Tuesday
November 25, 2014

Posts by Steve


Total # Posts: 27,004

Calculus
f = (ln x)^x ln f = x ln(lnx) 1/f f' = ln(lnx) + x(1/lnx)*1/x f' = (lnx)^x * (ln(lnx) + 1/lnx) This agrees with the extension of the normal power/exponent rule. If y = u^v where u and v are functions of x, then y' = v u^(v-1) u' + lnu * u^v v' = u^v (v/u u...
October 19, 2014

Math
The principal property of 0 is that for any real a, a*0 = 0 Now, suppose that we want to divide by 0. That means that if a/0 = b, then a = b*0 But b*0 is 0 for any b. That is, there is no real value of b for which b*0 is a nonzero number a. Think of the quotient when the ...
October 19, 2014

AP Calc. AB
y = dV/dt = 100,000 * 2(1 - t/50)(-1/50) = -4000 (1 - t/50) = -4000 + 80t This is (e) with all the noise removed
October 18, 2014

calculus
Since the domain of log(x) is x > 0, we need log(x) > 0 that is, 0 < x < 0.2 You can see this reflected in the graph found below. The domain is where the imaginary part is zero. http://www.wolframalpha.com/input/?i=log_.2%28log_.2%28x%29%29
October 18, 2014

ALGEBRA
just plug in -c for all the w's. A(-c) = √((-c)^2+13) = √(c^2+13)
October 18, 2014

algebra
since f|9| = f|-9| = 9, either x+5 = 9 or x+5 = -9 That's easy, now, right?
October 18, 2014

calculus
if the diagonal is d and the area is a, then we have d^2 = 2s^2 a = s^2 = d^2/2 now forget all that square root stuff, and use implicit differentiation: da = d dd we have a = 50, so d = 10 da = 4.45 4.45 = 10 dd dd = 0.45 You made a mistake in the line dD=A^(-1/2) dA It should...
October 18, 2014

Math
If there are g glasses of skim and m servings of meat .1g + 3.75m = 7.36 8.2g + 21m = 73 Now just solve and you get g = 4.1 m = 1.8 So, 5 glasses of mile and 2 servings of meat will provide the desired amounts
October 18, 2014

Calculus
correct all the way!
October 18, 2014

Calculus
correct
October 18, 2014

Calculus
this is exponential growth, where the rate of change is proportional to the population. Naturally, limited food will cause the population to level out, or even die off. Rather than just hang around for an answer, think about the hints given above. They contain all you need. ...
October 18, 2014

Math Algebra
correct.
October 18, 2014

calculus
how to factor what? ds/dt at t=5 is just 6*5+5 = 35
October 18, 2014

calculus
ds/dt is the velocity. Assuming you meant s(t) = 3t^2 + 5t + 3 ds/dt = 6t + 5 so plug in t=5.
October 18, 2014

calculus
look at the graphs here: http://www.wolframalpha.com/input/?i=plot+y+%3D+4cos%282x%29%2C+y%3D4 Now you have to clarify what you mean by "outside" a line
October 18, 2014

Algebra
#1 yes #2 no #3 no #4 yes why? a relation from x to y is a function if no x value maps to more than one y value. That is if f(a) = c and f(b)= c then a=b. Geometrically, it means that no vertical line can intersect the graph in more than one place. try graphing your relations ...
October 18, 2014

calculus
since x^2+y^2 = 36 2x dx/dt + 2y dy/dt = 0 when x=3, y=√27, so we have (3)(1/2) + √27 dy/dt = 0 so now you know how y is changing Since tanθ = y/x, sec^2θ dθ/dt = 1/x dy/dt - y/x^2 dx/dt Now just plug in your numbers again to find dθ/dt Of ...
October 18, 2014

Trigonometry
draw a diagram (h-2)/35 = tan60°
October 17, 2014

Calculus
this is exponential growth, where the rate of change is proportional to the population. Naturally, limited food will cause the population to level out, or even die off.
October 17, 2014

Calculus
This site discusses the problem, as well as a trick shortcut: http://math.stackexchange.com/questions/129249/maximize-volume-of-box-in-ellipsoid google will provide other solutions as well.
October 17, 2014

Algebra
The ordered pairs (1,6), (2,36), (3,216), (4,1296), and (5,7776) represent a function. What is a rule that represents this function?
October 17, 2014

