Thursday

November 26, 2015
**Calculus**

f(x)=x^n , where n is a positive integer greater or equal to 2. The graph of f(x) will have an inflection point when n is A. Even B. Odd C. Divisible by 3 D. For all values E. For no values
*Saturday, March 14, 2015 by Anonymous*

**Calculus**

If y=3/(sinx+cosx) , find dy/dx A. 3sinx-3cosx B. 3/(sinx+cosx)^2 C. -3/(sinx+cosx)^2 D. 3(cosx-sinx)/(sinx+cosx)^2 E. 3(sinx-cosx)/(1+2sinxcosx)
*Saturday, March 14, 2015 by Anonymous*

**Pre-Calculus**

How many parameters in a quadratic function in a vertex form change when you change the location of the vertex? ( P and Q change? The value of the coefficient( a ) may also change?)
*Saturday, March 14, 2015 by Lucina*

**Calculus check revised. **

y=-1/sqrt(x^2+1) , then dy/dx= A. x/(x^2+1)^1/2 B. x/(x^2+1)^3/2 C. -x/(x^2+1)^1/2 D. -x/(x^2+1)^3/2 E. x/(x^2+1) I got B.
*Saturday, March 14, 2015 by Sarah*

**Calculus check**

y=-1/sqrt(x^2+1) , then dy/dx= A. x/(x^2+1)^1/2 B. x/(x^2+1)^1/2 C. -x/(x^2+1)^1/2 D. -x/(x^2+1)^3/2 E. x/(x^2+1) I got B.
*Saturday, March 14, 2015 by Sarah*

**Calculus check**

If f(x)=sin^2(3-x) then f'(0)= A. -2cos3 B. -2sin3cos3 C. 6cos3 D. 2sin3cos3 E. 6sin3cos3 I got B
*Saturday, March 14, 2015 by Sarah*

**Calculus**

The limit as x approaches 4 ((-3x+1)/(x-4)^2) is A. -11 B. -13 C. Infinity D. Negative infinity E. DNE
*Saturday, March 14, 2015 by Anonymous*

**Calculus**

Find an equation of a line tangent to y = 2sin x whose slope is a maximum value in the interval (0, 2π] I believe the equation is y=2x-4pi. How is the b-value -4pi?
*Saturday, March 14, 2015 by Sara*

**Calculus**

How would I find the instantaneous rate of change using this formula y=3.9657(0.9982^x) and given a table of values?
*Friday, March 13, 2015 by Sara*

**Pre-Calculus**

I posted this question about an hour ago, got a response but still confused. Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers ...
*Friday, March 13, 2015 by Alyssa*

**Pre-Calculus **

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is smaller than ∠B2.) a = 34, c = 43, ∠A = 39&...
*Friday, March 13, 2015 by Alyssa*

**Calculus 1**

Find the derivative of the function. F(t) = e^(4t sin 2t)
*Friday, March 13, 2015 by TayB*

**Calculus 1**

Use logarithmic differentiation to find the derivative of the following equation. y = (2x+1)^5(x^4−3)^6
*Friday, March 13, 2015 by TayB*

**Calculus 1**

Use logarithmic differentiation to find the derivative of the function. y =sqrt(x)^3x
*Thursday, March 12, 2015 by TayB*

**Calculus 1**

Use logarithmic differentiation to find the derivative of the function. y = x^(8cosx)
*Thursday, March 12, 2015 by TayB*

**calculus**

A ladder 13 feet long is leaning against the side of a building. If the foot of the ladder is pulled away from the building at a constant rate of 8 inches per second, how fast is the area of the triangle formed by the ladder, the building, and the ground changing in feet ...
*Thursday, March 12, 2015 by beth*

**Pre-Calculus**

One walker was sponsored $100 plus $5 for the first kilometre, $10 for the second kilometre, $15 for the third kilometre, and so on. How far would this walker need to walk to earn $150? (I know it is 4 km, but I can't figure out how to write the general term.)
*Wednesday, March 11, 2015 by Lucina*

