Tuesday
September 2, 2014

Posts by Steve


Total # Posts: 24,565

geometry
gain of what? perimeter will gain 10% area will grow by a factor of 1.1^2 = 1.21, or 21%
May 18, 2014

average and instantaneous rate of change
average is measured over some finite time interval. Instantaneous is not. It is the limit of the average rate, as the measured interval decreases to zero.
May 18, 2014

algerbra
Ethan donates 1/25 of which money? His earnings, the total earned, the total donated, or what?
May 17, 2014

math
you can convert the hours to minutes 14 X 60 = 840 then add the 3 minutes 840 +3 =- 843 then divide 843/3 = 281 then divide by 60 = 4 hours and 41 minutes
May 17, 2014

Math
Simplify the expression 14 to the minus 4 power
May 17, 2014

Math
Simplify the expression (-8x) times 3x squared
May 17, 2014

Math homework help
AG CE FH
May 17, 2014

Math
5+3√2
May 17, 2014

Calculus
the 3.02375 is correct, but you lost a factor of 10^-8 So, what you really have is .03 micrograms
May 17, 2014

Math - Bazinga!
you gotta be kidding. I suggest you pick out one or two of the types of questions that bother you, post your solutions, and we can check and/or critique them.
May 17, 2014

Algebra
.85^4
May 16, 2014

Calc Help Please Again!
the volume is just a stack of thin discs, of thickness dx, and radius y So, the volume is the integral of pi * y^2 dx = pi*(e^2x + 8e^x + 16) all pretty straightforward. C'mon back if you get stuck, and show where.
May 16, 2014

Algebra 1
first, draw the asymptotes. Then pick a few values of x near the vertical asymptotes, so you get a feel for how y behaves in that region. Then pick a few more values a little farther away, and draw the curve, keeping in mind that it will approach the horizontal asymptote on ...
May 16, 2014

trigonometry
tanθ=1/7 means sinθ=1/√50 cos 2θ = 1-2sin^2θ = 1-1/25 = 24/25 tanØ=1/3 means sinØ=1/√10 and cosØ=3/√10 sin2Ø = 2sinØcosØ = 3/5 so, cos2Ø = 4/5 sin4Ø = 2sin2Øcos2Ø = 24/25
May 16, 2014

algebra
not geometric. The ratio between terms changes. What you have is a modified Fibonacci sequence, where for n>=2, T(n+1) = 2*(T(n-1)+T(n))
May 16, 2014

trig
Assuming L is the right angle, the other two angles are complementary cos(N) = sin(90-N) = sin(M) the co- in cosine, cotangent, cosecant means "complementary" as in complementary angle.
May 16, 2014

chemistry
how many moles in 13g of CS2? The equation tells you that it takes 5 times that many moles of C. same for SO2. Figure the moles of C, then take 2/5 that many of SO2. Then go back to grams. Again, figure the moles, and recall that one mole of a gas occupies 22.4L at STP.
May 16, 2014

math(urgent)
well, of course they have two answers. They wanted to know the amount invested at each of two interest rates! So, what don't you understand? They gave you the equation. If P1 is invested at 12% (which is evident from the equation), then the rest of the money (30000-P1) was...
May 16, 2014

geometry
draw a diagram of a vertical cross-section of the cone, and mark off the altitude. You have a right triangle. The radius of the base is found from r/7.5 = cot(70)
May 16, 2014

business and finite calc
28000 is 0.666 std below the mean 35000 is 2.666 std above the mean. Now go to your Z table. Or, you can play around with this stuff at http://davidmlane.com/hyperstat/z_table.html
May 16, 2014

math
I assume you mean y=2^x and y=-2^x plot them just as you would any other functions. Mark off some points on the x-axis, and calculate the y values, then plot the points. x 2^x -2 1/4 -1 1/2 0 1 1 2 2 4 ... -2^x is just -(2^x), so it is below the x-axis, instead of above it. To...
May 16, 2014

physics
the distance s(t) = 12t - t^2 + c for some c. Since s(1) = -10, c=-21, and so s(t) = -21 + 12t - t^2 a = dv/dt = -6t so just plug in t=4 plug in t= 0 and 10 to find where the particle is at each time, then get the displacement by evaluating s(10)-s(0)
May 16, 2014

algebra - typo?
do you mean two numbers a and ar such that a+ar=28 and a*ar = 512? If so, then there's no real solution. Maybe there's something wrong with the way the problem is presented, eh?
May 16, 2014

