Monday
April 21, 2014

# Homework Help: Math: Calculus

Recent Homework Questions About Calculus

pre calculus
The age of a document is in dispute, so archaeologists test for carbon-14. Due to radioactive decay, the amount A of carbon -14 present compared to the initial amount A0 after t years is given by the formula A(t) = A0e^-0.000124t . If 72% of the original amount of carbon- 14 ...
Saturday, February 8, 2014 at 11:06pm

pre calculus
A sum of $5000 is be invested in a bank. if the annual interest is 10% and compounded monthly, how long will it take for the original investment to double. Saturday, February 8, 2014 at 10:57pm pre calculus a) amount = 1000(1.025)^10 = 1280.08 b) amount = 1000 e^(5(.05)) = 1000 e^.25 = 1284.03 Saturday, February 8, 2014 at 10:36pm pre calculus Which is worth more after 5 years, an investment of$1000 at 5% interest compounded semi - annually(twice a year). or an investment of $1000 at 5% interest compounded continuously? Saturday, February 8, 2014 at 10:03pm Calculus Help as you recall from algebra I, the vertex of a parabola occurs when t = -b/2a. In this case, that is when t = 1 Or, using calculus, since ds/dt = 32-32t, ds/dt=0 when t=1 s=0 when t=1+√5, so plug that into ds/dt Saturday, February 8, 2014 at 5:45am 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 (... Saturday, February 8, 2014 at 1:01am Calculus 3 _ go with Damon Oww! I messed up the signs. Damon's values are correct. Friday, February 7, 2014 at 4:22pm Calculus 3 Hmmm. assuming some typos, I get (x^2+2x+1) + 4(y^2-y+1/4)+2(z^2+z/2+1/16) = 20+1+1+1/8 (x-1)^2 + 4(y-1/2)^2 + 2(z+1/4)^2 = 177/8 At this point we know that the center is at (1,1/2,1/4). We can go ahead and divide by 177/8 to get it into standard form, but it won't affect ... Friday, February 7, 2014 at 4:21pm Calculus 3 anyway that would put the center at x = -1 y = 1/2 z = -1/4 Friday, February 7, 2014 at 4:17pm Calculus 3 Find the center of the ellipsoid x^2+4y+2z^2+2x-4y+z = 20 I'm having trouble factoring to get the center points. Can someone please help. This is where I'm stuck. (x^2+2x+1)+4(y^2-y+1/4)+2(x^2+1/2z+1/16)​=20+1+1+1/8 (x+1)^2+ Now I don't know how to get the y ... Friday, February 7, 2014 at 3:45pm 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 Thursday, February 6, 2014 at 5:07pm calculus - incomplete Hard to tell which branch of the functions are defined at the discontinuity. That is, where is the solid dot, and where is the open circle? g(0) is hard to figure, since "discontinuity at 0,1" doesn't give a clear picture. Also, you have (2,0) twice in the list ... Thursday, February 6, 2014 at 2:32pm calculus assuming those 0's should be x's the first assertion is false. d/dx(tanx) = 1 at x=0, not everywhere. Kind of an odd problem, since the last 3 statements are all obviously true. Thursday, February 6, 2014 at 2:24pm calculus uio9 Thursday, February 6, 2014 at 2:19pm calculus (fg)' = f'g+fg' at x=1, we have 3*5 + 2(-4) = 7 Thursday, February 6, 2014 at 2:19pm calculus This is handily explained at http://answers.yahoo.com/question/index?