**Calculus 1**

If f(x)=3 sin x+ln(5x), find f '(x).
*Wednesday, March 11, 2015 by TayB*

**Pre-Calculus(Trignometry)**

There are 3 airports, A , E and G. G is 200km from A.E is 160 km from A From G the bearing of A is 052 degrees. From A the bearing of E is 216 degrees. What's the distance between A and G? 360- 216 = 144 144-52 = 128 144-128 = 16 a^2 = b^2+c^2-(2*b*c)*cos(A) a^2 = 160^2 + ...
*Tuesday, March 10, 2015 by Lucina*

**Calculus**

An observer is 36m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 26m horizontally from the observer. The angle of elevation of the elevator is the angle of the observer's line of sight makes with the horizontal (it may be...
*Tuesday, March 10, 2015 by Zee*

**Pre-Calculus**

Determine a quadratic function in vertex form given each set of characteristics. * minimum value of -24 and x-intercepts at -21 and -5 I have: (-21,0) and (-5,0) How would I find the x-coordinate of the vertex? (Thank you)
*Tuesday, March 10, 2015 by Lucina*

**Pre-Calculus**

Water is spraying from a nozzle in a fountain forming a parabolic path. The nozzle is 10 cm above the service of the water. The water achieves a max height of 100 cm above the waters surface and lands in the pool. The water spray is again 10 cm above the surface of the water ...
*Tuesday, March 10, 2015 by Lucina*

**Calculus**

An observer is 23m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 15m horizontally from the observer. The angle of elevation of the elevator is the angle of the observer's line of sight makes with the horizontal (it may be...
*Tuesday, March 10, 2015 by Zee*

**calculus**

If 3x^2 + y^2 = 7 then evaluate the second derivative of y with respect to x when x = 1 and y = 2. Round your answer to 2 decimal places.
*Tuesday, March 10, 2015 by Jordan*

**Calculus**

For which pair of functions f(x) and g(x) below will the lim f(x)/g(x)equal 0 x-infinity f(x) e^x; g(x) = x^3 f(x) x^5; g(x) = e^x f(x) x^3; g(x) = ln(x) f(x) x^negative 2; g(x) = e^negative x
*Tuesday, March 10, 2015 by Gary*

**Calculus**

A curve passes through the point (7,6) and has the property that the slope of the curve at every point P is 4 times the y-coordinate of P. What is the equation of the curve? Simplify the equation as much as possible.
*Monday, March 9, 2015 by Matt*

**Calculus**

For the question "Determine the equation of the tangent to the curve y = xtanx at the point with x-coordinate π." how is the answer -πx + y + π2 = 0?
*Monday, March 9, 2015 by Sara*

**Calculus 2**

find an equation to the curve at the point corresponding to the given value of the parameter. x = tcost y = tsint when t = π i know I am supposed to find dy and dx which is: dy = (product form) t*-sint + 1*cost simplifying = -tsint+cost dx = tcost+sint now, to find the I ...
*Monday, March 9, 2015 by Hanky*

**Calculus 1**

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+y^2=(2x^2+4y^2−x)^2 (0, 0.25) (cardioid)
*Monday, March 9, 2015 by TayB*

**Calculus (Integral)**

How would you take the integral of the following two functions: 1) ∫ 25 / e^x(25 + e^2x) dx 2) ∫ 7x / x^3 + 27 dx
*Monday, March 9, 2015 by Misa*

**Pre-Calculus**

What are the vertices and co vertices of the ellipse x^2/4 + y^2/25=1 I actually have no idea how to even start to solve this problem, so any help will be appreciated. Steps on how this problem is solved are also appreciated.
*Friday, March 6, 2015 by Julissa*

**Calculus**

Find the general solution for the differential equation. Leave your solution in implicit form. dx/dt=(2-x)sqrt(1-x)
*Thursday, March 5, 2015 by Anonymous*

**Calculus**

Find the general solution of the DE. Write your solution explicitly. y'=(y^(2)+y^(2)cosx)^2
*Thursday, March 5, 2015 by Cat*

**Calculus, HELP!!**

1) A rectangular page is to contain 24 square inches of print. The page has to have a 6-inch margin on top and at the bottom and a 1-inch margin on each side. Find the dimensions of the page that minimize the amount of paper used. 2) A cable runs along a wall from C to P at a ...
*Thursday, March 5, 2015 by Henry*

