Monday
December 22, 2014

Posts by steve


Total # Posts: 27,668

Algebra
No, you can't have h^-1 with both x and y in it. In fact, there are no x's here at all. Just interchange h and y and solve for the new h: y = (1+h)/(2-h) y(2-h) = (1+h) 2y - yh = 1+h h(1+y) = 2y-1 h = (2y-1)/(y+1) So, h^-1(y) = (2y-1)/(y+1) h^-1(5) = 9/6 = 3/2 check: h...
November 3, 2014

Math
rewrite as 3/9, 4/9, 5/9, ... 1/10, 4/10, ... 3/7, 4/7, 5/7 ... the 1st and 3rd are easy, but I'd have to pick 1/5 for (b) just because it's the only one with a 5 in the denominator. No idea on the pattern.
November 3, 2014

Algebra
Lots of problems posted, with no sign of effort on your part. No ideas at all?
November 3, 2014

Algebra
x = (3y-7)/(y+1) x(y+1) = 3y-7 xy + x = 3y - 7 y(x-3) = -(x+7) y = (7+x)/(3-x)
November 3, 2014

Algebra
E(t) is just a parabola. I'm sure you know how to find the vertex, where E is a maximum.
November 3, 2014

Math
4/9 * 36 = (4*4*9)/9 = 4*4 = 16
November 3, 2014

Math
If exactly 20, then it would be 8:12 So, since we have to add 5 marbles at a time (2+3=5), the next possibility is 10:15 makes 25 marbles
November 3, 2014

math
That depends - do the minutes roll over, or not? If not, then she had to buy 400 the 1st month 400 the 2nd month 600 the 3rd month That's $50+$50+$75 = $175 If they roll over at the end of the month, then she'd have to buy less in some cases.
November 3, 2014

Algebra
the max height is achieved at the vertex of the parabola, when t = 1 for (c), just solve 16t^2 - 32t - 240 = 0 16(t+3)(t-5) = 0 ...
November 3, 2014

Pre-Calc
90 days is 90/8.1 = 11.111 half-lives, so there would be 25*(1/2)^11.111 left
November 3, 2014

Math
well, -8 < -15/2 -3 < -3/2
November 3, 2014

math
2(x+y) = 25 xy = 32 x(25-2x)/2 = 32 25x-2x^2 = 64 2x^2-25x+64 = 0 x = 3.59 y=8.91
November 3, 2014

Math
m is undefined
November 3, 2014

Math
There are several ways to write the equation, depending on the information given: slope-intercept point-slope two-point x- and y-intercepts standard form general form So, read up on these topics, and you will learn several answers to your question
November 3, 2014

Maths
since 27 = 3*9, 3a-27 = 3a-3*9 = 3(a-9)
November 3, 2014

mathematics Probability
Since 2 is the only prime that is even, P(prime & even) = P(2) = 1/5
November 3, 2014

Math
raise 16 to the power on both sides. That gives 8 = 16^(3/4) take log base 3 on both sides 4 = log_3(81) This is because blogbN = N logbbN = N
November 3, 2014

Math
there is no other way. The roots are the zeroes are the x-intercepts. The quadratic formula always works. Use it when in trouble. Or, try and factor the polynomial x^2+8x+15 = 0 (x+3)(x+5) = 0 the roots are -3 and -5 Surely your algebra book covers the topic in several places.
November 3, 2014

Math
You must have access to some graphing utility. Here is a good one: http://www.wolframalpha.com/input/?i=-2%2F3+d^2+%2B+4d&a=*MC.d^2-_*Variable-&a=UnitClash_*d.*Days.dflt--
November 3, 2014

Math
The whole setup is bogus I'd go with (c), since it correctly notes that the solutions are -4 and 9. But -4+4 is (0), not (-8) If this is a proposed way to solve for zeroes, it's really stupid. x cannot be both -4 and 9 at the same time. Run far, run fast from this ...
November 3, 2014

Algebra
f(x) = 1/(ax+b) f^-1(x) = (1-bx)/(ax) So, we want 1+bx = 0 x = 1/b Or, if f^-1(x) = 0, f(0) = 1/b
November 3, 2014