​qid=20100519122921AAIzxX9 Thursday, February 6, 2014 at 2:12pm calculus Evaluate the limit as x approaches 0 of [tan(x+Δx)-tan(x)] /Δx: sec^ 2 (x) cot (x) sec (x) does not exist Thursday, February 6, 2014 at 1:18pm calculus Suppose f (1) = 2, f ΄(1) = 3, g(1) = 5, and g΄(1) = -4. Evaluate (f g)΄v at x = 1. Answer -12 7 10 23 Thursday, February 6, 2014 at 1:14pm calculus If limit as delta x approaches 0 of tan(0+Δx)-tan(0)/Δx =1 which of the following is false: d/dx [tanx]=1 the slope of y = tan(x) at x = 0 is 1 y = tan(x) is continuous at x = 0 y = tan(x) is differentiable at x = 0 Thursday, February 6, 2014 at 12:56pm calculus Suppose h(x) = f (g(x)) and the graphs of f and g are shown below. Describe the continuity of h at x = 0. how would you do this if you were given two graphs: F--- discontinuity at -2,0; point at -1,1; and point at 0,0 (to make a parabola) then discontinuity at 0,-1; and then ... Thursday, February 6, 2014 at 12:49pm Calculus the width of the water surface when the depth is y is 4y/3 So, the cross-section at depth y has area 1/2 * y * 4y/3 = 2y^2/3 So the volume of water when the depth is y is v = 10y^2 dv/dt = 20y dy/dt at y=2, 5/2 = 40 dy/dt dy/dt = 1/16 ft/min Thursday, February 6, 2014 at 5:29am Math (pre calculus) one: no (try x=2) two: yes Thursday, February 6, 2014 at 5:23am pre calculus just to unclutter things, let u = (1+x)^1/3. Then we have (3u-x/u^2)/u^2 = (3u^3-x)/u^4 = (3(1+x)-x)/(1+x)^4/3 = (2x+3)/(1+x)^4/3 Thursday, February 6, 2014 at 5:22am Math (pre calculus) 1/(1+x+h) - 1/(1+x) = ((1+x) - (1+x+h))/(1+x+h)(1+x) = -h/((1+x+h)(1+x)) Now divide that by h and you have -1/((1+x+h)(1+x)) Thursday, February 6, 2014 at 5:18am Math (pre calculus) please simplify (1/1+x+h) - (1 /1+x ) divided by h Thursday, February 6, 2014 at 1:49am pre calculus Correction: the question is to simplify the FRACTIONAL expression. Thursday, February 6, 2014 at 1:46am pre calculus Simplify the rational expression 3 (1 + x)^1/3 - x (1 + x)^-2/3 divided by (1 + x)^2/3 Thursday, February 6, 2014 at 1:44am Math (pre calculus) State whether the given equation is true for all values of the variables (disregard any value that makes a denominator zero) equation one (2/ 4 + x) = (1/2) + (2/x) equation two (1 + x + x^2 / x) = (1/x) + 1 + x Thursday, February 6, 2014 at 1:41am Calculus A trough is 15 ft long and 4 ft across the top, as shown in the figure. Its ends are isosceles triangles with height 3 ft. Water runs into the trough at the rate of 2.5 ft^3/min. How fast is the water level rising when it is 2 ft deep? Thursday, February 6, 2014 at 1:02am calculus P = k/V as v->0, P->∞ Wednesday, February 5, 2014 at 7:55pm calculus suppose you use symbols instead of words: f(x) = 3x-k for x < 5 = kx+1 for x >= 5 for f to be continuous at x=5, we need 15-k = 5k+1 14 = 6k k = 7/3 Wednesday, February 5, 2014 at 7:54pm calculus x^2+4x <= f(x) <= -(x^2+4x) If x = -2, -4 <= f(x) <= 4 I don't think squeezing applies. Wednesday, February 5, 2014 at 7:52pm calculus what is wrong with using symbols? 2x/(√x-2) the limit as x->4 is 8/0 which is undefined. In fact, since √x-2 is positive as x->4 from the right and negative as x->4 from the left, it's both unbounded and unequal from left and right. I think (b) is the ... Wednesday, February 5, 2014 at 7:49pm Pre-Calculus thanks Wednesday, February 5, 2014 at 7:46pm Pre-Calculus amount= origamount*1.5^timeInYears so in four years, amount=orig*1.5^4 earned=amount-orig=orig^1.5^4-orig 29250=orig (1.5^4-1) solve for orig, then then solve for amountafter4years, and amount after three years, and subtract. amounteared4thyr= orig(1.5^4-1.5^3) = orig (1.5^3)(... Wednesday, February 5, 2014 at 7:30pm Pre-Calculus A certain sum of money is invested in a business. in each year this investment earns 1 1/2 times as much as in the preceding year. If the investment earned a total of$29,250.00 in four years, how much did it earn in the fourth year?
Wednesday, February 5, 2014 at 7:22pm

