Monday

April 27, 2015

April 27, 2015

Number of results: 35,002

**Calculus**

Find the average value of the function on the given interval. f(x)=6x lnx; [1,e^2]
*November 26, 2011 by Jane*

**College Calculus**

Calculate the average over the given interval. f(x)=sin(pi/x)/x^2, [1,2]
*February 9, 2012 by Anonymous*

**math-average**

What is SUM AVERAGE? The professor mentioned that the exam average was 58 [out of 100] and sum average was 144
*March 6, 2008 by see*

**physics**

A 0.150 kg particle moves along an x axis according to x(t) = -13.00 + 2.00t + 3.50t2 - 2.50t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.45 s? I tried solving using s=Vit + (.5)at^2 but I can't find the ...
*September 22, 2009 by jeff*

**Physics**

A 0.150 kg particle moves along an x axis according to x(t) = -13.00 + 2.00t + 3.50t2 - 2.50t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.45 s? I tried solving using s=Vit + (.5)at^2 but I can't find the ...
*September 22, 2009 by richard*

**Physics**

A train accelerates from the rest at the station A at a rate of 0.8 m/s2 for 25 s, the travels at constant velocity for 77.5 s before it comes to rest at the station B after period of retardation lasting 20 s. What is the distance between stations A and B, and the average ...
*April 14, 2015 by Albert*

**Physics**

For no apparent reason, a poodle is running counter-clockwise at a constant speed of 3.00 m/s in a circle with radius 2.9. Let v_1 be the velocity vector at time t_1, and let v_2 be the velocity vector at time t_2. Consider \Delta v = v_2-v_1 and \Delta t = t_2 - t_1. Recall ...
*March 16, 2012 by Krista*

**physics**

A tennis ball with a velocity of +9.6 m/s to the right is thrown perpendicularly at a wall. After striking the wall, the ball rebounds in the opposite direction with a velocity of -5.8 m/s (to the left). If the ball is in contact with the wall for 0.013 s, what is the average ...
*October 6, 2012 by Mackenzie *

**Calculus**

f(t)= -2te^-t^2, [0,5] Find average value. Attempt: I know that the average value is the integration of f(t) from a to b divided by b-a. I used u substitution to get u= -t^2 and du= -2xdx. I changed the limits of integration to [0,25] and I got integral of e^u du. I am not ...
*October 29, 2009 by Alex*

**Physics**

A player strikes a hockey puck giving it a velocity of 47.673 m/s. The puck slides across the ice for 0.175 s after which time its velocity is 46.473 m/s. The acceleration of gravity is 9.8 m/s2 . The mass of the puck is 185 g. If the puck strikes the goalie’s pads and stops ...
*January 9, 2011 by Mike*

**physics**

An electron passes location h0.02m, 0.04m,−0.06mi, and 4 μs later is de- tected at location h0.02 m, 1.84 m,−0.86 mi. Find the average velocity of the elecron: ¯v = <vx, vy, vz> If the electron continues to travel at this av- erage velocity, find where ...
*January 19, 2014 by NADIA*

**Physics**

A dog running in an open field has components of velocity vx = 3.0m/s and vy = -1.1m/s at time t1 = 11.7s . For the time interval from t1 = 11.7s to t2 = 22.2s , the average acceleration of the dog has magnitude 0.55m/s2 and direction 34.5∘ measured from the +x−...
*January 22, 2015 by Kelly*

**Physics**

An archer puts a 0.28 kg arrow to the bow string. An average force of 200 N is exerted to draw the sting back 1.1 m. a) Assuming no frictional loss, what speed does the arrow leave the bow? b) If the arrow is shot straight up, how high does it rise? My thoughts: KE = 1/2mv^2. ...
*November 16, 2007 by Einstein*

**Physics**

During a lawnmower race, a rider starts from rest and accelerates at 1 m/s/s for 10 seconds. The rider then maintains a constant velocity for the remainder of the race, which takes an additional 20 seconds. A) How far was the race? B) What was the lawnmower's average velocity ...
*September 25, 2011 by Karla*

