Friday

November 28, 2014

November 28, 2014

Total # Posts: 27,042

**Math**

You want x such that x(1.029)^(9/12) = 3262.50 x = 3193.29
*October 20, 2014*

**Math**

If there were n questions, then .80n = 22 n = 22/0.8 = ? Oddly, the result is not an integer. Typo? Rounded score?
*October 20, 2014*

**calculus**

f(t) = 1/3 (9t^2 + t^5) f'(t) = 1/3 (18t + 5t^4) = 1/3 t(18+5t^4) f'=0 where x=0 or ±∜3.6
*October 20, 2014*

**MATHS**

Assuming a typo, I have 6m^2 + 31m + 33 = 0 (2m+3)(3m+11) = 0
*October 20, 2014*

**Calculus**

since e^4x is always positive, and f'(x) = 2x e^4x (2x+1) f'=0 when x=0 or x = -1/2 f' < 0 where x < -1/2 f' > 0 where -1/2 < x < 0 f' > 0 where x > 0 This is clearly shown at http://www.wolframalpha.com/input/?i=+x^2+e^%284x%29+for+-1...
*October 20, 2014*

**Calculus**

f(x) = 2x/(6x+12) f(1) = 1/9 f(4) = 2/9 (f(4)-f(1))/(4-1) = 1/27 The MVT says that there is c in [1,4] such that f'(c) = 1/135 f'(x) = 2/3 (x+2)^-2 So, 2/3 (c+2)^-2 = 1/27 c = 2.24 which is inside [1,4]
*October 20, 2014*

**Math**

just use the double-angle formula: cos2A = 2cos^2 A - 1
*October 20, 2014*

**Math**

what does "2x6x" mean
*October 20, 2014*

**Algebra**

hmmm taht would be when 110-30t = 40 so, just solve for t. Also, lose the "m".
*October 19, 2014*

**Algebra**

Start from 110 feet away, a person on a bicycle rides toward a checkpoint and then passes it. The rider is traveling at a constant of 30m feet per second. The distance between the bicycle and the checkpoint is given by the equation d=(110-30t). At what times is the bike 40 ...
*October 19, 2014*

**physics**

Treat the i and j components separately Also, noting that F = ma, (30.7-12.0+x) = -8.00*2.44 (17.0+8.00+y) = 6.00*2.44 That will give you the third force, xi+yj
*October 19, 2014*

**Math/Science**

Unless you tell us something about the velocity of the resulting 3-bullet lump, there's no way to tell anything about its mass. Also, are the three gun muzzles arranged in a circle parallel to the plane of the target?
*October 19, 2014*

**Calculus**

when the water has height y, its surface has diameter 4/6 y. So, v = 1/3 pi y^2 (2y/3) = 2/9 pi r^3 dv/dt = 2/3 pi r^2 dr/dt Now just plug in your numbers.
*October 19, 2014*

**Calculus**

Draw a diagram. If the boat is x meters from the pier, the rope haas length r, with r^2 = x^2+1 So, 2r dr/dt = 2x dx/dt when x=5, r=√26, so 2√26(-1) = 2(5) dx/dt dx/dt = -√26/5 so, the boat is approaching the dock at about 1.0 m/s Makes sense, since x and r ...
*October 19, 2014*

**Math**

No, (B). A occurs when the degree of deg(p) <= deg(q) C occurs where q(x) = 0 and p(x) ≠ 0 D occurs when deg(p) = deg(q)+1 where deg(p) is the degree of polynomial p(x) You were obviously grasping, since even your suggested answer did not match its description.
*October 19, 2014*

**math**

just google "pyramid area" and plug your numbers into the formula shown.
*October 19, 2014*

**geometry**

Y = ((5-1)/2,(5+5)/2) = (2,5) (-2,2) = ((X1+2)/2,(X2+8)/2) So, X = (-6,-4)
*October 19, 2014*

**Calculus**

the slope of the tangent line at x=a is 1/a. If the line goes through the origin, its equation is y = kx. Clearly, at x=e, the line through (e,1) has slope 1/e. So, a=e see http://www.wolframalpha.com/input/?i=plot+y%3Dlnx%2C+y+%3D+1%2Fe+x
*October 19, 2014*

