Thursday
October 30, 2014

Posts by steve


Total # Posts: 26,245

solve long divison polynomials
A good site for long division is ath calc101.com Just click on the "long division" tab to see all the details, in proper formatting.
October 5, 2014

cobet, maths
Umm, didn't you just say that 33 like both?
October 5, 2014

calculus
First off, I suspect a typo. Why have two y^2 terms? I figure you meant x^2 + 4xy +4y^2=40 Just do things term by term, and don't forget the product rule: 2x + 4y + 4xy' + 8yy' = 0 y'(4x+8y) = -(2x+4y) y' = -1/2 Weird, huh? Not if you note that x^2 + 4xy +...
October 5, 2014

math
Ummm. First off, what do M and O have to do with the length of AB?
October 5, 2014

Math
4x^2+4y^2-8x-20y+13=0 rearrange things a bit and you get 4x^2-8x + 4y^2-20y = -13 4(x^2-2x) + 4(y^2-5y) = -13 Now complete the squares: 4(x^2-2x+1) + 4(y^2-5y+25/4) = -13 + 4(1) + 4(25/4) 4(x-1)^2 + 4(y - 5/2)^2 = 16 (x-1)^2 + (y - 5/2)^2 = 4 Now does it look familiar?
October 5, 2014

Math
what's to solve? You have just defined a function.
October 5, 2014

physics
The situation can be modeled as though the 1st tank were stationary, and the 2nd tank were retreating at 20 m/s. The horizontal and vertical components of the shell's speed at firing are x: 43.4 m/s y: 246.2 m/s So, the height of the shell is h(t) = 246.2t - 4.9t^2 It hits...
October 5, 2014

Algebra
father's age is f. My age is m. (f-4) = 4(m-4) f+m = 53 Now just solve for f and m.
October 5, 2014

Pre-Calc
well, it's just f(x)/g(x) = (1/x)/(x^3) = 1/x^4 And I'm sure you can figure the domain. It's where the denominator is not zero.
October 5, 2014

Math
clearly, it's b and c try dividing out the x^2 factor
October 5, 2014

Calculus
You have ∫√(u^2-a^2) du, so set u = a secθ du = a secθ tanθ u^2-a^2 = a^2 tan^2θ so it becomes ∫ (a tanθ)(a secθ tanθ) dθ = a^2∫secθ tan^2θ dθ = a^2∫sec^3θ - secθ dθ Now, we all...
October 5, 2014

Calculus
well, if y = sin^2(u) y' = 2 sinu cosu u' u' = ln3 3^x y' = 2ln3 3^x sin(3^x) cos(3^x) = ln3 3^x sin(2*3^x) I think you got some of your 3's mixed up as powers of sin. You appear to have taken the derivative of sin^3 (3^x)
October 5, 2014

Algebra 2 (Please, help me!)
Take |x| shrink it horizontally by a factor of 2: |2x| shift it down 3: |2x|-3 Now shrink it vertically by a factor of 4: (|2x|-3)/4 http://www.wolframalpha.com/input/?i=plot+y%3D|x|%2C+y%3D%28|2x|-3%29%2F4
October 4, 2014

Math
Since the border is on both sides, 5 + 2(2 1/4) = 9.5 7 + 2(2 1/4) = 11.5 2(9.5+11.5) = 42
October 4, 2014

Math
X^2+4x=10 x^2+4x+4 = 10+4 (x+2)^2 = 14 x+2 = ±√14 x = -2±√14
October 4, 2014

Math
that will of course be x miles where 100+.60x = 50+.80x
October 4, 2014

algebra
How could a quadratic be anything like a linear function?
October 4, 2014

algebra
You could think of it as a shifted parabola, where 2x+3(x-2)^2 = 3(x-2)^2 + 2(x-2) + 4
October 4, 2014

algebra
Is there a question in there somewhere?
October 4, 2014

Calculus
the indicated line has slope -1. y' = 6x+4 6x+4 = -1 when x = -5/6 y(-5/6) = -5/4 So, the line is y = -(x+5/6) - 5/4 http://www.wolframalpha.com/input/?i=plot+y%3D3x^2%2B4x%2C+y+%3D+-%28x%2B5%2F6%29+-+5%2F4
October 4, 2014

Physics
How long does it take to drop 785m? 4.9t^2 = 785 Then the horizontal distance traveled in that time is 53.5t
October 4, 2014