**Physics (acceleration)**

1. Jasmine rode a horse down a path headed north. she started from rest and then accelerated at 0.5 m/s2 for 12 seconds and then travelled at a constant speed for 28 seconds. a.) what was her velocity after 12 seconds? b.) what was jasmines displacement after 10 seconds? c.) ...
*May 14, 2014 by Samaira*

**Calculus study**

A baseball team plays in a stadium that holds 52000 spectators. With the ticket price at $9 the average attendance has been 21000. When the price dropped to $6, the average attendance rose to 26000. a) Find the demand function p(x), where x is the number of the spectators. (...
*March 30, 2015 by Juan *

**Physics**

1)A car is moving with uniform accelaration. It moves along two point A and B and enters with velocity 50 m/s and 80 m/s respectively . Find the velocity when the car is moving in b/w the point A and B. Let t be the time measured from when the velocity is 50 m/s V = 50 + a t ...
*August 24, 2011 by Prathiksha *

**AP Calculus**

A particle is moving around the unit circle (the circle of radius 1 centered at the origin). At the point (.6, .8) the particle has horizontal velocity dx/dt=3. what is its vertical velocity dy/dt at that point? a)-3.875 b0-3.75 c)-2.25 d03.75 e)3.875
*December 15, 2010 by Jeff*

**Physics**

A runner completes an 850m race with two laps of the 425m track in the x-y plane centered at the origin in 1 mins, 50.6s . A runner rounds the track counterclockwise starting at the point (67.6 , 0). Find the runner's average velocity for the race. Find the runner's average ...
*February 8, 2012 by Tig*

**PHYSICS**

A race car's velocity increases from 3.6 m/s to 32.4 m/s over a 5-s time interval. What is its average acceleration?
*March 2, 2010 by Amanda *

**Science**

How can you tell the similarity between displacement and average velocity? I really do not know. Please help, and I will appreciate it. :)
*February 27, 2014 by Brady*

**Physics**

A person is travelling 6 km (E) then 4 km (N) and finally 2 km (W). Calculate the average speed And velocity. Show your work
*March 4, 2014 by Mika *

**Physics **

1)The speedometer on a car’s dashboard measure average speed average velocity instantaneous acceleration instantaneous speed 2)A car moving on a straight road increases its speed from 30 m/s to 50 m/s in a distance of 180 m. If the acceleration is constant, how much time ...
*October 2, 2013 by Maryam*

**Physics**

What is the average velocity of the cart when moving from position x = 0.10 m to position x = 1.10 m? For X=0.10m on the time it took the cart to reach that position it is 0.34s The velocity of the cart at 0.10m is 0.87 For x=1.10m on the time it took the cart to reach that ...
*September 3, 2014 by Christie :)*

**Physics**

A train moving at a constant speed of 61.0 km/h moves east for 35.0 min, then in a direction 50.0° east of due north for 10.0 min, and then west for 49.0 min. What is the average velocity of the train during this run? What is the magnitude of that velocity? What is the ...
*January 27, 2014 by Anonymous*

**General Physics 1**

1) A car moving with an initial velocity of 29.6 m/s decreases to a velocity of 17.9 m/s over a time interval of 4.08 seconds. (a.) What is the average acceleration of the car during this time? (b.) Assuming the acceleration is constant, how far did the car travel during this ...
*June 16, 2014 by Kyle*

**physics**

modern oil tankers weigh more than a half-million tons and have lengths of up to one-fourth mile. Such massive ships require a distance of 5.0 km (about 3.0 mi) and a time of 20 min to come to a stop from a top speed of 30 km/h. What is the magnitude of a such a ship's average...
*March 30, 2014 by Katie*

**Calculus Help**

If a ball is thrown vertically upward from the roof of 64 foot building with a velocity of 32 ft/sec, its height after t seconds is s(t)=64+32t–16t2. What is the maximum height the ball reaches "in ft"? What is the velocity of the ball when it hits the ground (height 0) "in ft...
*February 8, 2014 by Calculus Velocity*

**math**

The velocity(in feet per second) of a bouncing ball was recorded every second. The table shows the velocity for each second. Time(sec):|1|2|3|4|5| Velocity(ft/sec)|-15|-6|2|10|-11| What is the average velocity of the bouncing ball over 5 seconds? What is the highest record ...
*October 28, 2013 by Kai-Cin*