calculus
Which of the following best describes the limit as x approaches 4 of the quotient of 2 times x divided by the quantity negative 2 plus square root of x ? It exists and equals 4 It fails to exist because it is unbounded. It fails to exist because its one-sided limits are not ...
Wednesday, February 5, 2014 at 6:58pm

calculus
It is known that x 2 + 4x ≤ f(x) ≤ -x 2 -4x the interval [-4, 0]. Use the Squeeze Theorem to evaluate the limit as x approaches negative 2 of f of x. -4 0 4 Squeeze Theorem does not apply
Wednesday, February 5, 2014 at 6:58pm

calculus
Suppose f of x equals 3 times x minus k when x is less than 5 and equals 1 plus k times x when x is greater than or equal to 5.Find the value of k that would make f continuous at x = 5. -3 0 7/3 no such k will make f continuous
Wednesday, February 5, 2014 at 6:57pm

calculus
At a constant temperature, the pressure, P, and volume, V, of a trapped gas have the relationship P equals the quotient of k divided by V , where k is some positive constant. What occurs if the volume is compressed such that V → 0+? The pressure increases without bound. ...
Wednesday, February 5, 2014 at 6:56pm

Calculus 2
M = ∫[0,4]∫[x/2+4,√x+4] ​61; dy dx = ρ∫[0,4] (√x+4)-(x/2+4) dx = ρ∫[0,4] √x - x/2 dx = ρ (2/3)x^(3/2) - (1/4)x^2 [0,4] = ρ (2/3)(8)-(1/4)(16) = 4/3 ρ Mx = ∫[0,4]∫[x/2+4,√x+4] ​...
Wednesday, February 5, 2014 at 5:52pm

Calculus 2
Find Mx, My, and (x, y) for the laminas of uniform density ρ bounded by the graphs of the equations. y=sqrt(x)+4 y=(1/2)x+4 The I keep getting 20/3 for Mx but webassign acts like it is wrong.
Wednesday, February 5, 2014 at 1:51pm

calculus
at time t, the distance d is d^2 = (90-20t)^2 + (15t)^2 d^2 = 625t^2 - 3600t + 8100 2d dd/dt = 1250t-3600 dd/dt=0 when t=72/25 d(72/25) = 54
Wednesday, February 5, 2014 at 1:04pm

calculus
At midnight, ship B was 90 km due south of ship A. Ship A sailed east at 15 km/hr and ship B sailed north at 20 km/hr. At what time were they closest together?
Wednesday, February 5, 2014 at 10:38am

calculus
At midnight, ship B was 90 km due south of ship A. Ship A sailed east at 15 km/hr and ship B sailed north at 20 km/hr. At what time were they closest together?
Wednesday, February 5, 2014 at 10:35am

Calculus
u=1-3√x du = -3/(2√x) = (-3/2)(1/√x) you already have 1/√x, so the new integrand becomes ʃ 1/u (-2/3)du that should make it clear
Wednesday, February 5, 2014 at 6:04am

Calculus
I'd really like some help in solving an integral. ʃ 1/ √x (1-3√x) In numerator: 1 In denominator: the square root of x times 1 minus 3 times the square root of x The answer given is -2/3 ln l1-3√xl + C but I don't know how to get there.
Wednesday, February 5, 2014 at 12:05am