**Calculus**

1) A rectangular page is to contain 16 square inches of print. The page has to have a 2-inch margin on top and at the bottom and a 2-inch margin on each side. Find the dimensions of the page that minimize the amount of paper used. 2) A rectangular garden of area 480 square ...
*Thursday, March 5, 2015 by Gary*

**Calculus (Partial Derivatives)**

A car dealer determines that if gasoline-electric hybrid automobiles are sold for x dollars apiece and the price of gasoline is y cents per gallon, then approximately H hybrid cars will be sold each year, where H(x,y)=6000−13x^(1/2)+2(0.1y+20)^(3/2). She estimates...
*Wednesday, March 4, 2015 by Bill*

**Math (advice)**

So in my calculus class we learned about implicit differentiation today. The professor would stop and ask if we had any questions, which was nice. I didn't ask any questions though, because I don't really like to ask questions during class. I didn't really get ...
*Wednesday, March 4, 2015 by TayB*

**calculus**

differentiate y = 2^3x^2 read as two to the 3x squared power
*Wednesday, March 4, 2015 by paula*

**Calculus 1**

Find an equation of the tangent line to the curve at the given point. y =(1+2x)^12, (0,1)
*Wednesday, March 4, 2015 by TayB*

**Calculus 1**

The curve y =|x|/(sqrt(5−x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2,2).
*Wednesday, March 4, 2015 by TayB*

**Calculus 1**

Find an equation of the tangent line to the curve y = 6/(1+e^−x)at the point (0,3).
*Wednesday, March 4, 2015 by TayB*

**Calculus Physics**

A glass of orange juice is on the floor of a subway car traveling along a straight path at constant velocity. Everything's fine. The coefficient of static friction between the glass and the floor is 0.32. The subway suddenly accelerates forward. What is the maximum ...
*Wednesday, March 4, 2015 by Mik*

**Pre-calculus (trigonmetry)**

The Bermuda Triangle is an unmarked area in the Atlantic Ocean where there have been reports of unexplained disappearances of boats and planes and problems with radio communications. The triangle is an isosceles triangle with vertices at Miami, Florida, San Juan, Puerto Rico, ...
*Tuesday, March 3, 2015 by Lucina*

**calculus**

Find the arc length of the given function/curve on the given interval. y=ln(x-sqrt(x^(2)-1)); x ϵ [1, sqrt(2)]
*Tuesday, March 3, 2015 by kales*

**calculus**

If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.
*Tuesday, March 3, 2015 by Danijela*

**calculus**

Find the arc length of the given function/curve on the given interval. y=ln(x-sqrt(x^(2)-1)); x ϵ [1, sqrt(2)]
*Tuesday, March 3, 2015 by kales*

**calculus**

Find Indefinite Integral of dx/(x(x^4+1)). I think that Im complicating it too much. I moved the dx out making it 1/(x(x^4+1))dx than 1/(x^5+x)dx. I think i have to use formula indef integral of dx/(x^2+a^2) = 1/a(tan^-1(x/a)) but im stuck i dont know what to do next. I would ...
*Tuesday, March 3, 2015 by anna*

**calculus**

If u=(0,2,3) and v=(1,3,-1) find the projection of u onto v a) 1/3 u b) 3/11 v-> -> c) (1,1,-1) d) (1/3, 1, -1/3)
*Tuesday, March 3, 2015 by muntrey*

**Calculus, HELP!!!!!!!!!**

A cable runs along the wall from C to P at a cost of $6 per meter, and straight from P to M at a cost of $10 per meter. Let x be the distance from C to P. If M is 8 meters from the nearest point A on the wall where P lies, and A is 18 meters from point C, find x such that the ...
*Tuesday, March 3, 2015 by Francois*

**Calculus I**

A spherical balloon is inflated at a rate of 10 cm^3/min. How fast does the radius change when the radius is 20 cm? Need help with set up and work through of problem.
*Monday, March 2, 2015 by Mike*