**Calculus**

C(x)= 16sqrt(x) + (x^2)/1000 Find the production level that will minimize the average cost
*October 10, 2008 by Carl*

**calculus**

Find the numbers b such that the average value of f(x) on the interval [0, b] is equal to 9. f(x)=7+10x-3x^2
*February 2, 2009 by matt*

**Calculus**

If b is a positive constant, find the average value of the function f defined by f(x) = x2 + bx + 1 on the interval [-1,1]
*February 1, 2011 by Ishaan*

**pre-calculus--Please help, urgent.**

For the function f(x)= 8/x+7,find the average rate of change of f from 1 to x.
*September 20, 2012 by ladybug*

**calculus**

for the function f(x)=5/x+4, find the average rate of change of f from 1 to x. please show work
*December 13, 2012 by Heather*

**grade 12 calculus and vectors**

Determine the average rate of change form x = 1 to x = 4 for each function. a) y= x b) y=x^2 c) y=x^3 d) y=7
*February 6, 2014 by priyanka*

**Objects IN motion**

Table 2 shows the velocity of an object at different times. Time(s)| Velocity(cm/s east) 0 | 0 5 | 7.8 15 | 24.3 20 | 31.8 35 | 57.3 ___________________________ K they have given me the velocity for 5 s, 15, etc. but I want to know the velocity for the other numbers like 2s ...
*November 30, 2010 by Teya*

**calculus**

The Institute finds that the average student taking Elementary Shorthand will progress at a rate given by dQ/dt=k(80-Q) in a 20 -wk course, where Q(t) measures the number of words of dictation a student can take per minute after t wk in the course. If the average student can ...
*April 21, 2012 by help please.*

**Physics**

A billiard ball strikes and rebounds from the cushion of a pool table perpendicularly. The mass of the ball is 0.38 kg. The ball approaches the cushion with a velocity of +2.10 m/s and rebounds with a velocity of -2.00 m/s. The ball remains in contact with the cushion for a ...
*October 7, 2012 by Cheng*

**physics**

A billiard ball strikes and rebounds from the cushion of a pool table perpendicularly. The mass of the ball is 0.38 kg. The ball approaches the cushion with a velocity of +2.30 m/s and rebounds with a velocity of -1.90 m/s. The ball remains in contact with the cushion for a ...
*November 11, 2013 by bb*

**Math & Chemistry **

I having problems converting my answer to just cm. Given: Average Velocity = 1 m/s Water per day = 6,000 m^3/day Want to find the diameter of fluid flow. I am using the eqation: D = sqrt(4*q)/(pi*v) q= volumetric flow rate (6,000 m^3/day) v= velocity (1 m/s) when I solve I get...
*September 13, 2012 by Angel *

**trig**

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s= 2 sin pi t + 3 cos pi t, where t is measured in seconds. (a) Find the average velocity during each time period: (i)[1,2] (ii) [1,1.1] (iii) [1, 1....
*September 23, 2008 by Sarah*

**Physics**

A truck traveled along the National Highway from Calbayog to Oquendo which has a distance of 35 km. for 30 minutes. After delivering some materials, the driver rested for a while then drove back straight to Calbayog. The trip back took him 25 minutes. What is the average speed...
*January 2, 2011 by DAnielle*

**Physics**

If a tern travels 3.20 x 10^4 km south in 122 days, what is its average velocity in kilometers per day?
*September 14, 2009 by NoNo100*

**Physics**

If a tern travels 3.20 x 10^4 km south in 122 days, what is its average velocity in kilometers per day?
*September 14, 2009 by NoNo100*

**science**

a polar bear runs across the ice at an average velocity of 5.5 m/s. How far will she run in 3.5 minutes?
*January 29, 2010 by Margaret*

**chemisrty **

What is the ratio of the average velocity of hydrogen molecules to that of neon atoms at the same temperature and pressure?
*May 13, 2010 by someone*