MATH HELP PLEASE
Nope. all irrationals are real. It's gotta be B. How can a number be rational and irrational (which means NOT rational)?
October 17, 2014

Math
Not quite. The first term is 2/3, so the sum is 242/3 = 80 2/3 The first 4 terms are shown, and the next is 54. Their sum is 80 2/3 On #2, neither is a GP
October 17, 2014

Math
32/(1 + 1/2) = 64/3 you are correct
October 17, 2014

MATH HELP PLEASE
√21 is not 4.582575695 It is 4.582575695.... and is not a rational number How many different ways do we have to say the answer is CCCCCCCC??????
October 17, 2014

MATH HELP PLEASE
NO! 36 = 6^2, so sqrt(36) = 6, a rational number. 4^2 = 16 and 5^2 = 25 so 21 has no rational square root. The answer is C
October 17, 2014

Math
well, R·S = [-24/25,7/25] [-7/25,/24/25] Clearly this is a rotation matrix, for θ such that cosθ = 24/5 sinθ = 7/25 with appropriate signs. I forget where the + and - are applied.
October 17, 2014

Algebra
The ordered pairs (1,1), (2,8), (3,27), (4,64) , and (5,125) represent a function. What is a rule that represents this function? My answer is y = x cubed
October 17, 2014

Precalculus
you have (sinx-(cosx-1))/(sinx+(cosx-1)) multiply top and bottom by (sinx-(cosx-1)) and you have (sinx-(cosx-1))^2/(sin^2x - (cosx-1)^2) (sin^2x - 2sinx(cosx-1) + (cosx-1)^2) --------------------------------------- (sin^2x - cos^2x + 2cosx - 1) (sin^2x - 2sinx*cosx + 2sinx + ...
October 17, 2014

Math
use l'Hospital's rule. The limit is the same as [1/(1+h)]/1 = 1
October 17, 2014

Math
P = Po e^kt P/Po = e^kt kt = ln(P/Po) t = 1/k ln(P/Po) Just remember that e^x and ln(x) are inverse functions, just as √ and ^2 are inverses * and / are inverses + and - are inverses
October 17, 2014

MATH HELP PLEASE
Is 6 a rational number? YES! So, D is NOT the answer! A and B are also rational numbers. They are terminating decimals, so they are rational. Since 21 is not a perfect square (it is between 16 and 25) its square root is not rational.
October 17, 2014

MATH HELP PLEASE
√21 D is exactly 6
October 17, 2014

trigonometry
as usual, draw a diagram. You can easily see that if the distance is x, 2000/x = cos 60°
October 17, 2014

Trigonometry
the radius to (2,5) is at an angle θ such that tanθ = 5/2 So cosθ = 2/√29 sinθ = 5/√29 R' is at an angle (θ+45), so x = √29 cos(θ+45) y = √29 sin(θ+45) x = √29 (cosθ cos45 - sinθ sin45) = √29...
October 17, 2014

algebra
let's see what they say: .25q + 1.00d = 34.75 q = 3+4d Now just plug in q and you have .25(3+4d) + d = 34.75 .75 + 2d = 34.75 d = 17 so, q = 3+4d = 71
October 17, 2014

Math
2x^4 + 8/x^4 = 2(x^4 + 4/x^4) = 2(x^4 - 4 + 4/x^4) + 8 = 2(x^2 - 2/x^2)^2 + 8 This has its minimum value of 8 when x^2 - 2/x^2 = 0 x^4 - 2 = 0 x = ±∜2 ----------------------------- If there is only one point of intersection with the line y=x+c, then consider the ...
October 17, 2014

Math
You know that the minimum value is midway between the roots, so it occurs at x = ((-4)+(2p))/2 = p-2 So, we know that 2(p-2+4)(p-2-2p) = 2(p+2)(-2-p) = -2(p+2)^2 = -18 So, p+2 = 3 or -3 So, p = 1 or -5 Check: 2(x+4)(x-2) has its minimum at x = -1 2(3)(-3) = -18 2(x+4)(x+10) ...
October 17, 2014

