Monday

December 22, 2014

December 22, 2014

Total # Posts: 27,667

**algbra**

evidently the downstream speed is twice as fast as the upstream speed. So, 14+x = 2(14-x)
*October 31, 2014*

**maths**

If you mean 1/((x+2)(x+3)) - 1/((x-4)(x-5)) that would be ((x-4)(x-5) - (x+2)(x+3)) / ((x+2)(x+3)(x-4)(x-5)) = (14-14x)/((x+2)(x+3)(x-4)(x-5)) = (14-14x)/(x^4-4x^3-19x^2+46x+120) Now sure what you want to do with the other. And try using "-" instead of "_" ...
*October 31, 2014*

**Pre Calculus**

who said anything about sin-1 ?
*October 31, 2014*

**Math**

C=85+15H
*October 31, 2014*

**Solving inequalities**

just start with 1 and 20 1 20 Now try 2: 1 2 10 20 3, no 4? 1 2 4 5 10 20 and that's all! If you go past 4, you just run into factors already generated. In general, if you find all the factor up to √N, you will also have found all the ones greater than √N.
*October 31, 2014*

**Math**

google vector triple product and you will find lots of proofs. One that is relatively straightforward is at http://www.msci.memphis.edu/faculty/dwiggins/files/triplecross.htm You already know that AxB = -BxA, so that will help in the part (b).
*October 31, 2014*

**Calculus**

just evaluate f'(x) at x=25 f'(x) = -5/2 x^(-1/2) + 3/2 x^(1/2) = (-5/2)(1/5) + 3/2 (5) = 7
*October 31, 2014*

**Calculus**

f'(x) = 4x^3-40x f'(-1) = -4+40 = 36 f(-1) = 45 so the line is y-45 = 36(x+1)
*October 31, 2014*

**Calculus**

let u = x^12-2. Then we have h = u^3, so h' = 3u^2 u' = 3(x^12-2)^2 (12x^11) = 36 x^11 (x^12-2)^2
*October 31, 2014*

**trigonometry**

see the related questions below.
*October 31, 2014*

**Algebra**

correct
*October 31, 2014*

**algebra**

bowling alleys: A charges $5 for shoes and $6/game B charges $21 for shoes and $4/game how many games does it take for the day's bowling to be equal at the two alleys?
*October 30, 2014*

**algebra**

x/3 - 8 = 11 x = 57
*October 30, 2014*

**algebra**

2(5+s) = 28 s = 9
*October 30, 2014*

**math**

(1/2)(6/7)(1/3) = 1/7
*October 30, 2014*

**METRO**

6t+18r = 66 4t+7r = 29 t=2 r=3
*October 30, 2014*

**math**

-5x-4
*October 30, 2014*

**algebra**

-5x-4
*October 30, 2014*

**Algebra**

just sub in x+2 for x: f(x+2) = -5(x+2)+6 = -5x-4
*October 30, 2014*

**Math11**

#1 The MVT requires that f(x) be continuous and differentiable. Luckily, all polynomials meet these requirements. f(x) = 5x^2-3x+2 f'(x) = 10x-3 f(0) = 2 f(2) = 16 So, we want c where f'(c) = 7 10x-3 = 6 x = 0.9 The tangent line at x=0.9 is y-3.35 = 7(x-.9) y = 7x-2.95...
*October 30, 2014*

**Math**

Not quite the order is 0.8000000 0.8800000 0.8888888 0.8898989 0.8989898
*October 30, 2014*

**math**

rational zeros (plus or minus) 1,2,3,6,18 By Descartes' Rule of Signs, 1 positive root 2 or 0 negative roots a little synthetic division yields f(x) = (x+1)(x+3)(x-6)
*October 30, 2014*

**Geometry**

some hints to get you going: #1 tan 25° = .466 So, each step is .466 as high as it is wide. #2 tan 36.8° = 3/4 #3 tanθ = 12/15 = 4/5 θ = 38.7° arctan(10/7) = 55°
*October 30, 2014*