Algebra
#1 There must be a typo here. Not factorable #2 (x^2-25)(x^2+4) now it should be easy #3 a little tinkering shows that you have (x+3)(x^2-6x+13) again, complex roots.
May 16, 2014

Math - Int Trig
#31 since f'(x) = -3x^2+2 the extrema are at x = ±√(2/3) f' > 0 for -√(2/3) x < √(2/3) so f is decreasing on that interval, and increasing elsewhere. #32 Since f(x) is odd, and the x^3 coefficient is -1, it rises to the left and drops to ...
May 16, 2014

Math - Algebra2
#1 surely you don't have to ask about this one -- the terms get ever larger #2 is simply a geometric series, with |r| < 1, so it converges.
May 16, 2014

Math
actually, you start with one bacterium. You need a function that doubles every time you add 1 to the time. You probably already are aware that this models exponential growth, so what such function doubles as needed? 2^x does the job. So, starting at time x=0, at time x hours ...
May 16, 2014

Calculus
clearly f(x) increases as x increases, since the slope is always positive.
May 16, 2014

Math problem or trick
sounds like it to me, since no one (probably) was wearing both.
May 16, 2014

pre algebra
so, what's the trouble? Just fill in the table x x^2 : x-x^2 0 0 : 0-0 = 0 1 1 : 1-1 = 0 2 4 : 2-4 = -2 and so on for whatever values you want.
May 16, 2014

pre algebra
Write a table for the following quadratic function. y = x - x squared
May 16, 2014

pre algebra
Write a quadratic function rule for the following table x -10 -5 0 5 10 y 80 5 -20 5 80
May 15, 2014

algebra
well, what is 3500 + 200 ln(1000) ??
May 15, 2014

Finite Math
P(even,~8) = P(2,4,6,10,12) = 1/36 + 3/36 + 5/36 + 3/36 + 1/36 = 13/36 P(8) = 5/36 P(odd) = 1-(13/36 + 5/36) = 1/2 So, Fred gets 8*13/36 + 1*5/36 - 2*1/2 = 73/36, or about $2
May 15, 2014

Calculus
what is the slope? (f(x1)-f(x2)) / (x1-x2) both are positive, so the slope is always positive.
May 15, 2014

math
what you mean is .25x = 20 x = 80
May 15, 2014

MAT 201
10 days is 1.33 std below the mean 21 days is 2.33 std above the mean just consult your Z table.
May 15, 2014

Science
most important factor: do not watch the clock!
May 15, 2014

Maths
x y 30 84 90 74 So, every extra 60 trees reduces the yield by 10kg, so y = -(10/60)x + c Since y(30)=84, (-1/6)(30)+c = 84 c=89 y = -x/6 + 89 The total yield is trees * avgyield, so x(-x/6+89) = -x^2/6 + 89x This is just a parabola, where the vertex is at x = 3*89 You can ...
May 15, 2014

Physics
the police car is moving 20 km/hr faster, and must make up 1.6km. That will take 1.6km / 20km/hr = 1.6/20 hr No idea when that will be...
May 15, 2014

ALGEBRA
First step: sort the values from low to high. mean: add them up and divide by how many values there are median: the middle value -- same number less as greater. If there are an even number of values, take the average of the two center values. mode: The value(s) which occurs ...
May 15, 2014

Math (functions)
just substitute in 1,2,3,4,... for n 3*1+5 = 8 3*2+5 = 11 3*3+5 = 14 3*4+5 = 17 Or, just start with 8 and keep adding 3 for the next terms.
May 15, 2014

Math (functions)
It is indeed. Since f(x) = 3x-2 for f(1.5), everywhere you see an x, replace it with 1.5 and then do the math.
May 15, 2014

chemistry pls help me asap
.96g of O2 is .03 moles So, since it takes 2 moles of Y to combine with 3 moles of O, and we have .03 moles of O2 (.06 moles of O), we have .04 moles of Y. So, the molar mass of Y is 2.08/.04 = 52
May 15, 2014