Math
since h is the height above the water, it hits the water when h=0: -5t^2+10t+35 = 0 t = 1+2√2
November 3, 2014

Calculus
f' = -sinx-1 f'=0 at sinx = -1, so x = 3π/2 f" = -cosx, so f"(3π/2) = 0 Looks like an inflection point, not max or min. So, no extrema anywhere.
November 3, 2014

algebra
6p^2-2p+3 = 3 6p^2 - 2p = 0 2p(3p-1) = 0 p=0 or p = 1/3
November 3, 2014

Trigonometry
no idea whatcha got? Convert each length traveled to an x & y displacement. Then use the law of cosines to find the third length.
November 3, 2014

Trigonometry
Hmmm. The 72 feet is measured on the slope, not out from the pole horizontally. I get top of pole is at 40 + 72 sin17° downhill point is 72 cos 17° from point beneath the pole cable^2 = (40+72 sin17°)^2 + (72 cos 17°)^2
November 3, 2014

Trigonometry
As usual, draw a diagram. It is clear that if the nearer student is x away from the spot under the balloon, then h/x = tan 28° h/(x+7) = tan 15° Eliminate x and you have h/tan28° = h/tan15° - 7 Now just solve for h
November 3, 2014

algebra
a#3 = a^2/3 = 9 a^2 = 27 ...
November 3, 2014

Algebra
f^-1(x) = (x+8)/3 So, we want (x+8)/3 = 3x-8 x+8 = 9x-24 8x = 32 x = 4 3*4-8 = 4 (4+8)/3 = 4 Note that the same results could have been achieved by setting f(x) = x 3x-8 = x 2x = 8 x = 4 Why? because f(f^-1) = x by definition. So, if f^-1(x) = f(x), then f^-1(f) = f^-1(x) x = ...
November 3, 2014

Math
elimination, or matrix inverse?
November 3, 2014

math
Well, as long as I'm clarifying :-) :-) :-) That would be 45 seconds, not .45 seconds Or, if you insist on decimals, try .75 minutes!
November 3, 2014

math
Not quite. After 12 minutes he has climbed 12 meters In the 13th minute, he climbs the final 3 meters and is done. Final time is thus 12:45
November 3, 2014

calculus
since x^2+y^2 = 36 x dx/dt + y dy/dt = 0 since we want dy/dt = -dx/dt, (x-y) dx/dt = 0 true when x=y, as might be expected. Or, when x = 6/√2 All that stuff about 4m and .5 m/s is just noise, unless there are other parts to the problem.
November 3, 2014

Pre calculus
r = 7/(5+4sinθ) r(5+4sinθ) = 7 5r + 4rsinθ = 7 5r = 7 - 4y 25r^2 = (7-4y)^2 25x^2 + 25y^2 = 49 - 56y + 16y^2 25x^2 + 9y^2 + 56y = 49 25x^2 + 9(y+28/9)^2 = 49 + 9(28/9)^2 25x^2 + 9(y+28/9)^2 = 1225/9 x^2/9 + (y+28/9)^2/25 = (7/9)^2 See http://www.wolframalpha.com...
November 3, 2014

Calculus
f(x) = 5x√(x+2) is continuous and differentiable on [0,2], so the MVT applies. f(2) = 20 f(0) = 0 So, the slope of the secant is 10 MVT says that f'(c) = 20 somewhere in [0,2] f'(x) = 5(3x+4) / 2√(x+2) f'(c) = 0 if 5(3c+4) / 2√(c+2) = 10 5(3c+4...
November 3, 2014

math
If the airport is at (0,0) first leg is to (-2.819,1.026) the second leg is on a course of S20°W for a distance of x where 1.026-xcos20° = 0 x = 1.092 So, the 2nd leg is to (-3.192,0)
November 3, 2014

Algebra
I'm sure that by now you have figured out that I made an error: (u^2+1 - u^2) / u(u-1) 1 / u(u-1) Now set that equal to 1/u 1 / u(u-1) = 1/u 1 = u-1 u = 2 check: 5/2 - 2/1 = 1/2
November 2, 2014