**physics**

city of K is 27 km north of I. Head west at 11:00 in the morning and arrive at 8:30 in the evening. What is my average speed and velocity
*September 22, 2010 by Anonymous*

**11th grade**

a motorcycle changes velocity from 80km/h[N] to 100km/h[N] in 5.0 seconds. calculate her average acceleration
*September 29, 2010 by raman*

**physics**

A 2.2 kg purse is dropped from 55 m above before reaching the ground with a velocity of 25 m/s. What was the average air resistance.
*December 2, 2010 by joe*

**physics2**

6)Adam is running at an average velocity of 6 Km/h. How many meters would Omar run after 15 minutes?
*December 14, 2010 by faisal*

**physics **

if a race cars velocity increases from 4 m/s to 36 m/s over a 4 s time interval, it average acceleration would be 10 m/s2.
*April 2, 2012 by mike*

**physics**

A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t) = bt2 – ct3, where b = 2.40m/s2 and c = 0.120m/s3. (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. (b) ...
*October 12, 2010 by Anonymous*

**Calculus**

after t months on the job a postal clerk cn sort Q(t)=700-400e^-0.5t letters per hour. Wht is the average rate at which the clerk sorts mail during the first 3 months on the job. What is the average rte t which the clerk sorts mail during the first 3 months on the job? What is...
*August 1, 2012 by Marsha*

**Physics**

You have just discovered a planetary system consisting of a star (Dagobahr) and its two planets: Rool and Krau. Planet Rool has an average orbital radius 3 times as big as planet Krau. If planet Rool orbits Dagobahr in 2 earth years (1earth year = 365 days). a) how long is the...
*November 14, 2007 by Andrea*

**physics**

When a hammer strikes a nail, it is compressed along its length. Suppose that a steel nail 10.00 cm long and 3.00 mm in diameter is compressed an average of 65.0 µm by a 0.460 kg hammer during a 1.20 ms collision. (a) What average force was exerted on the nail by the hammer? (...
*October 1, 2014 by mathew*

**calculus**

Two runners, A and B run on a straight race track for 0</=t</=10 seconds. The graph below, which consists of two line segments, shows the velocity, in meters per second, of runner A. The velocity of runner B, in meters per second, is given by the function v defined by v(...
*November 22, 2008 by Kenneth*

**calculus**

g(t)=2+cos t; [0,pi] Can you help me find the average rate of change of the function over the given interval?
*January 20, 2011 by Kelly*

**pre-calculus**

suppose g(t)=kf(t). Find the average rate of change of g over the interval [a,b] in terms of f
*March 17, 2011 by Olivia*

**calculus**

find the average value of the function f(x,y)=xe^y over the plane region R is the triangle with vertices (0,0), (1,0) and (1,1)
*April 2, 2012 by mabel*

**calculus**

find the average value of the function f(x,y)=xe^y over the plane region R is the triangle with vertices (0,0), (1,0) and (1,1)
*April 5, 2012 by Anonymous*

**calculus**

find the average value of the function f(x,y)=e^(-x^2) over the plane region R which is the triangle with vertices (0,0), (1,0) and (1,1)
*June 12, 2012 by soffy*

**pre calculus**

find the average rate of change of f(x)=x^3-5x+3: a. from -6 to -3 b. from -1 to 2 c. from 2 to 8 I am so lost, can someone please show me how to do this?
*March 27, 2013 by courtney*

**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 ...
*March 25, 2014 by Q*

**Calculus**

well i have this homework question that says: A rock is dropped from the top of a 300-ft cliff. It's velocity at time t seconds is v(t0= -32 t feet per second. a.) Find the height of the rock above the ground at time t. b.) How long will the rock take to reach the ground? c.) ...
*May 11, 2009 by Caitlin*

**calculus and physics**

An explosion causes debris to rise vertically with an initial velocity of 75 ft/sec. a. In how many seconds does it attain maximum height? b. What is the maximum height? c. What is the speed of the debris as it reaches 12 ft on the way back to the ground? d. What is the ...
*October 1, 2012 by olivia*