Algebra
z- 1/5 > 1/4 My answer is z < 9/20
October 4, 2014

Physics
think on it. If the angle of elevation is 0, a = 0 if x = 90 degrees, a = g So, what trig function has its zero at x=0, and its max at x = 90 degrees?
October 4, 2014

Algebra
If m play in marching band, then m+250-130 = 375 m = 255 How did you arrive at 135? I can see 125, but not 135. Anyway, the question was not "how many play only in the marching band?"
October 4, 2014

math
Let x be the number of 10-person increases. So, since revenue is price*people, R(x) = (200+10x)(30-1.50x) That is just a parabola, with its vertex midway between the roots, at x = (-20+20)/2 = 0 That is, max revenue for just 200 people. That is assuming that the price decrease...
October 4, 2014

Algebra
3*85 <= 83+91+x <= 3*90 255 <= 174+x <= 270 81 <= x <= 96
October 4, 2014

Algebra
correct. But I suspect that was not really the question. If the question was asking for P', then that would be {2,4,6,8} When talking about sets, it's better to use the braces; otherwise, you just have a list, not a set.
October 4, 2014

Algebra
Hmmm. You think 5 is a factor of 16? If so, you need to review the term "factor". Better prune your list a bit.
October 4, 2014

AP Statistics
From the Z table, the 10% tail is 1.282 std from the mean. Since the 10% tail is used on both ends, the mean is halfway between where the tails start. That help?
October 4, 2014

algebra
x=1, y=2: x+y=3, 3x+2y=9 (8)(9)(x+y)/(3x+2y) = 24
October 4, 2014

Science
correct again.
October 3, 2014

Physics
Oops -- v = -9.8t
October 3, 2014

Physics
horizontal speed is constant: 30.9/3.03 m/s The vertical speed is v = at = -4.9t The angle x is such that tan(x) = Vy/Vx
October 3, 2014

Physics
the height is h(t) = 20.7t - 4.9t^2 That's just a parabola; the max height is at the vertex. Now just solve for t when h=0. To save yourself some work, the max height is reached at the center of its flight, so you really only need to calculate one of the above answers, ...
October 3, 2014

Science
You are correct.
October 3, 2014

math
6^2 = 36 1+3+5+7+9 = 25 + 4 = 29 2^5 = 32
October 3, 2014

math
200 * 0.1 = ? Ever hear of a calculator?
October 3, 2014

Math
True, but we also have (a+9)(a+16) = a^2 + 25a + 144
October 3, 2014

one last difference (math)
I think you need to reword your question. 1.2 is the fraction less than 1.8 Now, if you want to know how much less than 1.8 1.2 is, then of course that would be 1.8-1.2 = 0.6
October 3, 2014

math
So, did you use the table?
October 3, 2014

math 156
P(1+.04/4)^(4*6) = 35000 Now just solve for P.
October 3, 2014

math
Just match the values in pairs. A. Each pair adds up to 1002 B. Each pair adds up to 100 Now just figure out how many pairs there are.
October 3, 2014

algebra 2
x=9 2x+3y = 30 Now the rest of the questions get easier.
October 3, 2014

pre-calc
Clearly, since we have a semicircle, the width of the rectangle is half the length. So, A = (3x/2)(3x) P = 2(3x/2 + 3x)
October 3, 2014

Physics
If you are not familiar with the equations for trajectories, the wikipedia article for that subject has a good treatment. Just plug in your values for the equation of motion, and crank it out. If you get stuck, come on back with your work so far, and we can give you a nudge in...
October 3, 2014

Math
In that case, review your basic trig functions. cos(x) = 7/21 Now just find x, with that value for cosine.
October 3, 2014

Pre-Calc/Trig...
No idea. But the answer is clearly B, if for no other reason than that x and y have opposite signs on the left.
October 3, 2014

Pre-Calc/Trig...
recall the point-slope form of a line. In this case, y-1 = 3(x-10) Now massage that into one of the choices.
October 3, 2014

houston community college
Since PV=kT, PV/T is constant. So, since P is constant, V/T is constant. That means: 1.4/(27+271) = V/(177+271)
October 3, 2014

Calc
I don't know what the original problem was, but if the doubling time is 24 days, the formula for the amount present after t days is A(t) = Ao * 2^(t/24) Since 2 = e^ln2, that is equivalent to A(t) = Ao * e^(ln2/24 t)
October 3, 2014