Math
both correct
October 17, 2014

6th grade
just start listing them. If the order is cats, dogs, pigs, then he could have 12 1 1 11 2 1 11 1 2 10 3 1 10 2 2 10 1 3 and so on. If you look, you may discover a pattern to keep from having to list all of them.
October 17, 2014

Math
Just mentioning the 45 degree angle should have satisfied the teacher, since its sin and cos are both √2/2 IMO
October 17, 2014

Calc
Actually, it's shift 9 down then stretch vertically by 6 a stretch and then a shift is y = 6g(x) - 9
October 17, 2014

Calc
Describe e y = 6(g(x) - 9) as the result of first applying a stretch or compression and then applying a shift to g. First a ____________, by a factor of 6 __________ and then a ____________ by ________ units
October 17, 2014

mathematics
(60cm)(45cm)(x cm) = (54 dm^3)* (1000cm^3/dm^3) x = 20cm
October 17, 2014

calculus
what's the problem? Just use the good old quotient rule.
October 17, 2014

CALCULUS
The cross-section is a trapezoid of area (1+3)/2 * 6 = 12 m^2 So, the volume is 12 * 12 = 144 m^3 with only 1 m of water, the cross-section of the water is a triangle of area 3/2 m^2, so its volume of water is 18 m^3 Thus the pool is 18/144 = 1/8 full At depth y of water, the ...
October 17, 2014

math
You sure there's no typo here? The solution is really a mess: http://www.wolframalpha.com/input/?i=solve+y%22+%3D+3%28y-1%29^2&a=*C.solve-_*SolveWord-
October 17, 2014

calculus
f is decreasing when f' is negative and similarly for increasing f is concave down when f" is negative and similarly for concave up f = 3 + 4xe^-5x f' = 4(1-5x)e^-5x f" = 20(5x-2)e^-5x Hint: e^-5x is never zero
October 17, 2014

calculus
not sure what is the difference between an and {an} Do you mean |an|?
October 17, 2014

calculus
review your 1st and 2nd derivative meanings f' = -6(1+sinx)cosx f" = 6(sinx-cos(2x))
October 17, 2014

Algebra
Not sure what operation @ indicates. Now what all the ? signs are supposed to mean. Clearly the domain is the set of values of x for which f(x) is defined. There appears to be a change of definition in the domain. Is f(x) the same on both sides of that point? ow about using ...
October 17, 2014

math
since time = distance/speed, 8/s + 8/(s+15) = 2 So the speeds were 5 and 20 mi/hr
October 17, 2014

Calculus
well, that would be when p' = 0. So, p' = 50(-e^-x + 2xe^-x^2) You can use your favorite graphing utility or numerical method to find where p'(x) = 0. The graph of p(x) is at http://www.wolframalpha.com/input/?i=50%28e^-x+-+e^-x^2%29%2B10+for+0%3C%3Dx%3C%3D2 If you...
October 16, 2014

math
No idea. Just start listing them, fewest coins first. Then start breaking down into smaller values 50 10 50 5 5 50 5 1 1 1 1 1 50 1 1 1 1 1 1 1 1 1 1 25 25 10 ...
October 16, 2014

Calculus
you want to find where p'(x) has a max p' = 50(2x e^-x^2 - e^-x) See http://www.wolframalpha.com/input/?i=2x+e^-x^2+-+e^-x
October 16, 2014

Calculus..
you want where s' is the same for both particles -4sin(4x) = x^2-x+2 Better use a graphing utility of numeric method. See http://www.wolframalpha.com/input/?i=-4sin%284x%29+%3D+x^2-x%2B2
October 16, 2014

math
you will have factors of 5,10,15,20,25,30,35,40,45,50 which means you will have 5^12 There will be many more multiples of 2, so 10^12 will be a factor Looks like 12 zeros
October 16, 2014

Algebra2
powers of i cycle through. i^0 = 1 i^1 = i i^2 = -1 i^3 = -1 i^4 = 1 and so on. i^100 = (i^4)^25 = 1^25 = 1 I can't figure out what you're asking on the first part.
October 16, 2014

AP Calculus
think of a rectangle. The rectangle with the largest area is a square. So, 30^2 = 900 Any other two numbers with sum=60 will have a smaller product. They will be (30-k) and (30+k), whose product is 30^2 - k^2
October 16, 2014

