Wednesday

October 1, 2014

October 1, 2014

Total # Posts: 25,427

**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*

**Pre-Calculus**

(f◦g)(x) = f(g(x)) Since f(x) = 8x, f(g) = 8g = 8(2x+1) = 16x+8
*September 26, 2014*

**Trigonometry**

I'd use law of cosines to find the third side, then use Heron's formula for the area.
*September 26, 2014*

**algebra 2**

really? If x = 3, y=3*3-4 = 5
*September 26, 2014*

**algebra 2**

for #1, it's easy to substitute. You have two values for y, so set them equal. 3x-4 = -2x+11 5x = 15 x = 3 so, y=3x-4 = 5 For #2, 4x-y=1, so y=4x-1 Plug that in, and we have 5x+2y = 5x+2(4x-1) = 24 5x+8x-2 = 24 13x = 26 x = 2 so, y = 4x-1 = 7 There are lots of graphing ...
*September 26, 2014*

**math - typos**

x = (7y-8)/(3y-1) x(3y-1) = 7y-8 3xy-x = 7y-8 y(3x-7) = x-8 y = (x-8)/(3x-7)
*September 26, 2014*

**Math Problem (please help)**

wherever there is an x, plug in a 3 and then simplify: f(3) = (2*3^2 + 8*3)/(5*3^3 + 40) = (18+24)/(135+40) = 42/175 = 6/25
*September 26, 2014*

**Trigonometry**

if the third side is 2x, then x = 14 sin 55º, and the height is h = 14 cos 55º, so the area is hx = (14 cos55º)(14 sin55º) = 7 sin 110º
*September 26, 2014*

**Math Problem (please help)**

what's the trouble? Just plug in the values. For example, (fg)(x) = f(x)*g(x) = (7x-9)(8-x) = -7x^2 + 65x - 72 Do the others in like wise.
*September 26, 2014*

**Pre-Calc - Oops**

Bzzzt. E
*September 26, 2014*

**math**

well, did you try any of them? for (a) 1 divides 1 2 divides 18 3 divides 183 4 divides 1836 5 divides 18365 6 divides 183654 7 does not divide 1836549 so, try the others
*September 26, 2014*

**MATHS**

You will probably like the answer better if you enter .5^(1/1590) ...
*September 26, 2014*

**Pre-Calc**

I assume you mean √(x+2) + 5 That would be √x shifted left 2 and up 5 So, (b) x^2 -x^2 is flipped upside-down -x^2-3 is then shifted down 3 So, (b) again
*September 26, 2014*

**Math Problem (please help)**

(x+3)(252/x - 2) = 252 x = 18 Check: 18*14 = 21*12 = 252
*September 26, 2014*

**AP Physics**

a^2 = 15^2 + 6.5^2 a = 16.3 I expect you can determine the direction.
*September 26, 2014*

**sat**

3/12 and that's "three pitchers are" not "three pitcher's is"
*September 26, 2014*

**Algebra**

20+8x
*September 26, 2014*

**Calculus**

If the man's shadow has length s when his distance from the pole of height h is x, then using similar triangles, (x+s)/h = s/6 6x+6s = hs s(h-6) = 6x so, (h-6) ds/dt = 6 dx/dt ds/dt = 6*30/(h-6) = 180/(h-6) Now, we were given 15/h = 6/6, so h=15 Thus, ds/dt = 180/9 = 20 ft...
*September 25, 2014*

**math**

well, I guess you know which is the correct choice, eh? consider it this way. car A is 15 miles ahead when car B starts. B is only going 10 mi/hr faster than A, so it will take 15/10 hours to make up the difference. As Reiny showed, that means it takes 1.5 hours.
*September 25, 2014*

**math**

the mistake was in not showing the arrangement.
*September 25, 2014*

**Urgent geometry help**

Since there is no conditional specified, there can be no converse. However, given your interpretation, your converse is correct. The "will" isn't really necessary at all, if you consider coming and leaving as sort of chronic events, one conditional on the other.
*September 25, 2014*

**Algebra 1**

|n-34| <= 8
*September 25, 2014*

**Algebra**

|p-53| <= 5
*September 25, 2014*

**algebra**

clearly the minimum cost is at the vertex of the parabola, which is at x = -b/2a = 18.1/1.8
*September 25, 2014*

**AP Physics**

28 @ S45W = (-19.8,-19.8) 56 @ E = (50,0) 84 @ E53N = (50.5,67.1) Add them up to get (80.7,47.3) So, we need (-80.7,-47.3) to get back to (0,0), a displacement of 93.5 m
*September 25, 2014*

**Physics**

Speedboat A negotiates a curve whose radius is 100 m. Speedboat B negotiates a curve whose radius is 221 m. Each boat experiences the same centripetal acceleration. What is the ratio vA/vB of the speeds of the boats?
*September 25, 2014*

**Math-please check**

#1 of course not: |-6|=|6| but -6≠6 #2 same reasoning. y could be -8. You can say, therefore that if |a|=|b|, then a^2 = b^2.
*September 25, 2014*

**math...**

I think you meant b-9 > 20 Now add 9 to both sides to get b by itself: b > 29
*September 25, 2014*

**Math Help.**

clearly, x <= 1, so 3x <= 3 3x+1 <= 4 Looks like D to me. C would have an open circle on the 1, rather than a filled dot.
*September 25, 2014*

**geometry**

oldv = 1/3 pi r^2 h Now replace r with 4r and h with whatever fraction of h, say, 1/n, it has become. new v = 1/3 pi (4r)^2(1/n * h) = 1/3 pi * 16r^2 * h/n = oldv * 16/n
*September 25, 2014*

**Please math help**

A n n-10 10-n 7-n n-7 n-7 = -3, so n=4 B yes, it always works, as shown above
*September 25, 2014*

**Algebra**

7p^2+16=2151 7p^2 = 2135 p^2 = 305 p = √305
*September 25, 2014*

**Math**

Things would be a lot clearer if you wrote CN^2 = 13^2 + 18^2 - 2*13*18 cos 45 = 169 + 324 - 468*√2/2 = 162.07 CN = 12.73
*September 25, 2014*

**trignometry**

y^2*sin(x)*sin(z)/2*sin(y) area = z/2 * y sinX but, z/sinZ = y/sinY, so z = ysinZ/sinY area = ysinZ/2sinY * y sinX = y^2 sinZ sinX / 2sinY
*September 25, 2014*

**algebra**

(5.1*10^3)*(3.2*10^3) (5.1)(3.2)*(10^3)(10^3) 16.32 * 10^6 But that's not scientific notation, so you need to shift the decimal point to 1.632 * 10^7
*September 25, 2014*

**Algebra 2**

a = 2pi r h + 2 pi r^2 = 2pi((3x-2)(x+3) + (3x-2)^2) = 2pi(3x^2+7x-6 + 9x^2-12x+4) = 2pi(12x^2-5x-2)
*September 25, 2014*

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