**math**

each face is an isosceles triangle with base = 26 height = 35.4 I'm sure you know (a) how to find the area of a triangle (b) how many faces the pyramid has plug and chug
*October 19, 2014*

**Calculus**

y' = 4 * 2cos(x^3)(-sin(x^3))(3x^2) = 4(2)(cos 1)(-sin 1)(3) = -10.9 Looks like you got lost somewhere in the chain rule
*October 19, 2014*

**algebra**

since time = distance/speed, then if the first speed was x mph, 600/x = 600/(x+40) + 4 x = 60 Check: outbound: 60 mph: 10 hrs return: 100 mph: 6 hrs
*October 19, 2014*

**Math**

Assuming the ball's diameter is the smallest dimension of the block, it is 10cm in diameter. So, the fraction of the block occupied by the ball is (pi/6 * 10^3)/(14*12*10) = 31%
*October 19, 2014*

**Trigonometry**

draw a diagram. It is clear that tan 24° = (h-6)/70
*October 19, 2014*

**Math**

tanx = sinx/cosx, but (tanx)' = sec^2(x) 1 + .5(9/4) + 4 = 6.125
*October 19, 2014*

**College Algebra 1**

-4(x+9)^3(x-11)^4(x+6)>0 Since the (x-11)^4 is always positive for x≠11, and the -4 is always negative, and n^3 has the same sign as n, you really just have to worry about (x+9)(x+6) < 0 In between -6 and -9, x+9 > 0 and x+6 < 0, so the interval you need is...
*October 19, 2014*

**college algebra**

that said, here's a tip: 2x^2+x-21 = (2x+7)(x-3)
*October 19, 2014*

**college algeba**

First off, how about typing r(x) on one line? Is there a division in there somewhere? If so, do you mean r(x) = 6x/(x+8) ?? Whatever r(x) is, to evaluate at some value, just substitute that value in everywhere there's an x: r(2) = (6*2)/(2+8) = 12/10 Now just plug and chug...
*October 19, 2014*

**college algebra**

it drops 6000/year, so you will have -6000t in there somewhere. v started at 80000 That should do it.
*October 19, 2014*

**Algebra**

-6-2 = -8 5-(-3) = 8 ... so the subtrahend starts out with 2x^4-3x^3... Just look at the coefficients of like powers. They threw you a curve by scrambling up the order of the powers. The first step would be to write the polynomials in descending order, so it's easier to ...
*October 19, 2014*

**calculus**

If I read your formula correctly, f(x) = 12x cos(5x)-(30√3 x^2) + 16 The slope at any point on the curve is f'(x) = 12(cos5x - 5x(sin5x + √3)) So, the equation of the tangent line at x=h is y-f(h) = f'(h)(x-h) y-(12h cos(5h)-(30√3 h^2) + 16) = (12(...
*October 19, 2014*

**Math**

the new area is (1.1L)(0.9W) = 0.99 LW so now you can tell how much the area has changed.
*October 19, 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 = 4.16 m = 1.85
*October 19, 2014*

**Algebra**

Look for the low-hanging fruit first. No easy roots, like 1 or 2, but we do find F(x) = (x+4)(2x^3-13x^2+32x-13) =(x+4)(2x-1)(x^2-6x+13) Now use the quadratic formula for the complex roots. This one was a little messy, since the roots took a little trial and error. Synthetic ...
*October 19, 2014*

**math**

well, 5*4*3 = 60 so, r = 3
*October 19, 2014*

**algebra**

If |a+5| = 9, either a+5 = 9 or a+5 = -9 So, a = 4 or -14
*October 19, 2014*

**algebra**

f(x) = (2x+7)(x-3)
*October 19, 2014*

**Math**

you know the minimum value is midway between the roots, which are -4 and 2p. So, the vertex is at x = (-4+2p)/2 = p-2 So, now we want the y-coordinate of the vertex, which is y = 2(p-2+4)(p-2-2p) = 2(p+2)(-p-2) = -2(p+2)^2 If that is -18, then -2(p+2)^2 = -18 p+2 = ±3, ...
*October 19, 2014*

**math**

#2 x and y are related, but not directly or inversely. C and D are just nonsense. Weird question and answers. divide $780 into 4 parts of $195 each one part into savings, 3 parts into checking. So, $195 into savings $585 into savings
*October 19, 2014*

**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*

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