?

*Monday, December 7, 2015 by Sanaya*

**Calculus**

Find the derivative of f(x)=(2x)^(1/2)ln(15x)

*Monday, December 7, 2015 by Erik*

**Calculus**

Find the derivative of y=(2*x^(3/2))/(x^2+5)

*Monday, December 7, 2015 by Erik*

**Calculus**

A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15 ft/sec. At what rate is the player's distance from home base increasing when he is half way from first to second base?

*Monday, December 7, 2015 by Erik*

**calculus**

Sam has 1200 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Express the area of the field as a function of its dimension. Find the dimensions of the field that has the largest area.

*Monday, December 7, 2015 by hartati*

**Calculus**

How do I integrate sqrt of (1+e^(2x)) if doing u-sub.. u=sqrt of (1+e^(2x)) and ten using partial fraction...?

*Sunday, December 6, 2015 by Sanaya*

**Calculus**

Set up a double integral for calculating the flux of the vector field F⃗ (r⃗ )=r⃗ , where r⃗ =⟨x,y,z⟩, through the part of the upward oriented surface z=9(x^2+y^2) that lies above the disk x^2+y^2≤25.

*Sunday, December 6, 2015 by A*

**Calculus**

Find the surface area of the part of the sphere x2+y2+z2=81 that lies above the cone z=√(x2+y2)

*Sunday, December 6, 2015 by A*

**calculus**

what point of f(x)= e^(1-x^2) is concave down? I think it is 1/2 but I'm not sure

*Sunday, December 6, 2015 by tedd*

**calculus**

A satellite is free falling from a distance "d" of the surface of the moon with radius "r", with zero initial velocity. At what rate does the area of the portion of the moon visible to the satellite decrease at a time "t" after the free fall ...

*Saturday, December 5, 2015 by Steve*

**Calculus**

The approximate rate of change in the number of subscribers to wireless service is given by f’(t) = 1.498t + 1.626, where t represents the number of years since 1990. In 1992 (t = 2) there were approximately 8.893 million subscribers. Find the function that gives the ...

*Saturday, December 5, 2015 by Corey*

**Calculus**

Given dy/dt=4y and y(2)=400. Find y(7).

*Friday, December 4, 2015 by Erik*

**calculus**

The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.3. The initial population is 40. (1) What is the population after 30 days? (2) How long does it take for the ...

*Friday, December 4, 2015 by E*

**Calculus**

The rate of change of the population of a small town is dP/dt=kP Where P is the population, t is the time in years and k is the growth rate. If P=20000 when t=3 and P=30000 when t=5, what is the population when t=10? Round your answer to the nearest integer.

*Friday, December 4, 2015 by E*

**Pre calculus**

Use the given conditions to write an equation for the line in point-slope form. Passing through (-5, -7) and (-8, -6)

*Thursday, December 3, 2015 by maddie*

**Pre calculus**

Find the domain of the function. f(x) = -2x + 4 A. (-∞, 0) u(0, ∞) B. (-∞, ∞) C. [-4, ∞) D. (0, ∞)

*Thursday, December 3, 2015 by lexi*

**Calculus**

At time t (in days), the size S of a population of butterflies is given by the formula s= 600/1+49(0.6)^t. When does the maximum growth rate occur?

*Thursday, December 3, 2015 by Leslie*

**Pre calculus**

Find the domain of the function. f(x) = -2x + 4 A. (-∞, 0) u(0, ∞) B. (-∞, ∞) C. [-4, ∞) D. (0, ∞)

*Thursday, December 3, 2015 by lexi*

**Pre calculus**

Find the domain of the function. f(x) = sqrt 6-x A. (-∞, 6) (6, ∞) B. (-∞, sqrt6 ) (sqrt 6 , ∞) C. (-∞, sqrt6] D. (-∞, 6]

*Thursday, December 3, 2015 by Alex*

**Pre-Calculus**

Draw the picture and find the area of the parcel of land. Circle your to partial areas and your total area. You start herman a corn and walk 300 yards due north. Then, you turn N 63 degrees E and walk 260 yards. Then, you turn S 55 degrees E and walk 240 yards. Then, you walk ...

*Thursday, December 3, 2015 by Ash*

**calculus**

A satellite is free falling from a distance (d) of the surface of the moon with radius (R), with zero initial velocity. At what rate does the area of the portion of the moon visible to the satellite decrease at a time (t) after the free fall starts? When is this rate maximum? ...

*Wednesday, December 2, 2015 by Saif*

**calculus**

Use the Trapezoidal Rule to approximate ¡Ò8 4 ln(x2+5) dx using n=3. Round your answer to the fourth decimal place.

*Wednesday, December 2, 2015 by beth*

**Pre-calculus**

You start from an acorn and walk 300 yards do north. Then, you turn N 63° E and walk 260 yards. Then, you turn S 55° E and walk 240 yards. Then you walk back to the little acorn.