Algebra
I assume you mean (u^2+1)/(u^2-u) - u/(u-1) Clearly the LCD is u(u-1) (u^2+1 - u(u+1)) / u(u-1) (-u+1) / u(u-1) Now put both sides over the LCD, throw out u=0,1 and set the numerators equal. Then solve for u. What do you get?
November 2, 2014

Algebra
If the savings account pays x%, then (x+10)/x = 65/15 x = 3 check: .03m = 1500 m = 50000 So, $50K was invested .13(50000) = 6500
November 2, 2014

Algebra 2
there are 10 digits; only 8 allowed to start, so 8*10^6
November 2, 2014

Algebra check?
all correct good work. You can also check your answers by typing in the expression at wolframalpha.com
November 2, 2014

Algebra
If you're trying to find the expression for the area, you have for some reason combined the x^2 and x terms (a no-no). The area is 1/2(2x^2+4x+2)(x^2+3x-4) (x+1)^2 (x+4)(x-1) As you say, not sure which way to go. You have an expression for the area. Was there some other ...
November 2, 2014

algebra
huh. That's quite a question just to drop in. Have you not studied your algebra text? The basic idea is that if an equation is true, it remains true if you apply identical operations on both sides of the equal sign. The goal is to choose the operations in an order which ...
November 2, 2014

Math
You are correct to feel ill at ease. You have confused area and perimeter. You want (x+7)(6) = 120
November 2, 2014

algebra
After x miles, you want 8 - x/30 = 12 - x/18
November 2, 2014

Calculus I
If by optimal age, you mean producing the maximum offspring, then yes, you want to find where dr/dx = 0 r(x) = log(e^-.1x * 4x^1.5)/x That's kind of messy, and not tractable to algebraic solution. Netter use a graphical or numeric method. Looks like dr/dx=0 at x=1.07875 ...
November 2, 2014

Algebra
√7 (7-√7) + 9√7 7√7 - √7√7 + 9√7 16√7 - 7
November 2, 2014

Algebra 1B
You may be more familiar with the term "discriminant." The discriminant is b^2-4ac, the value inside the square root symbol. So, in this case, the surd being considered is the square root of the discriminant.
November 2, 2014

Math (I've been on this problem for 3 hours)
well, as I recall, the equilibrium price and quantity are where supply equals demand. So, we want 2p-q+10 = (p+q)(q+10)-3642 since q = 2p+10, that means (p+2p+10)(2p+10+10) = 3642 6p^2+80p-3442 = 0 p = 18.195 so, q = 46.390 Check: 2(18.195)-46.390 +10 = 0 (18.195+46.390)(56....
November 2, 2014

Math (I've been on this problem for 3 hours)
If the supply and demand functions for a commodity are given by 2p - q + 10 = 0 and (p + q)(q + 10) = 3642 respectively, find the equilibrium price and quantity that give market equilibrium. (Round your answers to two decimal places.) Equilibrium price =
November 2, 2014

physics
then it hits a brick wall, and bursts into flame. How much energy is released by the explosion of the fuel tank?
November 2, 2014

math
now: w and w+4, area = w(w+4) after growth, we have (w+3)(w+4+3) = w(w+3)+81 w^2+10w+21 = w^2+3w+81 7w = 60 w = 60/7 Now you can figure all the dimensions.
November 2, 2014

Math Please HELP
If the supply function for a commodity is given by the equation p = q2 + 12q + 700 and the demand function is given by the equation p = 1800 - 10q - q2, find the equilibrium quantity and equilibrium price. (Round your answers to two decimal places.)Thank You so much
November 2, 2014

Algebra 2
The maximum height of the ball is reached at t=25/32 Plug that in. If it is greater than 17, then I guess it would depend on how far away the wall is.
November 2, 2014