**college algebra**

after t minutes, the two isotopes have remaining amounts of 2^(-t/22) and 2^(-t/37) So, after one hour (60 minutes), the ratio of 162Ho/164Ho is just 2^(-60/22) / 2^(-60/37) = 2^(-60/22 + 60/37) = 2^(-450/407) = 2^-1.10565 = 0.465
*October 30, 2014*

**Statistics**

google for the users manual online.
*October 30, 2014*

**Math**

2x^2-14x -16 = 0 (x^2-7x) = 8 (x^2-7x+(7/2)^2) = 8 + (7/2)^2 (x - 7/2)^2 = 32/4 + 49/4 (x - 7/2)^2 = 81/4 x - 7/2 = ±9/2 x = 7/2 ± 9/2 x = -1,8
*October 30, 2014*

**physics**

t = (16.0-6.5)/3.6 = 3.47 seconds
*October 30, 2014*

**math**

is there a maximum speed? Seems like sufficient force could spin it as fast as you want. It's a stationary bike. It does not move!
*October 30, 2014*

**Algebra**

well, you can factor out the 2 and have 2(3x^2+2)(x+2) 3x^2+2 does not factor, since its discriminant is negative. After all, x^2 is always positive, so 3x^2+2 is always positive.
*October 30, 2014*

**Algebra**

both points have the same y-coordinate, so the equation is y = -3 To get that algebraically, note that the slope is 0/1 = 0 So, y = 0x+b y(-4) = -3, so b = -3 y = 0x - 3 or, just y = -3 slope is 3/5 so, use the point-slope form: y+5 = 3/5 (x-1) y = 3/5 x - 28/5 Doing your way...
*October 30, 2014*

**Algebra**

slope = -3/2 use the point-slope form, then change to slope-intercept: y-7 = -3/2 (x-5) y = -3/2 x + 29/2 The line is vertical, since both points have the same x-coordinate. So, x = -5 Always check for horizontal/vertical lines first.
*October 30, 2014*

**Math help!**

√((4+2)^2+(-6-2)^2) = √(6^2+8^2) = √(36+64) = √100 = 10 Better check your + and - signs
*October 30, 2014*

**Math**

f(t) = 15(t-3)(t-10) Clearly f(t) < 0 on the interval (3,10)
*October 30, 2014*

**math**

f(x) increasing when f'(x) > 0 f'(x) = 4x^3 - 60x^2 + 282x - 414 = 2(x-3)(2x^2-24x+69) The roots are 3,6±√(3/2) = 3.00,4.78,7.22 So, f' > 0 in (3,6-√(3/2) U (6+√(3/2),∞)
*October 30, 2014*

**Pre calc**

500 x 1000 area = x(2000-2x)
*October 30, 2014*

**Trigonometry**

multiply by 1-tanx to get (1-tanx)^2/(1-tan^2 x) = (1-2tanx+tan^2 x)/(1-tan^2 x) = (1+tan^2 x)/(1-tan^2 x) - 2tanx/(1-tan^2 x) = sec^2x/(1-tan^2 x) - tan2x = 1/(cos^2x-sin^2x) - tan2x = 1/cos2x - sin2x/cos2x = (1-sin2x)/cos2x Your carelessness with parentheses threw me off for...
*October 30, 2014*

**Calculus**

see the related questions below; just change the numbers.
*October 30, 2014*

**algebra**

x + 2/3 x + 1/2 x + 1/7 x = 97 97/42 x = 97 x = 42 check: 42 + 28 + 21 + 6 = 97
*October 30, 2014*

**business math**

c/4 - 6
*October 30, 2014*

**statistics**

4% lie 1.75 std below the mean. So, 60000-5000*1.75 = 51250 If the warranty is for 51250, 96% of the tires will exceed that mileage. You can enter your values and play around with Z table stuff at http://davidmlane.com/hyperstat/z_table.html
*October 30, 2014*