**Calculus I**

Sand falls from a hopper into a conical pile with radius equal to half its height. The sand is poured at a rate of 3 m^3 each minute. How fast is the radius increasing after 10 minutes? Need help with the set up and work through of the problem.
*Monday, March 2, 2015 by Mike*

**Calculus Physics**

Imagine a spaceship on its way to the moon from the earth. Find the point, as measured from the center of the earth, where the force of gravity due to the earth is balanced exactly by the gravity of the moon. This point lies on a line between the centers of the earth and the ...
*Monday, March 2, 2015 by danny*

**Calculus Physics**

A glass of orange juice is on the floor of a subway car traveling along a straight path at constant velocity. Everything's fine. The coefficient of static friction between the glass and the floor is 0.32. The subway suddenly accelerates forward. What is the maximum ...
*Monday, March 2, 2015 by danny*

**Calculus 2**

Can someone please show and explain step by step how to evaluate this integral? Problem #1)∫ 1/(x^3+x^2+x+1) dx This is what I got so far. I am not sure what to do thereafter after doing partial fraction decomposition (in which I got A = 1/2, B = 1/2, and C = 1/2) 1/(x^2...
*Monday, March 2, 2015 by Miki*

**calculus**

Plot three points with first coordinate equal to (-2.8) and join them
*Sunday, March 1, 2015 by hadasha*

**Calculus**

(1/sqrt(1-(3x/4)^2) * 3/4
*Sunday, March 1, 2015 by Sandra*

**Math Calculus (ALEVEL)**

Find the equation of the tangents to the curve x^2+3x-2y^2=4 at the points where the curve crosses the x- axis
*Sunday, March 1, 2015 by Anonymous*

**Calculus**

Find the area of the bounded region by the graph of x=2y-3 and x=y^2-2y in two ways (i) using x axis as refrence y axis (ii) using y axis as refrence x axis
*Sunday, March 1, 2015 by Akki*

**Calculus**

Find out the partial derivative w.r.t 'x' and 'y' of f (x,y) = log(y) x Now, log(y) x = ln x / ln y Partial Diff w.r.t 'x' = 1/ x ln y so can you find out what will be the partial derivatives w.r.t 'y'
*Sunday, March 1, 2015 by Akki*

**Calculus (Partial Derivatives)**

A car dealer determines that if gasoline-electric hybrid automobiles are sold for x dollars apiece and the price of gasoline is y cents per gallon, then approximately H hybrid cars will be sold each year, where H(x,y)=6000−13x^(1/2)+2(0.1y+20)^(3/2). She ...
*Saturday, February 28, 2015 by Bill*

**Calculus (Partial Derivatives)**

Using x hours of skilled labor and y hours of unskilled labor, a manufacturer can produce Q(x,y)=40xy1/5 units each week. Currently 20 hours of skilled labor and 243 hours of unskilled labor are being used. Suppose the manufacturer reduces the skilled labor level by 2 hours ...
*Saturday, February 28, 2015 by Bill*

**calculus 2 extremely difficult**

The function is r(t)= 400texp(-0.2t^2) and it shows the rate at which people show up in a line outside a theatre to buy tickets. t is the number of hours after 8:00am Assume there is no people at 8:00am and the patrons are served at a constant rate of 200 people after the ...
*Saturday, February 28, 2015 by Integration*

**calculus**

Find the area between the curves y=x^2 & x=2?
*Saturday, February 28, 2015 by Akki*

**calculus**

Find the area of the region bounded by the curves y=x^2 & y=2x???
*Saturday, February 28, 2015 by Akki*

**calculus**

Find relative Minimum and Maximum f'(x) = (9-4x^2)/ (x+1)^1/3
*Saturday, February 28, 2015 by Akki*

**Pre-calculus (Trigonometry)**

The rotating spotlight from the Coast Guard ship can illuminate up to a distance of 250 m. An observer on the shore is 500 m from the ship. HIs line of sight to the ship makes an angle of 20 degrees with the shoreline. What length of shoreline is illuminated by the spotlight...
*Friday, February 27, 2015 by Lucina*

**calculus**

limx¨0 sin ^3 (3x)/ x sin(x ^2)
*Friday, February 27, 2015 by Tuhafeni*

**Calculus**

Find an equation of the normal line to the parabola y=x^2−8x+1 that is parallel to the line x−6y =7.
*Thursday, February 26, 2015 by TayB*