Algebra
4x+7 < 11 4x < 4 x < 1 1-x <= -2 -x <= -3 x >= 3 so, x<1 or x>=3 see at http://www.wolframalpha.com/input/?i=solve+4x%2B7%3C11+or+1-x%3C%3D-2
May 15, 2014

Math
3 mi * 15 min/mi = 45 min
May 15, 2014

math(urgent)
what you have done is calculate the first year's growth. Now you have to add the 2nd year: 1000(1+.08)^(2-1) = 1080.00 Then the third year: 1000 1166.40+1080.00+1000.00 = 3246.40 As you can see, for n years, you would have 1000(1+1.08+1.08^2 + ... + 1.08^(n-1)) = 1000(1.08...
May 15, 2014

Math
(1/4) / 3 = 1/12 think about it. If you cut a yard into 4 pieces, and then cut each of those (1/4 yard) into 3 pieces, there are now 12 equal pieces, of 1/12 yard each.
May 15, 2014

geometry
17ft * 17ft * 4 ft = 1156 ft^3 Now to convert that to $, 1156 ft^3 * (1yd/3ft)^3 * $50/yd^3 = $2140.74
May 14, 2014

Geometry
a little inspection (or drawing) will reveal that ABCD is a rectangle with width=3 and height=2 EFGH is a rectangle with width=6 and height=4 Since the width and height have both been scaled by 2, the two rectangles are similar.
May 14, 2014

Help me trig.
tan(t/2) - sint = 0 (1-cost)/sint = sint 1-cost = sin^2 t 1-cost = 1-cos^2 t cost(1-cost) = 0 cost = 0 or 1 t = pi/2,pi,3pi/2 see http://www.wolframalpha.com/input/?i=solve+tan%28t%2F2%29+%3D+sint+for+t%3D0..2pi
May 14, 2014

Calculus
use the product rule y = sinx tan^3(x) y' = cosx tan^3(x) + sinx (tan^3(x))' for tan^3(x), use the chain rule and you get y' = cosx tan^3(x) + sinx(3tan^2(x) sec^2(x)) Now we can massage things a bit: sin^3/cos^2 + 3sin^3/cos^4 sin^3*cos/cos^3 + 3sin^3/cos^4 tan^3(...
May 14, 2014

Algebra
first step: what does 4x7 mean?
May 14, 2014

geo
well, we know that with center at (h,k) the circle's equation is (x-h)^2 + (y-k)^2 = 100 Since (20,10) is on the circle, at one end of the horizontal diameter, it is clear that the center of the circle is at (10,10). (x-10)^2 + (y-10)^2 = 100 Getting the triangle's ...
May 14, 2014

Algebra
solve for what? Also, is the denominator m, or (m+1)?
May 14, 2014

math/patterns
Hmmm. That 9 at the start is perplexing. For the other terms, each increases by 5, so the millionth term after the 16 should be 16+5million = 5,000,016. If you can fix the 9 issue, it becomes quite easy.
May 14, 2014

Algebra 1B
log(x^3) = 2
May 14, 2014

ALGEBRA
4√6 / √30 multiply top and bottom by √30 to get 4√6√30 / 30 4√180 / 30 4√36√5 / 30 4*6√5 / 30 4√5/5 Or, 4√6/√30 4√(6/30) 4√(1/5) 4/√5 4√5/5
May 14, 2014

Calculus
just the chain rule y = u^2 where u = tan(v) and v = x^4 y' = 2u u' y' = 2u sec^2(v) v' = 2u sec^2(v) (4x^3) = 8x^3 tan(x^4) sec^2(x^4) and, as usual, you can massage trig functions in various ways.
May 14, 2014

Math
x = 2z y = 2a x < y 2z < 2a z < a
May 14, 2014

Álgebra
raise both sides to the 3/4 power: z+2 = 4^(3/4) z+2 = 2^(3/2) z+2 = 2√2 z = 2(√2-1)
May 14, 2014