**Math**

Draw your Venn diagram of three intersecting circles. 30 in the center part Since 55 are married and have a cell phone, that leaves 25 in the unlabeled intersection of married and cell. Similarly, 5 in the cell-car intersection not already labeled. 25 in the unlabeled part of ...
*October 30, 2014*

**Algebra**

correct
*October 29, 2014*

**Algebra 2**

as with all parabolas, the vertex is at x = -b/2a, in this case t = 3 So, plug that in to get the max height f(t) = 16t(6-t) That will tell you how long it takes to hit the ground (f=0) As usual, the vertex is midway between the roots.
*October 29, 2014*

**math**

d = (135-100)/5 = 7 100+7 = 107
*October 29, 2014*

**AP physics**

we have initial velocity (Vx,Vy) y = Vy t - 4.9t^2 4.8Vy - 4.9*4.8^2 = 0 Vy = 23.52 x = Vx t 52 = Vx * 4.8 Vx = 10.83 So, v^2 = 10.83^2 + 23.52^2 v = 25.90 at an angle θ such that tanθ = Vy/Vx = 23.52/10.83 = 2.17 θ = 65.28° Now you can plug those values ...
*October 29, 2014*

**Math**

what, no calculator? Much faster than posting it here and waiting for a response.
*October 29, 2014*

**Math**

it's not an equation. It's just an expression. Punch in the numbers on your calculator to see its value.
*October 29, 2014*

**math**

leap years have 366 days
*October 29, 2014*

**math**

x = (c-7000)/210 No calculus needed; just algebra I
*October 29, 2014*

**math**

11/24 - 3/8 = 11/24 - 9/24 = 2/24 = 1/12
*October 29, 2014*

**math**

(2/3)(1/3)x = 4 2/9 x = 4 x = 18 check: spent 12 at A leaving 6 spent 2 at B, leaving 4
*October 29, 2014*

**calc**

v = 4/3 pi r^3 dv/dt = 4pi r^2 dr/dt a = 4pi r^2 da/dt = 8pi r dr/dt = 8pi r (dv/dt / (4pi r^2)) Now just plug in dv/dt and r
*October 29, 2014*

**calc**

PV^1.4 = C using the product and chain rules, V^1.4 dP/dt + 1.4PV^.4 dV/dt = 0 now just plug in your numbers
*October 29, 2014*

**calc**

After t hours, A is at (-(30+17t),0) B is at (0,16t) So the distance d is found by d^2 = (30+17t)^2 + (16t)^2 = 545t^2 + 1020t + 900 at t=6, d = 163.22 So, now we can find the rate of change for d: 2d dd/dt = 1090t + 1020 2*163.22 dd/dt = 7560 dd/dt = 23.16 knots
*October 29, 2014*

**Algebra I**

Short answer: yes, you are correct. Some explanation... just watch the units. You can always multiply by 1 without changing the value of the expression. 1m = 100cm, so 1m/100cm = 1 100cm/1m = 1 Now, keep the units with the values. They cancel, just like factors: 42m * 100cm/1m...
*October 29, 2014*

**currency exchange/ math**

U$130 * C$!/U$0.9315 = C$139.56 the commission is C$139.56 * 0.0055 = 0.77 So, the final amount received was 139.56-.77 = 138.79
*October 29, 2014*

**math**

1.8*0.3 = 0.54 each multiplicand has one decimal place. So, the product has two. Also, just by observation, 1.8 is almost 2, so the answer should be about twice as big as 0.3 (0.6)
*October 29, 2014*

**math**

fix the garbled sentence eye was three times as old .
*October 29, 2014*

**math**

since time = distance/speed, (d/2)/5 + (d/2)/10 = 3 d = 20 check: 10/5 + 10/10 = 2+1 = 3 hrs
*October 29, 2014*

**Math**

n! is basically an nth-degree polynomial (2n)! is a 2n-th degree polynomial n^n is an nth-degree polynomial so, (2n)!/n^n -> n^2n/n^n is like an nth-degree polynomial, and -> infinity
*October 29, 2014*