CALCULUS 2
Use calculus to find the volume of the following solid S: The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
Tuesday, February 4, 2014 at 10:47pm

Calculus
Tuesday, February 4, 2014 at 10:36pm

Calculus
I am wondering what rule you are using... I suspect it is Simpsons Rule, if so do that. That will give you the distance of the path. see http://answers.yahoo.com/question/index?​qid=20101016110803AAKwID9
Tuesday, February 4, 2014 at 10:36pm

Calculus
A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 60 ft is given by the following. y= 155-(1/40)(x-50)^2 Find the distance traveled by the kite.
Tuesday, February 4, 2014 at 10:27pm

Calculus
Find the distance traveled by the kite
Tuesday, February 4, 2014 at 10:24pm

Calculus
http://en.wikipedia.org/wiki/Simpson%27s​_rule
Tuesday, February 4, 2014 at 10:14pm

Calculus
and the question...?
Tuesday, February 4, 2014 at 10:12pm

Calculus
A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 60 ft is given by the following. y= 155-(1/40)(x-50)^2
Tuesday, February 4, 2014 at 10:09pm

Calculus
Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = tan x, 0 < x < π/9
Tuesday, February 4, 2014 at 10:08pm

calculus
just take the graph of y=x^3 and shift it right 5 and up 2.
Tuesday, February 4, 2014 at 5:25am

calculus
Use the principles of translating and reflecting to graph the function f(x)=(x-5)^3 +2
Tuesday, February 4, 2014 at 1:27am

pre calculus
determine the order of magnitude for the following: 1. a \$1 bill and a dime 2. two products scored a PH level of 6.1 and 4.o I can't figure out #1… but I did get #2 to be 10^2.1 Please help with #1 and check to see I did #2 right?
Monday, February 3, 2014 at 4:25pm

calculus
y = (-5x+4)/(10-5x) = (4-5x)/(10-5x) At x=2 there is a vertical asymptote, since 10-5x=0 As x gets large, y -> 1 since y = (4/x - 5)/(10/x - 5) -> -5/-5 = 1
Monday, February 3, 2014 at 5:47am

calculus
y= -5x + 4 OVER 10 - 5x find the asymptotes of the function
Monday, February 3, 2014 at 1:37am

Calculus II
Solve the initial value problem using Taylor Series and the following conditions: y'(t) = y(t) + 2t y(0) = A
Sunday, February 2, 2014 at 11:01pm

Calculus
8.42
Sunday, February 2, 2014 at 8:42pm

as you know, the average velocity is the integral divided by the time interval. Since the position is the integral of the velocity, the average velocity in [a,b] = (s(b)-s(a))/(b-a) So, we have i) (s(2)-s(1))/(2-1) = (2sin2π+3)-(2sinπ+3) = 0 ii) (s(1.1)-s(1))/(1.1-1...
Sunday, February 2, 2014 at 8:26pm

SHOW WORK PLEASE!!! 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 πt + 3 cos πt, where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the ...
Sunday, February 2, 2014 at 8:12pm

calculus
g = m t + b m = (17-8)/(47-28) = .4737 so g = .4737 t + b 8 = .4737 (28) + b so b = -5.263 so g = 0.4737 t - 5.263
Sunday, February 2, 2014 at 5:03am

calculus
In a lab experiment 8 grams of acid were produced in 28 minutes and 17 grams in 47 minutes. Let g be the number of grams and m be the number of minutes. Find a linear equation that you could use to calculate g for any number of minutes.
Sunday, February 2, 2014 at 3:28am

calculus
Consider the function f(x) = 5 (x - 5)^(2//3) . For this function there are two important intervals: (-\infty, A) and (A,\infty) where A is a critical number. Find A
Sunday, February 2, 2014 at 2:38am