**calculus and physics**

An explosion causes debris to rise vertically with an initial velocity of 75 ft/sec. a. In how many seconds does it attain maximum height? b. What is the maximum height? c. What is the speed of the debris as it reaches 12 ft on the way back to the ground? d. What is the ...
*October 1, 2012 by olivia*

** Calculus**

A cruise ship's captain sets the ship's velocity to be 26 knots at a heading of 080 degrees. The current is flowing toward a bearing of 153 degrees at a speed of 8 knots. What is the ground velocity of the cruise ship?
*May 2, 2010 by Bobby*

**Calculus**

a particle starts at time t = 0 and moves along the x axis so that its position at any time t>= 0 is given by x(t) = ((t-1)^3)(2t-3) a.find the velocity of the particle at any time t>= 0 b. for what values of t is the velocity of the particle negative? c. find the value ...
*September 10, 2009 by Lauren*

**Physics**

The earth moves around the sun in a nearly circular orbit of radius 1.50 x 1011 m. During the three summer months (an elapsed time of 7.89 x 106 s), the earth moves one-fourth of the distance around the sun. (a) What is the average speed of the earth? (b) What is the magnitude...
*September 7, 2013 by WR*

**Physics**

Jack and Jill exercise in a 25.0-m-long swimming pool. Jack swims nine lengths of the pool in 160.1 seconds (2 minutes and 40.1 seconds), while Jill, the faster swimmer, covers ten lengths in the same time interval. Find the average velocity and average speed of each swimmer.
*February 2, 2015 by Breauna*

**calculus**

A mass on a spring vibrates horizontally on a smooth level surface. Its equation of motion is x(t)=8sint, where t is in seconds and x in centimeter. a. Find the velocity and acceleration at time t b. Find the position, velocity, and acceleration of the mass at time t=2pi/3. In...
*October 4, 2011 by bob*

**Physics**

A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t) = bt2 - ct3, where b = 2.60 m/s2 and c = 0.150 m/s3. (a) Calculate the average velocity of the car for the time interval t = 0 to t = 8.0 s. m/s (b) ...
*February 4, 2011 by Anonymous*

**Physics**

The velocity vefot of a ball is v(t)=-3x+4y at any time. Its initial position is r=12x-4y. The components of the velocity vector are in m/s and the components of the position vector are in meters. The symbols x and y are the unit vetors in x and y directions respectively. Find...
*September 26, 2010 by Sarah*

**Physics - final velocity?**

At sea level, a hydrogen molecule in the air has an average kinetic energy of 5.53×10-21 J. Its mass is 3.32×10-27 kg. The hydrogen molecule shoots straight up without colliding with the molecules in the air. (Assume that you can use g = 9.81 m/s2; although we’ll see in ...
*February 12, 2011 by Em*

**Calculus**

A projectile is launched at an angle of 60 degrees to the horizontal from 6.5 ft above the ground at an initial speed of 150ft/sec. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts ...
*March 9, 2011 by Z32*

**Calcuslus-Calculus-Calculus **

A rocket arises from its launching pad with a velocity given. By 0.1 h m/s ,where h m is the height reached by the rocket at that time.the rocket is obserrvved from 2000 m away from the launch pad.at. What rate is the distance of the roocket from observer channging when the ...
*March 16, 2011 by Mehak*

**Physics**

It takes you 9.5min to walk with an average velocity of 1m/s to the north from the bus stop to the museum entrance. What is your displacement?
*September 10, 2009 by Anthony Smith*

**Ap Chem**

At 200K, the particles of gas X have an average velocity equal to that of Argon at 400K. What is the identity of X? He CO HF HBr F2
*October 18, 2010 by suzan*

**physic**

If you run a complete loop around an outdoor track(400m), in 100 second,what is your average velocity?
*July 12, 2011 by syida*

**science**

It take you 9.5 min to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance. What is your displacewment?
*September 11, 2011 by Chris*

**physics**

a race car's velocity increases from 4 m/s time interval, its average acceleration would be 10 m/s2 ? true or false ?
*February 28, 2012 by Anonymous*

**physics**

if a race car's velocity increases from 4 m/s to 36 m/s over a 4 s time interval, its average acceleration would be 10 m/s 2 ? IS THIS TRUE ?
*March 1, 2012 by Anonymous*