AP CALC. AB
f(x) = 3/x f'(x) = -3/x^2 So, we want -3/c^2 = 3(-3/4) c^2 = 4/3 ...
October 3, 2014

calc
when t=0, Q=0.414 = a e^.885 = 2.423, so Q = .414(2.423^t) population grows by a factor of 2.423 every period. well, duh: k = 0.885 = 88.5%, though it's not usually expressed as a percent. Actually, that's k if you express Q as a e^kt
October 3, 2014

trig
sin(x) = 12/15, so ...
October 3, 2014

Pre-Calculous
.887 = e^-.1199, so .887^1.2t = e^(-.1199*1.2t) = e^-.144t It's always better to show your work, so we can help correct the errors, if any.
October 3, 2014

AP Calc. AB
when the tangent passes through the origin, it is of the form y = kx So, we want places where the slope is y/x. y' = 20x^4 - 12x^3 + 30x So, we want places where 20x^4 - 12x^3 + 30x = (4x^5-3x^4+15x^2+6)/x That is, where 20x^5-12x^4+30x^2 = 4x^5-3x^4+15x^2+6 16x^5-9x^4+15x...
October 3, 2014

CALCULUS
you want 1.043^t = 2.0 t log 1.043 = log 2 t = log2/log1.043 = 16.5 years This is roughly in accordance with the rule of 72: 72/4.3 = 16.7
October 3, 2014

Math
since cot(z) has asymptotes at all multiples of pi, h(x) above will have asymptotes at all places where x/2 is a multiple of pi.
October 3, 2014

Physics
Two satellites, A and B, are in different circular orbits about the earth. The orbital speed of satellite A is eighty-two times that of satellite B. Find the ratio (TA/TB) of the periods of the satellites.
October 3, 2014

English
yes and yes
October 3, 2014

math
The size of the cut will not, of course, change the length of the board. It will, of course, affect the total length of the cut pieces, since 1.25" will be lost after 10 cuts. I suspect there is more to this problem than what you asked, but if you want answers, you have ...
October 3, 2014

geometry
That would be 672 - (-36) = ?
October 3, 2014

math
If $x go at 2%, the rest (4000-x) is at 5%. So, add up the interest on each part: .02x + .05(4000-x) = 155.00
October 3, 2014

algebra
If the plane's speed is p, and the wind's speed is w, then since distance = speed * time, 3(p+w) = 1500 3(p-w) = 1380 Now you can easily find p, and then w.
October 3, 2014

Math
yes.
October 3, 2014

physics
total distance: 15.9+25.3+34.3 = 75.5 mi total time: 15.9/51 + 25.3/41 + 34.3/38.6 = 1.82 hr So, avg speed is 75.5mi/1.82hr = 41.55 mi/hr
October 3, 2014

Math
no - that fixed fee of $32 wrecks the proportion.
October 3, 2014

Math
First, the income in 2010 is not P(10), it is P(3). P(t) is only defined for 2<t<6, where t is the years since 2007. P(3) = 6(3)-24 = -6, so P(t) is decreasing there. Note that P'(t)=0 when t=4. That means it is decreasing more slowly until t=4, then starts to ...
October 2, 2014

Calculus
You have the right idea, but y' = 1 - 1/(2√x) Setting that to zero, we get 1 - 1/(2√x) = 0 1/(2√x) = 1 2√x = 1 √x = 1/2 x = 1/4 As you can see from the graph, there is only the one point (1/4,-1/4) with a horizontal tangent. http://www....
October 2, 2014

Math
Do you know what the midpoint is? It is the point midway between A and C. That is, it is the same distance from A as it is from C. That is, AB = BC
October 2, 2014

Calc
both wrong. Better review the definition of continuous. sin(x)/x -> 1 as a limit as x->0, but 0/0 is not defined, so it is not continuous there.
October 2, 2014

Math
p = (74.5+124.2)/242 p is not 1.0, because of things called divorce and death.
October 2, 2014

physics
since the distance s = vt + 1/2 at^2, 4780*525 + 525^2/2 ax = 3.54*10^6 8850*525 + 525^2/2 ay = 7.77*10^6
October 2, 2014

math
For F(x,y) = 3y cosx, we have Fx = -3y sinx Fy = 3 cosx Fxx = -3y cosx Fyy = 0 Fxy = -3 sinx So, for a saddle point, we need Fx = 0 true for x=0,pi or y=0 Fy = 0 true for x=pi/2, 3pi/2 and all y Fxx * Fyy - (Fxy)^2 < 0 -3y cosx * 0 - (-3 sinx)^2 < 0 true for all x. The ...
October 2, 2014

math
42
October 2, 2014

pre calculus
since d/F is constant, .15/265 = .2/x and, .165/265 = x/100 Note that you don't really have to find k, the constant of proportionality. You can go ahead and find it, but your answers will be the same.
October 2, 2014

math
approximate: use 30 days per month. exact: get a calendar.
October 2, 2014

Math
At x=2, x-5 < 0, so the slope at x=2 is just -1. Ok, ok, algebraically, f(2+h) = |2+h-5|-7 = |-3+h|-7 Since the value is negative, that will be 3-h-7 = -4-h f(2) = |2-5|-7 = 3-7 = -4 -4-h - (-4) = -h Now, divide by h and you have -h/h = -1
October 2, 2014