AP Calculus
If we have base x^2 and height y, 2x^2 + 4xy = 600 v = x^2y = x^2(600-2x^2)/4x = 150x - x^3/2 Now just find x where v' = 0
October 16, 2014

math
If all we are interested in is the number of shares, all the info about their value is just noise. a+b = T a=79 79+b = T b = T-79 a = T-b b = T-a and so on
October 16, 2014

Math
the list must have pairs, working in from the ends. The only such lists I see are C and D
October 16, 2014

math
the definition of π is the ratio of the circumference to the diameter of a circle. So, C/d = π The diameter is twice the radius So, C/2r = π C/r = 2π
October 16, 2014

Algebra
between the two, they cover the 230 ft. So, after Belle has been swimming x seconds, 2x + 5(x-10) = 230 2x + 5x - 50 = 230 7x = 280 x = 40
October 16, 2014

math
Looks unchanged to me. Still A'B
October 16, 2014

Algebra
this is another just like the others. The relative speed of the 2nd car is 10 km/hr faster. In two hours, the 1st car has gone 60km. So, it takes 6 hrs for the 2nd car to catch up. By that time, the 1st car has been going for 8 hours. Or, as Reiny showed you, you want to find ...
October 16, 2014

Math
your inequality is correct. So, 750+35w > 1200 35w > 450 w > 12.8 Since she probably doesn't get paid till the end of the week, that means she'll need to work at least 13 more weeks to have the $1200 saved up.
October 16, 2014

Math algebra Help please
so the area is increased by a factor of 6^2
October 16, 2014

Math
Where's the product. You should have said (2+(n/3))*(a-4) I can see where it might also be (2+n)/3 * (n-4) That assumes that the two numbers are the same. If not, it'd be (2+a)/3 * (b-4)
October 16, 2014

Algebra
the trains are separating at 70+50=120 mi/hr When the 2nd train left, they were already 50 miles apart. So, the remaining 300 miles will take 300/120 hours. Add that to the original hour head-start.
October 16, 2014

Science
which disorder?
October 16, 2014

Math
where did you get the 4? the quotient of a and b is a/b. So, you have the quotient of 2 and the sum of a number and 5 2/(x+5)
October 16, 2014

science
the event is indeed the formation of the rock. From that point on, the strontium in the rock decays, allowing determination of the age of the rock.
October 16, 2014

Physics
Magnetic field = permeability x turn density x current For a solenoid of length L =0.745m with N =350 turns, the turn density is n=N/L turns/m. If the current in the solenoid is I =1.69 amperes and the relative permeability of the core is k =1( air) then the magnetic field at ...
October 16, 2014

Math
n = 2d-1 5n+10d = 855 now crunch the numbers.
October 16, 2014

Algebra
the real problem, as I see it, is that you don't know the formula. How can you be given a problem about perimeters and not have learned how the perimeter is figured?
October 16, 2014

Algebra
you know the perimeter is 2(width + length) So, now you are told that l = 3w and that 2((l+4)+(w-1)) = 102 since l=3w, that means 2((3w+4)+(w-1)) = 102 3w+4+w-1 = 51 4w+3 = 51 4w = 48 w = 12 Now you can figure the original length.
October 16, 2014

Algebra
2((3w+4)+(w-1)) = 102 w=12 2((2x+6)+(3x-1))) = 90 x=8 So, on both problems, you can now figure the answers needed.
October 16, 2014

Calculus
I find it a lot more readable just to use y', instead of all those dy/dx. And, there's no reason to rearrange the equation. arctan(x^5y)=xy^5 1/(1+x^10y^2) (5x^4 + x^5y') = y^5 + 5xy^4y' 5x^4y/(1+x^10y^2) + x^5y'/(1+x^10y^2) = y^5 + 5xy^4y' Now collect ...
October 16, 2014

Algebra
a = 2g-6 5a = 8g Now just solve for a.
October 16, 2014

Math
well, it's clear that cosθ = -1/2 There will be solutions in QII and QIII
October 16, 2014

Pre-Calc/Trig...
you know that if the product is zero, one of the factors must be zero. SO, you have x-3 = 0 or x+2 = 0 The solutions are therefore x = -2 or x = 3. I assume you can now pick the solution with the lower value. Don't forget your algebra I, now that you're taking pre-calc!
October 16, 2014