**Calculus II**

A square plate of side 3 m is submerged in water at an incline of 30 degrees with the horizontal. Calculate the fluid force on one side of the plate if the top of the plate lies at a depth of 6 m. (* The only thing i can think to use is the equation: p * g * (S from a to b of...
*Thursday, February 26, 2015 by Alex*

**linear algebra**

Let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ⊕ g by (f ⊕ g)(t) = f(t) + g(t). If f is in V and c is a scalar, we define c f by (c f)(t) = cf(t). Then V is a vector space, which is denoted by C(−&#...
*Thursday, February 26, 2015 by kirsten*

**Calculus**

Differentiate the function. y = e^(x+2)+8 y'=?
*Thursday, February 26, 2015 by TayB*

**Calculus**

Find an equation of the tangent line to the curve at the given point. y =x^4+4x^2−x,(1,4) y=?
*Thursday, February 26, 2015 by TayB*

**Calculus**

Differentiate the function. g(u) = sqrt(2)u+sqrt(7u) g'(u)=?
*Thursday, February 26, 2015 by TayB*

**math**

let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ¨’ g by (f ¨’ g)(t) = f(t) + g(t). If f is in V and c is a scalar, we define c f by (c f)(t) = cf(t). Then V is a vector space, which is denoted by C(&#...
*Thursday, February 26, 2015 by sara*

**calculus**

Salmonella bacteria, found on almost all chicken and eggs,grow rapidly in a nice warm place. If just a few hundredbacteria are left on the cutting board when a chicken is cut up,and they get into a potato salad, the population beginscompounding. suppose the number present in ...
*Thursday, February 26, 2015 by Trang Thuy Doan*

**Calculus**

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y= 2e^(−x), y= 2, x= 6; about y = 4. How exactly do you set up the integral? I know that I am supposed to use the washer method but I can't figure out...
*Thursday, February 26, 2015 by Jed*

**Calculus Chain rule**

y = (6x^2-6)^4/x I would appreciate it more if work was shown. Thank you (I have the answer but want to know how to do it)
*Wednesday, February 25, 2015 by Tom*

**Calculus 2 II**

integral from 0 to 1 of x-4/(x^2-5x+6) I do believe we can integrate with partial fractions, and I should factor it in order to create a linear case 1 thingy so then, it will be: x-4/(x-2)(x-3) After that, I will find the value of a/(x-2) + b/(x-3). But I suck at matrices but ...
*Wednesday, February 25, 2015 by Hanky7*

**calculus**

Describe three situations in which you may want to know the projection of one vector onto another.
*Wednesday, February 25, 2015 by ffej*

**College Math (Calculus)**

Suppose the length of a rectangular box, with lengths x,y,z are changing at the following rates dx/dt = 2 cm /sec dy/dt = -3 cm /sec dz/dt = 1 cm/ sec when x =4, y=3 z=2, Find i) Rate at which volume is changing wrt time, ii) Rate at which the diagonal length of the box is ...
*Wednesday, February 25, 2015 by Wboy*

**Calculus**

1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^-1 x is 1/(|x|*sqrt(x^2 -1)). 4. Find the derivative of 2^(e^(sin x)). ...
*Tuesday, February 24, 2015 by Anonymous*

**Pre-Calculus(Trigonometry)**

An 8-m boom is used to move a bundle of piping from point A to point B. Determine the exact vertical displacement of the of the boom when the operator moves it form 30 degrees to 60 degrees. (Just need work checked) --------------------------------------- I drew two triangles ...
*Tuesday, February 24, 2015 by Lucina *

**Pre-Calculus ( Trigonometry)**

The point P(k, 24) is 25 units from the origin. If P lies on the terminal arm of an angle, theta, in standard position, 0 < theta < 360,determine the measure of theta. Unsure how to go on from here. I'd appreciate if someone can guide me through the first few steps ...
*Tuesday, February 24, 2015 by Lucina*

