Tuesday
October 21, 2014

Posts by steve


Total # Posts: 25,963

Math
as with any vector of length r on an angle of t, x = r cos(t) y = r sin(t) So, plug in your numbers.
September 30, 2014

math
98 - (-94) = 98+94 = ?
September 29, 2014

Precalculus
use the vertical and horizontal line tests. If no line cuts the graph in more than one place, the function is 1-1 and has an inverse. That is, each x value maps to exactly one y value, and vice-versa.
September 29, 2014

horizon elementry
v = at, so 8 = a(.5) a = 16 m/s^2
September 29, 2014

precal
ok. now what?
September 29, 2014

Precalculus
Look at the bottom row of the table, dude!
September 29, 2014

Material Behavior
I don't know what F is, but dU/dr = Am/r^(m+1) - Bn/r^(n+1) So, plug in r0 and you have dU/dr(r0) = Am/r0^(m+1) - Bn/r0^(n+1)
September 29, 2014

Math
almost. 3/7 = .4286 so -3 3/7 is 2nd in the list
September 29, 2014

Algebra
it means it is ill posed. The math is correct, but the problem doesn't take into account real-world conditions. Just ignore it, as this is an algebra class, not a physics class. Still, you might point it out to the teacher, not that it will do any good.
September 29, 2014

Algebra
well, clearly the temperature is now -247 - 2*11 = -269 The only problem is that hydrogen freezes at -259
September 29, 2014

Math
36+81 = 9(4+9) or 3(12+27)
September 29, 2014

Geometry
If the numbers are m and n, and m is even, then m=2k. If the sum is even, say 2x, then 2k+n = 2x n = 2x-2k = 2(x-k) So, it is clear that n is also even, since it is a multiple of 2.
September 29, 2014

math
2*16 + 2*3 = 38 or, 2(16+5)-4 = 38 why the two ways of writing the expression?
September 29, 2014

Math
recall that (a+b)(a-b) = a^2-b^2 so, (3+√5)(3-√5) = 9-5 = 4 So, to simplify such fractions, look for the "square conjugate" if you will, of the denominator. 4/(3+√5) = 4(3-√5) / (3+√5)(3-√5) = 4(3-√5)/4 = 3-√5 And do ...
September 29, 2014

Algebra
recall that (a-b)(a+b) = a^2-b^2 so, (3+√5)(3-√5) = 9-5 = 4 So, to simplify such fractions, look for the "square conjugate" if you will, of the denominator. 4/(3+√5) = 4(3-√5) / (3+√5)(3-√5) = 4(3-√5)/4 = 3-√5 And do ...
September 29, 2014

Math
4y(2y^4+3y^2+1) 4y(2y^2+1)(y^2+1)
September 29, 2014

math
1+1+3 = 5 1+2+2 = 5 And you can shuffle those around, making 3+3 = 6 ways to spin 5
September 29, 2014

math
well, you have 2.47f+54.1 = 166.21 So, |h-166.21| <= 3.72 166.21-3.72 <= h <= 166.21+3.72 and so on
September 29, 2014

math
f(x-6)+5
September 29, 2014

7th grade math
good work
September 29, 2014

Pre-Calculus/Trigonometry
(3 -1)(2) (5 2)(6) = (0) (22)
September 29, 2014

algebra 2
10 inconsistent 11 consistent dependent 12 consistent independent
September 29, 2014

Pre-Calculus/Trigonometry
no solutions to x+y = 3 x+y = 4
September 29, 2014

Math (Trig)
sin2x+sin4x = 2sin3x cosx cos2x+cos4x = 2cos3x cosx Now divide to get tan3x
September 29, 2014

math
LCM(9,10,14) = 630
September 29, 2014

AP Calc B/C
If u = e^x, then (e^x)/(1-e^2x)^3/2 dx = du/(1-u^2)^3/2 Now you can easily find that the integral is u/√(1-u^2) which is what Reiny provided.
September 29, 2014