**algebra**

see all the details here: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx Just enter your coefficients and watch the fun
*October 29, 2014*

**Geometry**

well, just do what the rule says: (x,y)->(x,y-5) = (-8,-3) means x = -8 and y-5 = -3 x = -8 and y = 2 reflection: (x,y)->(-5-(x+5),y) = (-x-10,y) glide: (x,y)->(x,y-5) means (-x-10,y) -> (-x-10,y-5) So, P->(-8,-3) = (-x-10,y-5) means that -x-10 = -8 y-5 = -3 x...
*October 29, 2014*

**geometric progression**

T6 = ar^5 = a*10^5 = 2000 a = 2*10^3 / 10^5 = 2*20^-2 = 0.02 Check: 0.02 0.2 2 20 200 2000 ...
*October 29, 2014*

**calculus**

LOVE IT! Assuming the lantern is in fact shining, we have If the length of rope from the man to the pulley is z, and the man is x ft away from the wall, we have x^2+30^2 = z^2 z dz/dt = x dx/dt when x=40, z=50 and the lantern is at height 36-10 = 26 If the lantern is at height...
*October 29, 2014*

**geometry**

I pick D
*October 29, 2014*

**math**

150/x = tan 34°
*October 29, 2014*

**Algebra**

That's because there's a mistake in the problem. Even if it were all invested at 4.2%, she'd earn .042*15000 = $630 in interest. That $21 interest is bogus. It must be $2100 or something.
*October 28, 2014*

**AP Calculus**

infinite discontinuities are not removable. (x^2+4x+3) = (x+3)(x+1) x^2-9 = (x+3)(x-3) So, for all values of x except x = -3, f(x) = (x+1)/(x-3) At x = -3, f(x) = 0/0, which can be any value; it is undefined. The discontinuity there is removable, if f(-3) is defined to be 1/3.
*October 28, 2014*

**Calculus**

2x + y + xy' + 2yy' = 0 y'(x+2y) = -(2x+y) y' = -(2x+y)/(x+2y) So, y'=0 when 2x+y = 0 So, if y = -2x, x^2-2x^2+4x^2 = 6 3x^2 = 6 x = √2 So, y = -2√2 At (√2,-2√2) and (-√2,2√2) the tangent is horizontal. Check: http://www....
*October 28, 2014*

**Geometry/Algebra**

y-7 = -5/2 (x+4) y-7 = -5/2 x - 5/2(4) y-7 = -5/2 x - 10 y = -5/2 x - 3
*October 28, 2014*

**Math**

f'(x) = x(2logx - 1)/(logx)^2 So, since f and f' are not defined at x=0, f'(x) = 0 when 2logx = 1 logx = 1/2 x = √e f(√e) = e/(1/2) = 2e See the graph at http://www.wolframalpha.com/input/?i=%28x^2%29%2F%28ln%28x%29%29+for+x+%3D+0..3
*October 28, 2014*

**Math**

well, you need 1/3 pi(5^2)h = pi(5^2)(12) 1/3 h = 12 h = 36 This should be clear since the volume of a cone is 1/3 the volume of an equivalent cylinder. So, if you want the cone of the same radius to have the volume of a cylinder, it must be 3 times as tall.
*October 28, 2014*

**Calculus**

as usual for quadratics, the vertex is at t = -b/2a = 308/(14/3) = 66 Odd, since g is 1/6 of earth's, I expected the equation to be -16/6 t^2
*October 28, 2014*

**Calculus**

wh = 380 a = (w+16)(h+4) = (w+16)(380/w + 4) = 4w + 444 + 6080/w da/dw = 4 - 6080/w^2 minimum area when da/dw = 0. So solve that and evaluate w and h. Then the poster dimensions are w+16 and h+4.
*October 28, 2014*

**Calculus**

set da/dw = 0 when w + 2h + πw/2 = 49 a = wh + π/8 w^2 = w(49 - (1+π/2)w)/2 + π/8 w^2
*October 28, 2014*

