Wednesday
October 22, 2014

Posts by steve


Total # Posts: 25,978

physics
no idea - what is it filled with?
October 22, 2014

statistics
12500 rec * 30min/rec * 1hr/60min * 1emp/2080hr = (12500*30)/(60*2080) = 3.0 emp
October 22, 2014

math
pure gold is 24K, so 22K gold is 22/24 = .917 18K gold is 18/24 = .750 14K gold is 14/24 = .583 The problem clearly has a typo when it mentions 18K gold. A 22K statue the same weight as a 14K statue contains more gold. The difference is (22-14)/24 * 73.5 or, given all the ...
October 22, 2014

math
15*852 = 12,780 assuming all those who bought tickets watched the show ...
October 22, 2014

Math
well, check your math. Starting with $60, that means 20 on books, leaving 40 16 on games, leaving 24 6 on DVD, leaving 18 3 on candy, leaving 15 We have a winner! Your final step in concluding that if 1/4 of the money is $15 then the whole was $60 is correct. But your original...
October 22, 2014

physics
s = vt + 1/2 at^2 Now just plug in v=247, a=28, t=8.7
October 22, 2014

math
if the model has diameter 31.9 cm, its area is π*31.9^2 = 3196.92 cm^2 So, divide that by 2 and then by 10 to get the number of jars
October 22, 2014

Math 222
in the first, each term contains a power of a and a power of b. You need to find the highest power of a and b that divides each term. That would look like a^2 a^2 b + a^2 b^2 b Now factor out the a^2 b, leaving the indicated solution. Recall that a^m a^n = a^(m+n) Review the ...
October 22, 2014

physics
constant speed means zero acceleration!
October 21, 2014

Math 222
I assume you want to factor the expressions? a^4b + a^2b^3 = a^2b(a^2+b^2) z^2 + 18z + 45 = (z+3)(z+15)
October 21, 2014

calculus
arcsin(ix) = i arcsinh(x)
October 21, 2014

math
600rev / (44 8/9 rev/min) = 13 37/101 min
October 21, 2014

Physics
(83.59)(1.44/9.81)
October 21, 2014

math
come on 1/2 = .5000 2/3 = .6666 So, anything in between, such as .58345... .66217...
October 21, 2014

math
24/18 = 4/3 6.12/4.5 = 1.36 That's pretty close to the same ratio, so just scale up by 18/4.5 = 4 Just multiply each dimension by 4. That will produce a size of 18 by 24.48
October 21, 2014

Math
the sides are 22,x,2x-2, so we have 2x-2-x < 22 < 2x-2+x x < 24 < 3x So, it looks like 8 < x < 24
October 21, 2014

Trigonometry
what you have is cosθ + 1 = 2cos^2θ - 1 2cos^2θ - cosθ - 2 = 0 so, solve that quadratic for cosθ and pick the choice.
October 21, 2014

Algebra
d = 2q 5n+10d+25q = 440 There will probably be no single solution, since you only have two equations.
October 21, 2014

Math HELP!
A. No - 3.2 is real, not integer B. true C. No - 2/3 is not a perfect square D. No - NO integer is irrational You were just guessing, I presume.
October 21, 2014

math
there is only one answer. I guess they want you to attack it in three different ways. Seems kind of pointless to me.
October 21, 2014

maths
just set up the equations: a+2d + a+6d = 38 a+8d = 37 Now just solve for a and d.
October 21, 2014

Algebra
the second car is going 15 mph faster than the first when the 2nd cars starts out, the 1st car has gone 50 miles already. So, how long does it take to make up 50 miles, going a relative speed of 15 mi/hr?
October 21, 2014

Math
just set up two expressions for the costs, and set them equal. For m minutes, you want .08m = 6.00 + .02m Now just find m which makes the two values equal.
October 21, 2014

Algebra: Answer Check
looks good to me.
October 21, 2014

Calculus
It appears you are trying to approximate ∛7.9 So, if y = ∛x, then dy = 1/(3∛(x^2)) dx at x=8, y=2, so if dx = -0.1, dy = 1/(3∛64) (-0.1) = -1/240 = -.0042 So, ∛7.9 ≈ 1.9958 check: ∛7.9 is 1.9916 The estimate is expected to be a bit ...
October 21, 2014

Homework (Science)
it hits the ground when the height is zero. So, just solve 32.5t - 4.9t^2 = 0
October 21, 2014

Math
consecutive integers differ by 1. Pick any two adjacent elements of the list below: 1,2,3,4,5,6,7,8,9,... For example, 6 and 7. Those are consecutive integers. SO, you have two numbers, a=n and b=n+1 n/2 + (n+1)/2 = (n + n+1)/2 = (2n+1)/2 = n + 1/2 Since n is positive, n >...
October 21, 2014

Algebra
Change the 60 to -60 and then the underlined portion will be correct. Changing the underlined 20 to -20 would also work, but then you have nonsense: -3 < N < -20 which cannot be true for any value of N If you know about tags, you can use the u and /u tags to enclose ...
October 21, 2014

math
229 is clearly bogus! That is below the mean! I get 1.75 std above the mean for the top 4% better check that figure again.
October 20, 2014

Pre-Calc
(T-A)/(To-A) = e^-kt We have (60-93)/(45-93) = e^(-23k) e^(-23k) = .6875 k = .0163 So, now we want to find when T=77 e^(-.0163t) = (77-93)/(45-93) = 0.333 t = 67.4 minutes Nice model, but I'm sure that in real life, after more than an hour, that pop is very nearly 93 degrees!
October 20, 2014

Math
10 ∑(2k+4) = 144 k=2 You want to find the upper summation limit for the other values. So, what is n ∑(2k+4) = n(n+5) k=1 Note that Sum(2,10) = sum(1,10) - sum(1,1) = 150-6 = 144 Sum(4,12) = Sum(1,12)-Sum(1,3) = 204-24 = 180
October 20, 2014

Math 11
(A) 19 cot25° + 26.8 cot47° (B) 19 csc25° + 26.8 csc47° Draw a diagram and review your basic trig function definitions
October 20, 2014

math
how many digits? You could have anything from 2 to 11111111...2 where there are 98 1's
October 20, 2014

calc
so, how many intervals? Give us your idea of a table of values for the approximation.
October 20, 2014

calculus
f'(x) = 2x-5 f'(1) = -3 So, the line with slope -3 through (1,-2) is y+2 = -3(x-1) Not sure what your four-step process is.
October 20, 2014

Math
18 boys play something. If b play both, then 13+15-b = 18
October 20, 2014

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

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