**Calculus**

Let a thing rod of length a have a density distribution function p(x)+10e^(-.1x), where x is measured in cm and p in grams per centimeter. A) if the mass of the rod is 30 g, what is the value of a? B) For the 30g rod, will the center of mass lie at its midpoint, to the left, ...
*Tuesday, February 24, 2015 by Lauren*

**business math**

A local Barnes and Noble paid a $79.44 net price for each calculus textbook. The publisher offered a 20% trade discount. What was the publisher’s list price?
*Tuesday, February 24, 2015 by melanie*

**[Calculus] U-substitution for Integrals**

Integral of cos(x)*a^sin(x) + C dx = Integral of cos(x)*sin(x)^a + C dx = Let a be a fixed positive number. I'm clueless is to how to solve for a...
*Monday, February 23, 2015 by Ian*

**[Calculus] U-substitution for Integrals**

Integrate from 1 to 5 of (3x-5)^5 dx = Integrate from a to b of f(u) du where (I have solved this part) u = 3x-5 du = 3 a = 0 b = 12 The original value of the integral is 165888 via calculator here's my last question, and it has to be in terms of u: f(u) = ? (Again, in ...
*Monday, February 23, 2015 by Ian*

**Calculus 2**

Consider a trough with triangular ends where the tank is 10 feet long, top is 5 feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water of weight density 62.4 pounds/ft^3, and pump is used to empty the tank until the water ...
*Monday, February 23, 2015 by Lauren*

**Calculus 2**

Let a thing rod of length a have a density distribution function p(x)+10e^(-.1x), where x is measured in cm and p in grams per centimeter. A) if the mass of the rod is 30 g, what is the value of a? B) For the 30g rod, will the center of mass lie at its midpoint, to the left, ...
*Monday, February 23, 2015 by Jordan*

**calculus**

State whether or not the following statements are true. Justify your reasoning.? a. Vector a • (Vector b + Vector c) = Vector a • Vector b + Vector a • Vector c b. Vector a × (Vector b + Vector c) = Vector a × Vector b + Vector a × Vector c c. ...
*Monday, February 23, 2015 by anon*

**Pre-Calculus (Trigonometry)**

An angle in standard position such that sinÈ = 5/13. Determine the possible values of È, to the nearest degree. Answer: I got 23°. (How do I get the second one?)
*Sunday, February 22, 2015 by Lucina*

**calculus**

given the velocity of a particle traveling along the y-axis by v(t)=tsin(t^2)
*Sunday, February 22, 2015 by sam*

**Calculus**

When given the f graph, how do you determine extrema of F(x)? Concavity of F(x)?
*Sunday, February 22, 2015 by Anonymous*

**calculus**

Find the integral of (sin^5 x)(cos^5 x)
*Sunday, February 22, 2015 by tolu*

**calculus**

A woman is attached to a bungee cord from a bridge that is 38m above a river. Her height in meters above the river t seconds after the jump is y(t)=19(1 + e^-1xcos(t)) for t>0. What is her velocity at t=1 and t=4?
*Saturday, February 21, 2015 by Zee*

**Calculus**

Evaluate: the integral from pi/8 to pi/6 csc2xcot2xdx
*Saturday, February 21, 2015 by Anonymous*

**Calculus**

Evaluate by U-substitution: the integral of xcubedroot(x-2) dx
*Saturday, February 21, 2015 by Anonymous*

**Calculus **

A spring has a natural length of 18 cm. If a 22-N force is required to keep it stretched to a length of 24 cm, how much work W is required to stretch it from 18 cm to 21 cm? (Round your answer to two decimal places.) Arg, another question that has me stumped! Would love some ...
*Friday, February 20, 2015 by Mr. Garvoti *

**Calculus **

If 54 J of work are needed to stretch a spring from 15 cm to 21 cm and 90 J are needed to stretch it from 21 cm to 27 cm, what is the natural length of the spring? Any help would be appreciated!
*Friday, February 20, 2015 by Mr. Garvoti *

**AP calculus**

If 54 J of work are needed to stretch a spring from 15 cm to 21 cm and 90 J are needed to stretch it from 21 cm to 27 cm, what is the natural length of the spring?
*Friday, February 20, 2015 by Sam*