Math
horizontal travel: x = Vxt = v cos50° = 0.6428v t .6428v t = 20.75 v = 32.2806/t y = Vy t - 16t^2 = 0.7660v t - 16t^2 = 0.7660(32.2806/t)t - 16t^2 = 24.7270 - 16t^2 y=0 when t = 1.243 Vy (1.243) - 16(1.243^2) = 0 Vy = 19.89 SO, y = 19.89t - 16t^2 Now just find the vertex ...
November 2, 2014

calculus
Hmmm. Consider u^2 = 3x+4, so x = (u^2-4)/3 2u du = 3 dx x+3 = (u^2+5)/3 x^2 = (u^2-4)^2/9 x^2 / (x+3)√(3x+4) dx = 2(u^2-4) / 9(u^2+5) du = (2u^2-26)/9 + 18/(u^2+5) Integrate that to get 2/27 u (u^2-39) + 18/√5 arctan(u/√5) = 2/27 √(3x+4)(3x-35) + 18/&#...
November 2, 2014

MATHS
9*20 + 3*10 = 180+30 = 210
November 2, 2014

math
If x liters of water are added, then .10(5) = .04(5+x)
November 2, 2014

Algebra
If the formula is v = √(h-8) then you are correct: √(203-8) = √195 = 13.96
November 2, 2014

math
y = 10832.236 x
November 2, 2014

Calculus
at the moment in question, the rocket is 5 miles from the observer. h/4 = tanθ dh/dt = 4 sec^2θ dθ/dt 6 = 4(5/4)^2 dθ/dt 24/25 = dθ/dt I expect you can deduce the units.
November 2, 2014

Calculus
well, what is .0588 * 1609^1.25 ?
November 1, 2014

inequality
70 + .02x < .09x
November 1, 2014

Calculus
revenue is demand*price r = p(9000-100p) = 9000p - 100p^2 marginal revenue is dr/dp = 9000-200p
November 1, 2014

Algebra
If x & y = the following table what is the function of x? x = 1,2,3,4 Y = 1,3,5,7
November 1, 2014

Algebra 2
think back to your algebra I. Where is the vertex of a parabola? remember x = -b/2a ?
November 1, 2014

algebra
300+280-320 = 260 So, 260 bought both. That means that 280-260=20 buy only DVDs
November 1, 2014

College Intermediate Algebra
x^2+4x+3
November 1, 2014

college algebra
(x-3)^2 + 10(x-3) + 24 (x-3+6)(x-3+4) (x+3)(x+1)
November 1, 2014

st xaviers matj
mark A construct AB Mark circle of radius AB+3, center A construct perpendicular at B where the circle intersects the perpendicular is C. now construct AD and CD
November 1, 2014

Math Help
#1 d e^(x^2+6) = e^5x x^2+6 = 5x x^2-5x+6 = 0 x = 2,3
November 1, 2014

Math
(a) 2x+3y = 580 Now you try (b)
November 1, 2014

Calculus
Of course it will work. Since you're learning about using derivatives to locate extrema, why would you think it would not work? dc/dt = (0.02t - 0.001) e^(-0.05t) since e^(-0.05t) is never zero, you want 0.02t - 0.001 = 0
November 1, 2014

calculus
v = 4/3 pi r^3 dv/dt = 4 pi r^2 dr/dt so, dr/dt = (dv/dt) / 4pi r^2 a = 4pi r^2 da/dt = 8pi r dr/dt = 8pi r (dv/dt)/4pir^2 = 2/r dv/dt Now plug in your numbers.
November 1, 2014

Math
f' = 1/x f'(1) = 1 f(1) = 0 So, you have a point (1,0) and a slope (1), so y = x-1 now plug in x = 1.12
November 1, 2014

Math
The radius of earth is 6371 km We have rθ = 8000, so θ = 8000/6371 = 71.9° Y is at 20.6°E 35.1°S Now, at latitude Ø, the radius of the circle of latitude is r' = r cosØ So, r' = 6371 cos 35.1° = 5210 km At that latitude, 8000km ...
November 1, 2014

MATHS
2y+3d = 7.5 3y+2d = 8.0 now just solve for y and d.
November 1, 2014

Math
f(x) = x^20 roots: 0 I think you might want to impose a few more conditions.
November 1, 2014

physics
(1/2)(1.25)(2^2) + 2.5(t-2) = 1.5t t = 2.5 2.5*1.5 = 3.75 If the 25s/0.38km is supposed to be the answer, I suspect the units have gotten garbled.
October 31, 2014