Math
If it was T, then T-18-8+1+2+4+5 = 34 T = 48
September 29, 2014

math problem solving
Looks like 5 to me
September 29, 2014

algebra
34m + 14 = 30m + 22 4m = 8 m = 2
September 29, 2014

math
some multiples of 7 and 3 are 21 42 63 84 Looks like they all work
September 29, 2014

DISCRETE MATH
There are 10 letters, with 3 S's, 3 T's, 2 I's, so 10!/(3!3!2!) = 50400
September 29, 2014

engineering science
the direction remains the same, and v can be found by conserving momentum: 10(8) + 6(4) = (10+8)v
September 29, 2014

Quadratic Functions
it means, graph the function, and look where it crosses the x-axis. Those are the solutions to f(x) = 0.
September 29, 2014

Help Please
Of course not. You just need to find x and y such that x^2+y^2 = 361 So, x and y can be 1,√360 2,√357 3,√352 ... √61,√300 √101,√260 and many, many more.
September 29, 2014

SBGG
the perimeter of the wheel is 7π cm = .07π = .022 m So, 132 m/min * 1min/60s * 1rev/.022m = 100 rev/s
September 29, 2014

Calculus
just use the chain rule: let r = log(u) dr/dθ = 1/u du/dθ let u = cos^2(v) du/dθ = 2cosv(-sinv) dv/dθ let v = 4θ dv/dθ = 4 So, dr/dθ = sec^2(4θ) (-2cos4θsin4θ) (4) = -8tan4θ Or, you could just recall that log(cos^2(4θ...
September 29, 2014

math mks
I see it as what was the temperature at 9 am? -8+15 = 7
September 29, 2014

math
in theory, the ball will never come to rest, since its bounce height is never zero. But, you can see the height of the nth bounce is 7(2/3)^n So, since the distance traveled is both up and down, the sequence is 7 + 2*7(2/3) + 2*7(2/3)^2 + ... so, if r=2/3, = 7 + 14(r+r^2+...) ...
September 29, 2014

Math
a^x is an exponential function, for any number a. the quotient (hence the ratio) of two polynomials is called a rational function.
September 28, 2014

Finite
sounds like real life.
September 28, 2014

math
the fraction riding bikes is 5/32, so of the 800 5/32 * 800 rode bikes.
September 28, 2014

Find the pattern problem solving
taxi: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 ... bike/trike: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 moped: 9 15 21 27 33 39 45 51 57 truck: 1 25 35 55 49 30 taxis 9 mopeds 5 trucks so, 16 humans: 12 bikes, 4 trikes total wheels: 4*30 + 9*2 + 5*6 + 12*2 + 4*3 = 204
September 28, 2014

MATH
horizontal has slope 0, so y does not change. So, the line is y=8
September 28, 2014

algebra
If she spends x hours cycling, the rest (8.5-x) is spent running. Since distance = time * speed, 14x + 8(8.5-x) = 101 Now just solve for x and figure 8.5-x
September 28, 2014

math
28 - 9x = -12 - 11x as you say, add 9x to both sides, and you get 28 = -12 - 2x Now add 12 to both sides and you get 40 = -2x Now divide by -2 and you get -20 = x There's no reason to add 11x to both sides after all the x's are together. If you did do that, you have 28...
September 28, 2014

statistics
If the distribution is normal, and the std is high enough, the probability could approach 0.5
September 28, 2014

Algebra
just use the good old distributive property: (2nr - nr^2)r - (2nr - nr^2) . 2r 2nr^2 - nr^3 - (2nr^2 - 2nr^3) 2nr^2 - nr^3 - 2nr^2 + 2nr^3 nr^3
September 28, 2014

math.help pls
f(x)=(472 - 2x^2)^1/3 so, f(8) = (472 - 128)^1/3 = 344^1/3 f(8+h) = (472 - 2(8+h)^2)^1/3 = (344 - (32h+2h^2))^1/3 By the binomial theorem, that is 344^1/3 - (1/3)(344^-2/3)(32h+2h^2) + a bunch of stuff with higher powers of h Now subtract and you have f((8+h)-f(8)) = (-1/3)(...
September 28, 2014