Geometry
4v = (4,8) w = (3,-4) so, now just subtract them
May 14, 2014

Math, Please Help
since the terms are number an, then n is any integer from one onward. n>=1. since a4 = a1*r^3, 1024r^3 = -16 r^3 = -16/1024 = -2^4/2^10 = -2^-6 So, r = -2^-2 = -1/4 a6 = a4*r^2 = -16 * 1/16 = -1
May 14, 2014

precalculus
We have a circle and a straight line. So, either the line intersects the circle in two points, or it is tangent at just one point, or it misses the circle entirely. Since y = 4-x, plug that in to get x^2 + (4-x)^2 = 10 x^2 + x^2 - 8x + 16 = 10 2x^2 - 8x + 6 = 0 Since b^2-4ac ...
May 14, 2014

Calculus
easy way: sin2x/cos2x = tan2x so the derivative is just 2sec^2(2x) hard way, using the quotient rule: [2cos(2x)cos(2x) - sin(2x)(-2sin(2x))]/cos^2(2x) 2(cos^2(2x)+sin^2(2x))/cos^2(2x) 2/cos^2(2x) 2sec^2(2x)
May 14, 2014

math
assuming simple interest, 50000*(3/4)*r = 4500 r = 4/3 * 4500/50000 = .12 or 12%
May 14, 2014

math
since you add exponents when multiplying, you just need to find three ways to add numbers to get 11: 5^11 = 5^3 * 5^8 5^11 = 5^0 * 5^11 5^11 = 5^-4 * 5^15 There are lots of other ways; not quite so many if you insist on only positive powers.
May 14, 2014

Algebra
solve just like regular equations, working both at once. -4 <= 3+7x < 24 subtract 3 everywhere to get -7 <= 7x < 21 now divide through by 7: -1 <= x < 3
May 14, 2014

Algebra - eh?
I just see one, and yes, -4 <= 10
May 14, 2014

Math
2900*e^(.04*6)
May 14, 2014

Math
this is just a simple arithmetic progression, with a = 19 d = 1 Since there are 27-9+1=9 rows, S9 = 9/2 (19+27) = 207
May 14, 2014

Pre-Calc
First question: Of the 27 customers, how can there be 25 happy and 3 unhappy? in any case, just some the geometric progression, using the ratio r=3 or 6, as appropriate.
May 14, 2014

math - typo?
just put the clues into symbols: x+y+z = 15000 x = y+z+3000 3x+2y+2z=30000 or, x+y+z = 15000 x-y-z = 3000 3x+2y+2z = 30000 adding the first two, we get x = 9000 so, y+z = 6000 But then 3x+2(y+z) = 39000 Did I miss something? If so, fix it and then apply the same steps.
May 14, 2014

Geometry
looks like it to me. Though the phrasing is strange. Better would be the angle of rotation of line l with respect to line m
May 14, 2014

Pre-cal
A) log(x+1)+3logx log(x+1)+log(x^3) log (x+1)(x^3) log(x^4+x^3) B) 2log(np)-3log(p) log((np)^2)-log(p^3) log(n^2p^2)-log(p^3) log(n^2p^2/p^3) log(n^2/p) the base 4 is not important. These steps hold regardless of the base. If the base is not 4, but the 4 is included in the ...
May 14, 2014

Math
just multiply x and y by 3.
May 14, 2014

math
you can play around with such problems here: http://davidmlane.com/hyperstat/z_table.html
May 14, 2014

Algebra
h(t) = 2+25t-4.9t^2 h=12 when 2+25t-4.9t^2 = 12 t= 0.44 and 4.66 seconds
May 14, 2014

Math
1/x = 1/1 + 1/2 = 3/2 x = 2/3
May 13, 2014

math
12:45 - 6:15 = 5.5 hours That's 1 hour plus 9 additional half-hours.
May 13, 2014

Intermediate Algebra
f(x) = 3x^2-5x+1 g(x) = 2x-5 (fog)(x) = f(g) = 3g^2-5g+1 = 3(2x-5)^2 - 5(2x-5) + 1 = 3(4x^2-20x+25) - 5(2x-5) + 1 = 12x^2-60x+75-10x+25+1 = 12x^2-70x+101 Looks like you messed up on the -5(2x-5) part
May 13, 2014