CALCULUS
I don't understand. Why are you adding 1/4? to both sides? I don't see how you are getting a quadratic formula from this. More importantly, thank you guys for the help!
Sunday, February 2, 2014 at 12:29am

calculus
I guess the foxes were factored in when calculating the surviving rabbit population, eh?
Saturday, February 1, 2014 at 6:41pm

calculus
I bet we want the maximum, but usually the foxes are included in these island problems. dP/dt = 0 at max = 120 -1.6 t^3 t^3 = 120 t = 4.93 months
Saturday, February 1, 2014 at 6:23pm

Calculus & Vectors
240 * 1.25 = 300 @ N20W = <-102.6,281.9> 240 * 2.00 = 480 @ N80E = <472.7,83.4> add 'em up to get <370.1,315.3> So, the distance back is 486.2 300+480+486.2 = 1266.2 km at 240 km/hr = 5.3 hours
Saturday, February 1, 2014 at 6:18pm

Calculus & Vectors
A search and rescue aircraft, travelling at a speed of 240 km/h starts out at a heading of N 20 degrees West. After travelling for 1h and 15 min, it turns to a heading of N 80 degrees E and continues for another two hours before returning to base. Find the total distance the ...
Saturday, February 1, 2014 at 6:10pm

calculus - and?
in the words of Larry King, "What's the question?"
Saturday, February 1, 2014 at 5:32pm

calculus
The rabbit population on a small island is observed to be given by the function P(t)=120t−0.4t4+700 where t is the time (in months) since observations of the island began.
Saturday, February 1, 2014 at 5:28pm

CALCULUS
Whoops !
Saturday, February 1, 2014 at 11:47am

calculus
Well if you only have five days total, hopefully it only takes the remaining one day to solve it! Otherwise, you're in trouble!
Saturday, February 1, 2014 at 11:32am

CALCULUS
noticed an error from line 2 to line 3 y^2 - y = x y^2 - y + 1/4 = x + 1/4 (y - 1/2)^2 =(4x+1)/4 y - 1/2 = ±√(4x+1)/2 y = 1/2 ± √(4x+1)/2 = (1 ± √(4x+1) )/2 , x ≥ -1/4
Saturday, February 1, 2014 at 10:37am

CALCULUS
x = y^2 - y y^2 - y + 1 = x + 1 (y-1)^2 = x + 1 y -1 = sqrt (x+1) y = 1 + sqrt (x+1)
Saturday, February 1, 2014 at 9:46am

COURSE HELP PLEASE ms sue qq
In high school, these courses are usually called Algebra I Algebra II Geometry Pre-calculus AP Calculus Biology AP Biology Chemistry AP Chemistry Physics AP Physics Work with your counselor to make sure you take the required courses for graduation AND as many of these as ...
Saturday, February 1, 2014 at 9:41am

CALCULUS
Find a formula for the inverse of the function. y=x^2-x, x>=(greater than or equal to) 1/2 Please give me a step by step explanation. I think my algebra is wrong... Ty
Saturday, February 1, 2014 at 9:16am

calculus
Four out of five days were used to create a problem, how many days will it take to solve it?
Saturday, February 1, 2014 at 8:21am

calculus
Four out of five days were used to create a problem, how many day will it take to solve it?
Saturday, February 1, 2014 at 8:21am

integral calculus
If you mean ∫[x,4] x/(x-4) dx that's a bit unusual to have the variable of integration as one of the limits. But ok, let's work it out as-is. ∫x/(x-4) dx = x + 4 log(x-4) Evaluating that at 4 and x, we have (4+4log(0))-(x+4log(x-4)) Looks like -∞ to ...
Friday, January 31, 2014 at 10:56pm

integral calculus
Evaluate the limit limit gose from x to 4 (x/x-4)integral from x to 4
Friday, January 31, 2014 at 10:04pm