Math
that is correct
September 28, 2014

Calculus
Reiny's solution is cool, using implicit differentiation. You can also do it by noting that 2 = e^(ln 2) So, 2^x = e^(ln 2 * x) and now use the chain rule: d/dx e^u = e^u du/dx, so d/dx e^(ln 2 * x) = ln2 * e^(ln 2 * x) = ln2 * 2^x
September 28, 2014

AP Calc. AB
clearly, due to conservation of energy, etc., the arrow will strike with the same velocity as it left, but in the opposite direction. just solve 53t - 0.62 t^2 = 0 t(53-0.62t) = 0 t = 53/0.62 = 85.4839
September 28, 2014

Math
I think you meant 12a^2 - 5a - 2 = (3a-2)(4a+1) After the path, each dimension is increased by 2, so the new total area is (3a-2+2)(4a+1+2) = (3a)(4a+3) Now subtract the original area to get the area of the path: (3a)(4a+3)-(3a-2)(4a+1) now just simplify that Finally, just ...
September 28, 2014

Math
since C = 2πr, and speed = distance/time, speed = 2π*15000 mi/18 hr = 5236 mi/hr
September 28, 2014

Math
only if the angles are right angles so that the diagonal satisfies the Pythagorean Theorem. That is, if 80^2 + 32^2 = 86^2 does it?
September 28, 2014

Pre-Calc (Point of Inter.)
This problem is discussed at https://answers.yahoo.com/question/index?qid=20101127042533AA17HTY
September 28, 2014

Algebra 2
For x tables and y chairs, we want to maximize p=100x+80y subject to 3x+2y <= 42 2x+6y <= 42 Now use your favorite linear programming tool to find that they make the most with 12 tables and 3 chairs.
September 28, 2014

Pre-Calc (Circles). Please help :(
the area of C5 = 25π The area of the annulus between C3 and C4 is 16π-9π = 7π so, p = 7/25
September 28, 2014

math analysis
we want 1/x < ε 1/ε < x So, if x > 1/ε, 1/x < ε
September 28, 2014

High school algebra
it is well known (and should be noted by you) that 60 mi/hr = 88ft/s So, you have (88/60)(88) = 129 1/15 ft/s
September 28, 2014

Geometry
the midpoint is just the average of the two ends, so its coordinates are x = (-4+9)/2 = 5/2 y = (-2-6)/2 = -4 So, M = (5/2,-4) It would be better had you posted your work, so we could verify accuracy or note mistakes. Also, answer keys are sometimes wrong, so that's always...
September 28, 2014

maths
assuming a constant rate of cooling, it will take x total minutes, where 300 - (300-200)/3 x = 70 x = 6.9 So, in 3.9 more minutes it will have cooled to 70°F
September 28, 2014

geometry
The two radii are r and 14-r, so πr^2 + π(14-r)^2 = 160π (assuming the strange character is supposed to be pi) r^2 + 196 - 28r + r^2 = 160 Now just solve for r.
September 28, 2014

Calculus Minima Problems
if she lands a distance x from the closest point on shore, she is 6-x from the village. So, she will row √(x^2+36) km run 6-x km So, her travel time will be t = √(x^2+36)/10 + (6-x)/20 dt/dx = (2x - √(x^2+36)) / 20√(x^2+36) Since the denominator is ...
September 28, 2014

math
since the figure is isosceles, the diagonals are equal. So, 8x-7 = 5x+2 Now, just solve for x and evaluate the length.
September 28, 2014

trigo
Ah. If you just wanted to verify that cos 3x = 4cos^3 x - 3cos x, then consider cos 3x = cos(2x+x) = cos(2x)cos(x) - sin(2x)sin(x) = (2cos^2(x)-1)(cos x) - (2sin x cos x)(sin x) = 2cos^3(x)-cos(x) - 2sin^2(x)cos(x) = 2cos^3(x) - cos(x) - 2(1-cos^2(x))cos(x) = 2cos^3x - cosx - ...
September 28, 2014