Math
pretty good, but you know that cot π/4 = 1 csc π/4 = √2, so m = -12(1)(2) = -24 So the line is y-3 = -24(x-π/4)
October 2, 2014

geometry
If the points are in a aline, then I expect AB + BC = Ac So, 9a + 12a = 42 21a = 42 a = 2 Now you can figure out the lengths AB and BC
October 2, 2014

Math (Implicit Differention)
of course, you can simplify that last result to just √3, since it is (3^(3/2))^(1/3) = 3^(1/2) Also, you dropped/gained a minus sign in there somewhere. The point is in QII, where the slope is positive.
October 2, 2014

calculus
x^2/3+y^2/3=4 2/3 x^-1/3 + 2/3 y^-1/3 y' = 0 y' = -(y/x)^1/3 So, at (-1,3√3), y' = -(3√3/-1)^(1/3) = √3 You can see the graphs at http://www.wolframalpha.com/input/?i=plot++x^%282%2F3%29%2By^%282%2F3%29%3D4+%2C+y+%3D+-%E2%88%9A3%28x-1%29+%2B+3%E2%...
October 2, 2014

Math - Please Check My Answer - Probably Last One!
the ratio is just (πr^2h) / (2r)^2*h πr^2h / 4r^2h π/4
October 2, 2014

Math - Please Check My Answer
D is correct. In A, 3x^0 = 3*1 = 3, while (3x)^0 = 1 (assuming x is not zero)
October 2, 2014

AC DC Circuit fundamentals
since they are in series, the voltage drop is divided up into 2/3 across the 10k 1/3 across the 5k since R = R1+R2 = 5+10 = 15 k, and 10 is 2/3 of 15, 5 is 1/3 of 15.
October 2, 2014

Trigonometry
f(x-a) is f(x) shifted right by a. So, yours is shifted left by 5. f(x)+k is f(k) shifted up by k.
October 2, 2014

Math
4(x+15) >= 120 x+15 >= 30 x >= 15
October 2, 2014

Math
3/2 + 23 since max of sine is 1.
October 2, 2014

Math
right again.
October 2, 2014

Math
both correct!
October 2, 2014

Trigonometry
since the maximum of sin(x) is 1, d(t) achieves a maximum of 3/2 + 23.
October 2, 2014

Math
Just do hex long division, as at http://mathforum.org/library/drmath/view/63375.html However, it is sometimes easier to convert to decimal, divide, and convert back.
October 2, 2014

Algebra ll
division by zero is not defined. What is 12/0? 0/0? So, for a rational function, the domain excludes any values where the denominator is zero, because the domain is the set of values of x for which f(x) is defined. For f(x) = (x^2 - 25)/2 the domain is all real numbers; there ...
October 2, 2014

Simplify this Expression?
You can do it using the distributive property as J and Ms Sue did, or you can use it implicitly, working term by term z-2z+4z+6 -z+4z+6 3z+6 Their answers basically factored out the z, as in z-2z+4z+6 (1-2+4)z+6 (3)z+6 3z+6
October 2, 2014

geometry
think of alternate interior angles, or consecutive interior angles.
October 2, 2014

Trigonometry
Just do things as you normally would. tan 28 = 0.5317, so you have (20-x)/6.11 = 0.5317 20-x = 3.25 x = 16.75 Don't forget your algebra I just because you're taking trig now!
October 2, 2014

math
Looks to me like .013
October 2, 2014

Plane and Spherical Trigonometry
Use the law of cosines. The third side can be found using AC^2 = 20^2 + 35^2 - 2(20)(35)cos(180-80)°
October 2, 2014

math
(g-48)(g-20) = 480 g = 60 So, the grandfather is 60. ...
October 2, 2014

Math
1/4 * 1/2 = 1/8
October 2, 2014

math
(14 - (15/3))/2 = 9/2
October 2, 2014

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