**Physica**

The position of a particle is given by equation X(t)=2t^2 where t in second and X in metere. The average velocity during time interval from t=1 s to t=5 s is.......
*July 11, 2012 by Q2*

**Physics**

It takes you 10min to walk with an average velocity of 1.2m/s to the north from the bus stop to the restaurant entrance. What is your displacement?
*September 16, 2013 by Abdullah*

**physics**

Calculate the average velocity for a remote controlled vehicle that starts with a speed of 1.0 m/s [forward] and then accelerates at 0.08 m/s2 [backward] for 4.0 s.
*June 3, 2014 by grey*

**physics**

Calculate the average velocity for a remote controlled vehicle that starts with a speed of 1.0 m/s [forward] and then accelerates at 0.08 m/s2 [backward] for 4.0 s.
*June 6, 2014 by grey*

**physics**

a particuler moves along the sides AB,BC,CD of a square of side 25m with a speed of 15m/s. Its average velocity is?
*August 9, 2014 by nikhil*

**calculus**

The height (in feet) attained by a rocket t seconds into flight is giving by the function h(t)= -1/3t^3 + 16t^2 + 33t + 10 When is the rocket rising? When is the rocket decreasing? when does it reach its maximum height above the ground? what is the maximum height? what is the ...
*November 30, 2011 by chris*

**Calculus**

for f(x)=-x^2 +1, which value is the largest magnitude? a) average rate of change from x=-1 to x=1 b) instanteneuous rate of change at x=3 c) instanteneous rate of change at x=0 average rate of change from x=-4 to x=0
*July 4, 2012 by g*

**Calculus!**

What is the velocity of an object dropped from a height of 350 m when it hits the ground?
*September 21, 2007 by ali*

**calculus**

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

**Physics (Velocity in two dimensions)**

Please help: The displacement vector for a 15.0 second interval of a jet airplane's flight is (3850, −2430) m. (a) What is the magnitude of the average velocity? (b) At what angle, measured from the positive x axis, did the airplane fly during this time interval? Express...
*February 21, 2013 by Kathy*

**Physics (Velocity in two dimensions)**

Please help, The displacement vector for a 15.0 second interval of a jet airplane's flight is (3850, −2430) m. (a) What is the magnitude of the average velocity? (b) At what angle, measured from the positive x axis, did the airplane fly during this time interval? Express...
*February 21, 2013 by Kathy*

**ENG102**

Question 1. A car moves 26 km due east then 14 km due north. It then turns along a path running north-east with 15 km, then 17 km due west. If the time for the entire journey is 2 hrs, Find; (a) the car’s average speed in m/s (b) the car’s average velocity in km/h . SOLVE THIS...
*May 1, 2012 by DESMOND*

**Physics**

A dock worker applies a constant horizontal force of 79.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in the first 6.00 s. What is the mass of the block of ice? Work done = final kinetic ...
*September 19, 2006 by Veronica*

**Re: PHYSICS**

"Relative" is an important word. Block L of mass mL = 1.90 kg and block R of mass mR = 0.500 kg are held in place with a compressed spring between them. When the blocks are released, the spring sends them sliding across a frictionless floor. (The spring has negligible mass and...
*February 27, 2007 by COFFEE*

**Physics 141**

A snowmobile moves according to the velocity-time graph shown in the drawing. What is the snowmobile's average acceleration during each of the segments A, B, and C? The scale for the time axis is 100 s per increment, and the scale for the velocity axis is 110 m/s per increment.
*January 30, 2014 by Hope*

**Calculus**

Find the average value over the given interval. y=3x^5; [-3,3] I can't seem to get the answer, 0. 1/(3+3) [integral -3 to 3 (3x^5)dx] and I get 273/2
*January 24, 2008 by Anonymous*

**Calculus**

Find the average value of the function on the given interval: f(x)=cos(16x), [0,pi/2] The answer I got is 1.
*January 27, 2010 by <3*

**Calculus**

Find (1) marginal and (2)the average functions for the following total function. Evaluate them at Q=3 and Q=5 π=q^2+13q+78
*November 21, 2012 by Rae*