Math
cosθ = -1/2 solutions in QII and QIII
October 16, 2014

Trigonometry
remember your double-angle formula tan2A = 2tanA/(1-tan^2 A) so, 2tanA/(1-tan^2 A) - 2tanA = -1 2tanA * tan^2 A = tan^2 A - 1 2tan^3 A - tan^2 A + 1 = 0 Hmmm. Nasty. You need to solve 2x^3 - x^2 + 1 = 0 and then take the arctan of whatever solution you find.
October 16, 2014

math
Since B+D-(B&D) = 320, 300 + D - 280 = 320 D = 300 300-280 = 20 buy only DVDs. Or, you can reason that if 300 bought Blu-ray, and 280 of those also bought DVD, then only 20 bought just Blu-ray. So, That means that the remaining 20 bought only DVDs
October 16, 2014

Advanced math
since 1,1,1,1,1... has its function ∞ ∑x^n = 1/(1-x) n=0 take the derivative ∑nx^(n-1) = 1/(1-x)^2 now replace n-1 with n and you have ∑(n+1)x^n = 1/(1-x)^2 generates 1,2,3,4,5,...
October 16, 2014

Math
well, you know the solutions will all be in QI and QIV and you know cosθ = 1/2
October 16, 2014

Advanced math
Take a look here: http://math.stackexchange.com/questions/54961/the-number-of-partitions-of-n-into-distinct-parts-equals-the-number-of-partiti and I think you will see how to build the proof you want.
October 16, 2014

Programming
print "mileage at start" read milesout print "mileage at end" read milesin print "liters consumed" read fuel rate = (milesin-milesout)/fuel print "fuel consumtion rate: ",rate," miles/liter" Now go code it up and adjust the ...
October 16, 2014

Math
check the ratio of successive terms. If it's constant, you have a GP (4x-2)/2x =?= (6x-4)/(4x-2) (2x+2)/(x+1) =?= (5x+1)/(2x+2) Looks like neither to me.
October 15, 2014

math
3√45x-√27x+17√3x-9√125x^3 3*3√5x - 3√3x+17√3x-9*5x√5x -36√5x + 14√3x or, if you will, 2√x (7√3-18√5)
October 15, 2014

8th grade
If cost = revenue for x cameras, then 2050+7x = 17x x=205 Assuming you mean 50 more than the break-even number, then since profit = revenue - cost, p = 17*255 - (2050+7*255) Another way to look at it is that the profit per camera is 17-7=10 dollars. So, with zero profit at 205...
October 15, 2014

Algebra Help
since you have 2x^2, the parabola opens upward So, it must have a minimum, which occurs at x = -16/4
October 15, 2014

Math
you are correct.
October 15, 2014

Trigonometry
I'd do it like this: in QII if sinA = 12/13, cosA = -5/13 in QIV, if sinB = -7/25, cosB = 24/25 So, tanA = -12/5 tanB = -7/24 tan(A-B) = ((-12/5)-(-7/24))/(1+(-12/5)(-7/24)) = (-253/120) / (204/120) = -253/204
October 15, 2014

Math
see a similar problem at http://www.jiskha.com/display.cgi?id=1413396134
October 15, 2014

calculus
For the graph, see http://www.wolframalpha.com/input/?i=+r+%3D+2sin%5E2%CE%B8 For the area, recall that in polar coordinates, a = ∫∫ r dr dθ = ∫[0,2π] ∫[0,2sin^2θ] r dr dθ = ∫[0,2π] 1/2 r^2 dθ [[0,2sin^2θ] = &#...
October 15, 2014

algebra
You will need x lbs, where the ratio of lbs/people remains the same. That is, 3/8 = x/10 30 = 8x x = 15/4 = 3 3/4 lbs Oh, and you'll also need a larger pie pan...
October 15, 2014

Argebra 2
enough for the anticipated pies, I guess. Sure there's not something more you want to tell us? Like how many lbs it takes to make a pie? Or how many cups, or something? If you really don't know any more than this, better look online for recipes, and they'll tell ...
October 15, 2014

Pre-Calc/Trig...
x^2 (x-2)^2 shift right 2 5(x-2)^2 stretch vertically by 5 5(x-2)^2+1 shift up 1 That should help decide.
October 15, 2014

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