Calculus
Thank you!
Friday, January 31, 2014 at 10:00pm

Calculus
point in first plane 0,0 something (0 , 0 , 10) d = | 10*0 -8*0 +2*10 -3 | /sqrt(10^2+8^2+4^2) = 17/13.4
Friday, January 31, 2014 at 8:07pm

Calculus
here is an example of how to do this: http://www.math.ucla.edu/~ronmiech/Calcu​lus_Problems/32A/chap11/section5/718d65/​718_65.html
Friday, January 31, 2014 at 8:01pm

Calculus
when x gets really big positive this is y = 2 (big) / sqrt(big ^2) which is y = 2 when x gets really big negative y = 2 (-big number) / big number which is y = - 2 well, let's look at the derivative since they say so [ (x^2+x+1)2 - 2x(.5)(x^2+x+1)^-.5(2x) ]/(x^2+x+1) yuuk...
Friday, January 31, 2014 at 5:50pm

Calculus
we have two points in that plane (8, 0, -2) and (6, 3, 3) a vector through those points has direction (6-8)i + 3 j + (2+2)k = -2 i + 3 j + 4 k so we have two vectors parallel to plane, their cross product is normal to the plane i j k -2 5 2 the given line direction -2 3 4 the ...
Friday, January 31, 2014 at 5:35pm

Calculus
Let f be the function given by f(x)= 2x/(sqrt(x^2 +x +1)) c. Write an equation for each horizontal asymptote of the graph of f. d. Find the range of f. Use f'(x) to justify your answer.
Friday, January 31, 2014 at 5:26pm

Calculus
vector normal to plane has direction 3 i + 2 j + 6 k line normal to plane through point is (1, -5 , 9) + (3, 2, 6) t where does that hit the plane? 3(1+3t) + 2(-5+2t) + 6(9+6t) = 5 solve for t go back and use that t to get x, y, z in plane x = 1+3t y = -5+2t z = 9+6t then d^2...
Friday, January 31, 2014 at 5:09pm

Calculus
pick a point in plane #1, say (2,3,1) Now just use the distance formula to get the distance to 6x-6y+6z=3 or, equivalently, 2x-2y+2z-1 = 0 d = |2*2-2*3+2*1-1|/√(2^2+2^2+1^2) = 1/√5
Friday, January 31, 2014 at 4:47pm

Calculus
see http://www.jiskha.com/display.cgi?id=139​1198824 for the method
Friday, January 31, 2014 at 4:36pm

Calculus
(1+4t) +2 (4t) -(2-3t) = -1 solve for t then use that t to find x, y z
Friday, January 31, 2014 at 4:35pm

Calculus
going from the first point to the second dx = 3 dy = -2 dz = 4 so my line direction is 3 i -2 j + 4 k and my line in parametric form is (1,0,1) + (3, -2, 4) t at intersection x = 1+3t y = -2 t z = 1+4t and we know x + y + z = 10 2 + 5 t = 10 t = 8/5 so x = 1 + 24/5 = 29/5 y...
Friday, January 31, 2014 at 4:32pm

Calculus
perpendicular to the direction 1 i - 1 j + 2 k Vxi + Vyj + Vzk if perpendicular dot product is 0 Vx - Vy + 2 Vz = 0 also parallel to plane x+y+z = constant 2 so normal to the normal to that plane 1 i + 1 j + 1 k Vxi + Vyj + Vzk Vx + Vy + Vz = 0 so we have Vx - Vy + 2 Vz = 0 Vx...
Friday, January 31, 2014 at 4:14pm

Calculus
Find the distance between the given parallel planes. 4z = 4y − 4x, 6z = 3 − 6x + 6y
Friday, January 31, 2014 at 3:15pm

Calculus
Find the distance between the given parallel planes. 5x−4y+z=10, 10x−8y+2z=3
Friday, January 31, 2014 at 3:14pm

Calculus
Find the distance from the point to the given plane. (−3,8,7), x−2y−4z=8
Friday, January 31, 2014 at 3:13pm

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