trigo
If you want to know the solutions to 4cos^3x - 3 cos x = 0, cos x (4cos^2 x - 3) = 0 so, cos x = 0 or cos x = ±√3/2 You should recognize those values, as they come up often.
September 28, 2014

algebra
Been there, done that, half an hour ago. It helps if you check your previous posting before doing it again... http://www.jiskha.com/display.cgi?id=1411871416
September 27, 2014

math
A square is the largest area for a given perimeter, if all sides are included. In this case, one side is not, so suppose the side parallel to the wall has length x, and the other sides have length y. x+2y = 24 The area is a = xy = (24-2y)y = 24y-2y^2 You know that this is just...
September 27, 2014

geometric sequence
ar + ar^4 = 7/2 ar^2 + ar^5 = -7 divide and you have r(1+r^3) / r^2(1+r^3) = -1/2 1/r = -1/2 r = -2 So, a = 1/4 Check. The sequence is 1/4 -1/2 1 -2 4 -8 -1/2 + 4 = 7/2 1 + (-8) = -7
September 27, 2014

algebra
Work with the total cost of each part of the mix. They have to add up the the final cost. So, if there are x lbs of $8 coffee, the rest (60-x) has to be the $4 coffee. 8x + 4(60-x) = 5.25(60) x = 18.75
September 27, 2014

Algebra 1
just collect terms with the same power and then simplify: 6-t-t^4 + 9t+t^4 = (-1+1)t^4 + (-1+9)t + 6 = 8t+6 It is customary to list the highest power first, and then descend. Notice how the t^4 terms vanish because -1+1 = 0
September 27, 2014

algebra
well, just plug in your numbers: f(35) = 0.019*35^2 + 35 + 14 = 72.275 and so on with other values
September 27, 2014

Algebra
Since the fence is mentioned, you really should check to see that the ladder will clear the fence. Using the given distances, and similar triangles, if the ladder lies on top of the fence, it will reach up to a height h, found by 9/8 = h/10 h = 12.5 In this case, the ladder ...
September 27, 2014

physics
5π/4 what about it? It's just a number. It is much easier to use in calculations than its decimal approximation of 3.927
September 27, 2014

Pre-Calc
by the time you get to pre-calc, you surely know how to evaluate a function for a specific value. Just plug it in! f(2) = 3*2^2 + 2*2 + 4 f(a+h) = 3(a+h)^2 + 2(a+h) + 4 and you can expand that if you wish
September 27, 2014

Chemistry
if the stock solution is 0.450M, then if you add x mL of water, you have 0.450(14.0) = 0.350(14.0+x) x = 4.0 check: the concentration is to be reduced by a factor of .35/.45, so the volume must be increased by a factor of .45/.35 .45/.35 * 14 = 18, so we added 4 mL of water.
September 27, 2014

math
assuming you want integer dimensions, just find the factors of 2460: 2x2x3x5x41 Now, you can mix and match, as long as you use them all once each. For example, 2*3 x 2*5*41 = 6x410
September 27, 2014

Math
better explain what it is you want to do. "9x" is an incomplete expression.
September 27, 2014

ap physics
depends on your speed, doesn't it? I guess you weren't paying attention, either in class or in your posting.
September 27, 2014

math
dunno - what is a family of graphs? enter your functions in the box at wolframalpha.com and it will show the graphs. Then you can play around with different parameters.
September 27, 2014

Calculus
I think you both misread the question. We want a line tangent to ln(x) which passes through (0,0). Since the slope of the tangent is 1/x, we want a line through (0,0) and (h,ln(h)) with slope 1/h. Clearly, at x=e, y=1 and the slope is 1/e, so y = x/e is the tangent at (e,1) ...
September 27, 2014