Math
since a = 4pi r^2, 4pi r^2 = 100pi r = 5 so, now use your volume formula.
October 31, 2014

Algebra
a%b = √(a^2+b^2) so, just plug in your numbers: 5%12 = (-5)%(-12) = 13 so, you have (13)%(13) = 13√2
October 31, 2014

Algebra
f^-1(x) = (x+5)/2 so, you want x where 2x-5 = (x+5)/2 x=5
October 31, 2014

algebra
N=2√x, O=x^2 So, just work your way out through the parentheses: N(O(N(O(N(O(3)))))) N(O(N(O(N(9))))) N(O(N(O(6)))) ... Or, note that N(O(x)) = 2√(O(x)) = 2√x^2 = 2x So, you have N(O)^3 = 2^3*3 = 24
October 31, 2014

Algebra 2
w(w+7) = 120 8(15) = 120
October 31, 2014

math
(-3+10)/(-4+5) = 7/1 = 7 Note that x changed by 1 and y changed by 7.
October 31, 2014

calculus
hint: find g(0) and g(1) find where g'(s) = 0, then evaluate g there. pick the min and max of those values.
October 31, 2014

Math
2(w+3w) >= 48 4w >= 24 w >= 6
October 31, 2014

Calculus
27^(4/3) = 81 y = x^(4/3) dy = (4/3)x^(1/3) dx so, if dx = -0.1 dy = (4/3)(3)(-0.1) = -0.4 So, 26.9^(4/3) ≈ 80.6 In fact 26.9^(4/3) = 80.6002 pretty close, eh?
October 31, 2014

physics
You lifted it 1.26m (assuming the table is sitting on the floor) so, what?
October 31, 2014

Calculus
apparently you mean f(x) = ∛x f(125) = 5 f'(x) = 1/3∛x^2 f'(125) = 1/75 So, now you have a point and a slope. The line is y-5 = 1/75 (x-125)
October 31, 2014

algebra
g(x) has unbalanced parentheses. I will assume you meant g(x) = √f(x) - 2 h(2) = f(g(2)) = f(√(f(2))-2) = f(√(9)-2) = f(3-2) = f(1) = 7 f^-1(x) = (x+5)/2, so we need 2x-5 = (x+5)/2 4x-10 = x+5 3x = 15 x = 5 plug in x=5 for both functions to verify that it is ...
October 31, 2014

Math
P(n) = 20000(2^n) Let now be when n=0 four years ago, n = -4, so P(-4) = 20000(2^-4) = 20000/16 = 1250 Now do the same for n = -8 and n=2 You don't really need to set n=0. Suppose we started k years ago. That means that now would be P(k). So, 4 years ago would be P(k-4) = ...
October 31, 2014

calculus please help asap
TFTFT
October 31, 2014

calculus
at x=0, the slope is 5 SO, near x=0, y=5x is the linear approximation.
October 31, 2014

calculus
at x=0 the slope is 2/√5 at x=0, y = √5 So, the line there is y = (2/√5)x + √5 http://www.wolframalpha.com/input/?i=plot+y%3D%E2%88%9A%285%2B4x%29%2Cy%3D2%2F%E2%88%9A5+x%2B%E2%88%9A5+for+x+%3D+-2+to+2
October 31, 2014

Calculus
so, what did you plug in? What was your final answer?
October 31, 2014

Calculus
df = √3 dx so, plug in dx=.4 to see how much f has increased
October 31, 2014

Calculus
f(64) = 8 f'(64) = 1/16 so, the line is y-8 = 1/16 (x-64)
October 31, 2014

Calculus
as usual, sinθ = y/r cosθ = x/r You know x,y,r so get the functions
October 31, 2014

Math Calculous
No, you want the angle whose sine is .409 Since sin(30°) is 0.5, your angle will be somewhat less than that. Use your calculator. There is probably a 2nd function button, then hit sin. Check whether it is in degrees or radians mode.
October 31, 2014

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