**Calculus**

If the base has width 2x and height y, then the area is a = 2xy = 2x(4-x^2) so find x when da/dx =0
*October 28, 2014*

**Algebra 2 & trig**

If x at 5.5%, the rest (7500-x) is at 6%. So, add up the interest: .055x + .06(7500x) = 435
*October 28, 2014*

**Math 130**

The lateral area is just 2πrh, so doubling either has the same effect The area of the ends, however, is 2πr^2, so it's likely that doubling r has a greater effect. However, since the area is not directly proportional to either, the relative sizes of r and h will ...
*October 28, 2014*

**calculus**

inflection points where f" = 0 f" = 2(2-9x^2)/(3x+2)^2 f"=0 when 2-9x^2 = 0
*October 28, 2014*

**Math**

you have approximately 300mi/10hr or about 30 mi/hr Clearly (4) is the only viable choice
*October 28, 2014*

**algebra 2**

plug in x=1 and y=2 (1+2)^-2 = 1/9 1^-2 + 2^-2 = 5/4
*October 28, 2014*

**Physics**

to conserve momentum, (1.93*10^4)(3.12) + (2)(1.93*10^4)(1.04) = 3(1.93*10^4)(v) 3.12+2.08 = 5.79v v = 0.898 m/s Old KE = 1/2 m*3.12^2 + 1/2 * 2m * 1.04^2 = 5.949m new KE = 1/2 * 3m * 0.898^2 = 1.209m loss of KE = 4.739m = 9.147*10^4 J
*October 28, 2014*

**Physics**

pressure is force/area force is equal to weight, so (a)
*October 28, 2014*

**sci**

as are all theories, (a) It has, in fact, changed several times already.
*October 28, 2014*

**math**

C = kn
*October 28, 2014*

**math**

it's the fractional part of a decimal number. .123 is the mantissa of 61.123 It is often used when describing logarithms base 10. If the mantissa is .3010 log 2 = 0.3010 log 20 = 1.3010 log 200 = 2.3010 the mantissa provides the basic number, from 1 to 10. The ...
*October 28, 2014*

**math**

well, 108/1.2 = 90
*October 28, 2014*

**physics**

to balance, m1 x1 = m2 x2 so, (50.0)(1.90) = (45.0)(x2) cinchy, right?
*October 28, 2014*

**Math 5 grade - typo?**

first problem. The sum of the even digits cannot be an odd number.
*October 27, 2014*

**Math Help..!**

63.28 - 27.45 = ?
*October 27, 2014*

**Math**

1/x=(x-34)/(2x^2) multiply by 2x^2: 2x = x-34 x = -34
*October 27, 2014*

**Math**

If we assume there are 18 fewer walkers than bus riders, and there are 6 walkers, then if we let x be the number of riders, then x - 18 = 6
*October 27, 2014*

**Algebra**

slope = -1/3 point-slope form: y+2 = -1/3 (x-4) Now rearrange that into slope-intercept form.
*October 27, 2014*

**math**

If $x at 10%, the rest $(1000-x) is at 8%. So, add up the interest .10x + .08(10000-x) = 950
*October 27, 2014*

**math**

x/8 = 2x/9 + 1
*October 27, 2014*

**math**

consider the % of juice before and after adding x liters of water: .10(5) = .04(5+x)
*October 27, 2014*

**math**

if anna's speed is s, then since distance = speed*time, 9s = 9(1.2s)-10 9s = 10.8s - 10 1.8s = 10 s = 5.55 m/s
*October 27, 2014*

**Wording/Vocab**

well, reanimate means to bring the dead back to life. In an article on Mary Shelley, it says, "She was familiar with the ideas of using dead bodies for study, the newer theory of using electricity to animate the dead,..." so, while animate is more often used ...
*October 27, 2014*

**math**

4/10 -1/5 9/15-1/3 4/12-1/6 find the difference
*October 27, 2014*

**Math**

x(.60)(.40)(.30) = 0.50 x = 6.94 The drop the 2nd year is 6.94(.60)(.60) = 2.50
*October 27, 2014*

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