Math 6th Grade
next time don't list your choice on the same line as an incorrect answer. you are correct
May 13, 2014

Math 6th Grade
look at the number line. -15 is to the right of -21 So, -15 > -21 you are correct, though placing your choice on the same line as an incorrect answer threw me for a second...
May 13, 2014

Calculus
use the chain rule y = f(u(x)) y' = df/du * du/dx here, u = -x, so dy/dx = 5cos(-x)(-1) = -5cos(-x) which, since cos(-x)=cos(x), is -5cos(x) Or, you can note that sin(-x) = -sin(x), so what you have is y = -5sin(x) y' = -5cos(x)
May 13, 2014

Math
can we assume that no student is in more than one group? If so, then we want 190/545 * 360 degrees.
May 13, 2014

Trig 2
Hmmm. I think what we have here is a failure to communicate... The graph of sin(2x) is here. You can plainly see that it reaches its maximum at x = pi/4. http://www.wolframalpha.com/input/?i=sin%282x%29 Not sure what quadratic you are referring to. If you instead meant sin^2(x...
May 13, 2014

Trig 2
sin(2x) is always between -1 and 1. Since sin(pi/2) is the first time that it reaches 1, sin(2x)=1 when 2x = pi/2 That is, when x = pi/4 If you don't know wtf, just take a look at the graph and see where it reaches its maximum.
May 13, 2014

alegbra
what, no calculator? 150((1+.8/1)^(40)-1)/(.80*1) I'm assuming n=1, since you don't say... you can figure the answer, but I seriously doubt there is an 80% annuity out there...
May 13, 2014

Trig help
the period of cos(kx) is 2pi/k So, cos(pi x) has period 2 #2 pi/3
May 13, 2014

math
4/50 * 3/49
May 13, 2014

Precalculus
the center says that the ellipse is (x-2)^2/a^2 + (y+3)^2/b^2 = 1 Since both vertex and focus are at y=-3, the long axis is horizontal. 5-2=3, so a=3 3-2=1, so c=1 b^2+c^2 = a^2, so b^2 = 8 (x-2)^2/9 + (y+3)^2/8 = 1 graph and analysis at http://www.wolframalpha.com/input/?i=...
May 13, 2014

Geometry
Euler's Theorem says that OH^2 = R(R-2r) where r is the inradius Hmmm. I'll have to think on how to figure r without knowing a,b,c...
May 13, 2014

Math - Trigonometry
If we label the diagram as follows: P = plane A = point on ground just below the plane B = airport C = town we want to find BC 2.3/AB = tan 32 2.3/(AB+BC) = tan 18 eliminating the AB we have 2.3/tan32 = 2.3/tan18 - BC Now just solve for BC.
May 13, 2014

Calculus
the first place where e^x = x^3 is near x = 1.857 So, we have a narrow strip extending from x=0 out to about (1.857,6.406) The solid is a set of triangles of base e^x-x^3 and height 3 times that. So, the volume of the solid is v = ∫[0,1.857] (1/2)(e^x-x^3)* (3)(e^x-x^3) ...
May 13, 2014

Algebra 2 help please
the angle is in QII, so pi-(2pi/3) = pi/3
May 13, 2014

Algebra 1
rearrange things just a bit and you have 5y^2-20 - y^2z + 4z 5(y^2-4) - z(y^2-4) (5-z)(y^2-4) (5-z)(y+2)(y-2)
May 13, 2014

Algebra
correct
May 13, 2014

Algebra
#1 correct #2 correct, if you consider all the players as identical. good work.
May 13, 2014

Algebra 1 Answer Evaluation
Looks good to me. Did you try plugging in your point to see whether it fits the equation? That's always a good first step.
May 13, 2014

Calc
(a) (f(3+.03)-f(3))/.03 = (3.1209-3)/.03 = 4.03 (b) f'(x) = 2x-2 f'(3) = 4 (c) f(3) = 3 So, now you have a point and a slope. The line is easy to express. (d) Now just plug 2.98 into that line. (e) where is f'(x) = 0?
May 13, 2014

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