Math problems.
multiplication and division first, then addition and subtraction, all done left to right: 15 – 6 • 9 ÷ 2 + 10 15 – 54 ÷ 2 + 10 15 - 27 + 10 -12 + 10 -2 Evaluate parenthesized expressions first of all: 4 • (6 + 3) + 5 4 • (9) + 5 36 + 5 41
September 27, 2014

physics
See an almost identical problem in the first related question below.
September 27, 2014

math
0 is 4 to the left of 4 So, the other end's x value is 4 to the right of 4, or 8. Do y the same way.
September 27, 2014

math
No, since area = side^2 It is not a constant multiple of the side length.
September 27, 2014

Physics
At time t > ∆t, position of A: v(t-∆t) + 1/2 (v/∆t)t^2 position of B: 1/2 a(t-∆t)^2 So, now you need to find when the positions are the same: v(t-∆t) + 1/2 (v/∆t)t^2 = 1/2 a(t-∆t)^2 2vt - 2v∆t + (v/∆t)t^2 = at^2 - 2a&#...
September 27, 2014

math
since 3 < pi < 4, √9 < pi √16 In fact, since pi^2 = 9.86, √9 < pi < √10
September 27, 2014

Trig
clearly, x^2/a^2 + y^2/27^2 = 1 at x=24, y=9, so 24^2/a^2 + 9^2/27^2 = 1 24^2/a^2 + 1/9 = 1 24^2/a^2 = 8/9 a^2 = 24^2 * 9/8 = 648 x^2/648 + y^2/729 = 1
September 27, 2014

algebra
No idea what "if a sheet is 0.003 8" means. Also, say 1 cm^3 for volume.
September 27, 2014

Math
it's because x^2+6 has no factors in common with x^2+3
September 27, 2014

algebra 2
#3 since one equation tells us that y = -3x+6, use it in the other equation: 2y = 10x-36 2(-3x+6) = 10x-36 -6x+12 = 10x-36 -16x = -48 x = 3 Do #4 the same way
September 27, 2014

Algebra
If the short piece is x, then x + 4x = 20 Now find x, and then 4x.
September 27, 2014

Algebra 2
all I did was clear the fractions, just as you would if you were doing, say, x/2 = 3/7 7x = 3*2 After that, I just expanded terms and simplified. You never said what you wanted to do with the fractions. Naturally, if y=4 and x=1, (y-1)/(x+3) = 3/4
September 27, 2014

Algebra 2
(y-1)/(x+3) = 3/4 4(y-1) = 3(x+3) 4y-4 = 3x+9 3x-4y+13 = 0 Not sure where you want to go with this.
September 27, 2014

Physics
The range of the projectile is R(x) = 15.5^2 * sin(84°)/9.81 = 24.36 m The height is y(t) = 15.5 sin 42° t - 4.9t^2, so it takes 2.12 seconds to fall back to the initial height. So, the runner has to run toward the thrower at (30-24.36)/2.12 = 2.66 m/s
September 26, 2014

Math Homework
(fg)(x) = f(x)*g(x) = (x^2)(4x-5) = 4x^3 - 5x^2 (g/f)(x) = g(x)/f(x) = (1/x^2) / (1/x) = 1/x^2 * x/1 = x/x^2 = 1/x
September 26, 2014

Pre-Calc
g(f) = 5-f = 5-(3x+5) = -3x f(g) = g+2 = (4-x^2)+2 = 6-x^2 f(g) = g^2 = (x-1)^2 = x^2-2x+1 Hmmm.
September 26, 2014

Math help, anyone?
#6,7 are positive, the rest are negative
September 26, 2014

Calculus
#1 using l'Hospital's Rule, ( t^(1/3) - 1)/(t^(1/2) - 1) -> (1/3 t^2/3)/(1/2 t^1/2) = 2/3 t^-1/6 = 2/3 at t=1 If y=2^x, y' = ln2 2^x at x=0, that's just ln2 So, the line is y-1 = ln2(x) so, y = ln2 x + 1 So, the slope is ln2 = 0.693 See http://www....
September 26, 2014

Pre-Calc
I would draw it just like x^2, but with the vertex at (4,-2) instead of (0,0).
September 26, 2014

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