*Tuesday, December 1, 2015 by Dee*

**Calculus 1**

The acceleration function (in m/s^2) and the initial velocity are given for a particle moving along a line. a(t)=t+4, v(0)=4, 0 ≤ t ≤ 11 (a) Find the velocity at time t. (b) Find the distance traveled during the give time interval.

*Tuesday, December 1, 2015 by TayB*

**Calculus III**

The surface x^2−y^2=36 can be described using spherical coordinates in the form ρ=g(θ,ϕ)=

*Monday, November 30, 2015 by Steven*

**calculus**

An open box is to be made out of a 10-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

*Monday, November 30, 2015 by javy*

**Pre-Calculus**

f(x) = cos(x) on the interval [−2π, 2π] (a) Find the x-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.) (b) Find the y-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.) (c) Find the ...

*Sunday, November 29, 2015 by Sam*

**Calculus- Damon, Steve, Reiny**

I forgot to mention that I am trying to find sigma squared.. given that the mean is r and p(x)= (1/r)(e^(-x/r)) on the interval [0,infinity), where r>0.. note: sigma squared= integral sign (-inf, inf) (x-M)^2 p(x) dx i got (r^2 - 2r)^(1/2) for sigma, but my answer is wrong...

*Saturday, November 28, 2015 by Christina*

**Calculus**

I tried to integrate this: intergral sign with an interval from -inifinity to + infinity function: (x-r)^2 (1/r) (e^(-x/r)) with respect to dx..... I know that Steve set up the u-substitution but I seem to never arrive at an answer... It seems like I keep integrating and ...

*Saturday, November 28, 2015 by Christina*

**Calculus**

How do you integrate (x-r)^2 (1/r) (e^(-x/r)) from the interval negative infinity to positive infinity?

*Friday, November 27, 2015 by Sanaya*

**Calculus**

How do you integrate (x-r)^2 (1/r) (e^(-x/r)) from the interval negative infinity to positive infinity?

*Friday, November 27, 2015 by Christina*

**Math calculus **

The top and bottom margins of a poster are 8 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area?

*Friday, November 27, 2015 by MArıam *

**calculus**

integrate (e^t + e^-t)²

*Friday, November 27, 2015 by ligas*

**Integral Calculus**

Integrate (tan^-1 X)/(1+x²) dx please help, I don't know how to start this one

*Friday, November 27, 2015 by ligas*

**Integral Calculus**

Integrate (tan^-1 X)/(1+x²) dx please help, I don't know how to start this one

*Friday, November 27, 2015 by ligas*

**calculus**

integrate (e^t + e^-t)²

*Friday, November 27, 2015 by ligas*

**Pre Calculus HELP!?**

The length of a day in Philadelphia, Pennsylvania, is given by the sinusoidal function, f(t), which represents the number of hours of daylight t days into the year: f(t)= 10+2.8sin(2pi/365)*(t-1.35). How many hours of daylight are there on the 100th day of the year? Round the ...

*Thursday, November 26, 2015 by Ellie*

**Pre-Calculus HELP!!**

The length of a day in Philadelphia, Pennsylvania, is given by the sinusoidal function, f(t), which represents the number of hours of daylight t days into the year: f(x)=11+2.2sin(2pi/365)t-1.25).How many hours of daylight are there on the twelfth day of the year? Round the ...

*Thursday, November 26, 2015 by Ellie*

**calculus**

integrate (e^t + e^-t)²

*Wednesday, November 25, 2015 by ligas*

**Pre-Calculus HELP!**

Explain how the transformations of the functions f(x)=15sin(x) and f(x)=sin(x)+15 differ. I see that f(x)=sin(x)+15 experiences a vertical shift, but I am not sure about the transformation that f(x)=15sin(x) experiences. Thank you for your help!

*Wednesday, November 25, 2015 by Ellie*

**Calculus 1**

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = x^−3, 2 ≤ x ≤ 5

*Wednesday, November 25, 2015 by TayB*

**Calculus 1**

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = cube root(x) , 0 ≤ x ≤ 27

*Wednesday, November 25, 2015 by TayB*

**Calculus III**

Evaluate ∭W f(x,y,z)dV for the function f and region W specified: f(x,y,z) = 18(x+y) W: y≤ z≤x ; 0≤y≤x ; 0≤x≤1 ∭W (18(x+y))dV =

*Tuesday, November 24, 2015 by Steven*

**Calculus**

If f is an exponential function of the form f(x)=C times a^x with growth factor 5 and f(5)=14. What is f(6)? I know f(6) is 70 but how do you set up the equation to get 70?

*Tuesday, November 24, 2015 by Dale*

**calculus**

what are the inflection points of 5x^2-45/x^2-25

*Monday, November 23, 2015 by marissa*

**Calculus**

Integrate e^(-t/r) WITH RESPECT TO dt?

*Monday, November 23, 2015 by Sanaya*

**Calculus**

The amount remaining of a radioactive substance after t hours is given by A(t) = 100ekt. After 12 hours, the initial amount has decreased by 4%. How much remains after 48 hours? What is the half-life of the substance?

*Monday, November 23, 2015 by Bill*

**Pre-calculus**

Initially 600 milligrams of a radioactive substance was present. After 7 hours the mass had decreased by 3%. Construct an exponential model A(t) = A0ekt for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24 hours.

*Monday, November 23, 2015 by Kim*

**Calculus**

find the maximum volume of a cylinder whose height and radius do not exceed a combined total of 12cm

*Monday, November 23, 2015 by Emma*

**Calculus**

Let f(x)=5x^(9/5)−45x^(4/5). Find the largest open interval(s) where f(x) increases.

*Monday, November 23, 2015 by Kevin*

**Calculus**

Calculate μ and σ, where σ is the standard deviation, defined by the following. σ^2 = integral between (−∞,∞) (x-μ)^2 p(x) dx The smaller the value of σ the more tightly clustered are the values of the random variable X about the...

*Sunday, November 22, 2015 by Christina*

**Calculus**

How do you integrate e^(-t/r) dt?

*Sunday, November 22, 2015 by Sanaya*

**Calculus**

Calculate μ and σ, where σ is the standard deviation, defined by the following. σ^2 = integral between (−∞,∞) (x-μ)^2 p(x) dx The smaller the value of σ the more tightly clustered are the values of the random variable X about the...

*Sunday, November 22, 2015 by Anonymous*

**Calculus**

How do you integrate e^(-t/r)?

*Sunday, November 22, 2015 by Sanaya*

**Calculus**

Integrate x/(6x-5) dx The answer is 1/6 x + 5/36 ln abs (36x-30) + C... But I don't understand why it is 5/36 times ln.. I thought that when you factored out the 5 you would get 5 times ln abs (36x-30)..

*Saturday, November 21, 2015 by Sanaya*

**Calculus**

A window is designed to be the area between a parabolic section and a straight base. The height is 0.640 m and the base is 1.60 m. What is the area of the window?

*Saturday, November 21, 2015 by Anonymous*

**Calculus**

Calculate integral [0, infinity) xe^(-x) dx

*Saturday, November 21, 2015 by Sanaya*

**Calculus**

Find the solution t the differential equation dz/dt = 2te^z that passes through the origin. My answer is -In (1-t^2), but my answer is populating as incorrect. Can someone help please?

*Friday, November 20, 2015 by Latoya*

**Calculus**

Solve the initial value problem 2y" + 5y' - 3y = 0 y(0) =7, y'(0) = 7 Can someone please help. The answer I came up with is 35 exp(-x) - 28 exp(-3x/2), but my answer is wrong.

*Friday, November 20, 2015 by Latoya*

**Calculus**

For the vector field G⃗ =(yexy+3cos(3x+y))i⃗ +(xexy+cos(3x+y))j⃗ , find the line integral of G⃗ along the curve C from the origin along the x-axis to the point (3,0) and then counterclockwise around the circumference of the circle x2+y2=9 to the point (...

*Friday, November 20, 2015 by A*

**Calculus**

Integral sign 8x/(x-1) dx Is it 8x+8ln abs (x-1)+C ?

*Thursday, November 19, 2015 by Sanaya*

**Calculus**

Evaluate the integral. Problem#1 Integral sign 4dx/[(x+3)(x^2 +3x) Does it matter where A, B, and C is placed over. Is there a particular order? Is it ..... (A/x)+(B/(x+3))+(c/(x+3)^2=4 Or ... (A/x+3)+(B/x)+(C/(x+3)^2)=4 I am confused because I get different answers each time ...

*Thursday, November 19, 2015 by Sanaya*

**Calculus**

Evaluate using long division. The integral of x/6x-5 dx How do I divide this?

*Thursday, November 19, 2015 by Sanaya*

**Calculus 1 **

Find each limit: (a) lim x->1 (ln(x)+2x-2)/(x^2-1) (b) lim x->infinity (x^2)/(e^x)

*Thursday, November 19, 2015 by TayB*

**Calculus 1 **

Find the local maximum and minimum for the function f(x)=2x^3-3x^2-120x+10

*Thursday, November 19, 2015 by TayB*

**Calculus III**

Use symmetry to evaluate the double integral ∫∫R(10+x^2⋅y^5) dA, R=[0, 6]×[−4, 4]. (Give your answer as an exact number.) ∫∫R(10+x^2⋅y^5) dA=

*Wednesday, November 18, 2015 by Stevo*

**Pre Calculus 1**

thirty percent of a radioactive substance decays in four years. assuming the decay is exponential, find the half life of the substance. the beginning of 1975 the population of a country was 40 million and growing at a rate of 3% per year. Assume that the growth is exponential...

*Wednesday, November 18, 2015 by Yasmine*

**Business Calculus**

The skeleton has lost 56 percent of their carbon-14. The constant proportionality is approximately k=0.000124. Estimate the age of the bones.

*Wednesday, November 18, 2015 by Amy*