Friday

December 19, 2014

December 19, 2014

Total # Posts: 27,632

**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*

**math**

disagree. odd*odd = odd example: 3*5 = 15 odd numbers have the form 2k+1 where k is an integer. So, two odd numbers multiplied are (2m+1)(2n+1) = 4mn+2m+2n+1 = 2(2mn+m+n)+1 = 2k+1 where k = 2mn+m+n
*October 27, 2014*

**Math**

from your handy Z table, you find that 24 is 2/2.1 = 0.952 std above the mean P(Z>0.952) = 0.17 See the app at http://davidmlane.com/hyperstat/z_table.html
*October 27, 2014*

**College algebra**

slope (m) = (9-11)/(6-4) = -1 so, y=-x+b y(4)=11, so b=15 y = -x+15
*October 27, 2014*

**math**

1+1 = 2 12/20+15/20 = 27/20 -> 2 Hmm. Looks the same to me.
*October 27, 2014*

**math**

consider the sum 3/5+3/4. round each fraction and estimate the sum. add the two fraction using a common denominator and then round the result. which estimate is closer to the actual answer.
*October 27, 2014*

**math**

if the school record for the softball throw is 78 ft about how much farther must Robert throw the ball to match the record. a 15ft b 16ft c 18 ft d 20ft
*October 27, 2014*

**math**

4/8-1/4 find the diffence
*October 27, 2014*

**math**

3 1/4 + 2 5/6 estimate each sum or difference
*October 27, 2014*

**Algebra**

a square has the max area for a given perimeter.
*October 27, 2014*

**math**

9/10-3/5 find the difference
*October 27, 2014*

**Stats**

you can play around with Z table stuff at http://davidmlane.com/hyperstat/z_table.html It has very nice input forms so you can specify tails or middle regions.
*October 27, 2014*

**Math**

Since v = 1/3 pi r^2 h I get v = (1/3)(3.14)(9)(8) = 75.36 How did you get your answer?
*October 27, 2014*

**physics**

A small block of mass m = 225 g is released from rest at point circled A along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 27.5 cm as shown in the figure below. (a) Calculate the gravitational potential energy of the block-Earth ...
*October 27, 2014*

**Algebra, help please!!!**

well, clearly, if you want values between 4.30000000000000... and 4.33333333333333... All you need to do is replace the string of zeroes with something less than 33333333333333... So, you could have 4.3123456789 4.3010101010 4.33333322222 Similarly for the other one
*October 27, 2014*

**algebra. help!**

|110-30t| = 40 so, either 110-30t = 40 30t = 70 t = 7/3 = 2.3 or -(110-30t) = 40 -110+30t = 40 30t = 150 t = 5 So, (A) is correct
*October 27, 2014*

**algebra. help!**

3x+10 >= 4 3x >= -6 x >= -2 (A) 2.25x >= 180 x >= 80 you are correct
*October 27, 2014*

**Calculus: need clarification to where the #'s go**

y = 2√(4x+4) = 4√(x+1) THE DISTANCE D IS FOUND USING d^2 = x^2+y^2 = x^2+16(x+1) = x^2+16x+16 when x=3, d=√73 so, 2d dd/dt = (2x+16) dx/dt d dd/dt = (x+8) dx/dt so, now for the numbers: √73 dd/dt = 11(5) dd/dt = 55/√73
*October 27, 2014*

**Pre-Calc/Trig**

it depends. as a function of time, or of distance? wikipedia's article on trajectory has many useful equations.
*October 27, 2014*

**Algebra**

(2a-b)^3 = (2a)^3 - 3(2a)^2b + 3(2a)b^2 - b^3 = 8a^3 - 12a^2b + 6ab^2 - b^3 better review your binomial coefficients. I think you used 2 instead of 3. the other is correct
*October 27, 2014*

**Math Homework**

3x^2+2x > 2x^2-3 x^2 + 2x + 3 > 0 since the discriminant is negative (4-12), this has no real roots. That is, it does not cross the x-axis. Since f(0) = 3 > 0, f(x) is always > 0, so the solution is all real numbers. 4x^2 - x < 0 x(4x-1) < 0 Recall what you ...
*October 27, 2014*

**algebra**

Since the domain of f is all x, the range of f(6x) is the same as the range of f(x). The graph is just contracted horizontally by a factor of 6. The range is unaffected. So, the range of g(x) = f(6x)+1 is just [-11,3]+1 = [-10,4] Things would have been stickier had the domain ...
*October 27, 2014*

**Calculus: need clarification to where the #'s go**

just use the formula v = 4/3 pi r^3 a = 4pi r^2, so dv/dt = 4pi r^2 dr/dt = a dr/dt da/dt = 8pi r dr/dt v(14) = 11494 a(14) = 2463 So, we have 80 = 2463 dr/dt da/dt = 8pi(14)(80/2463) = 11.43
*October 27, 2014*

**Algebra**

Hmm. I get 2x(3x^2-4xy+2y^2) + 5y(3x^2-4xy+2y^2) = 6x^3 - 8x^2y + 4xy^2 + 15x^2y - 20xy^2 + 10y^3 = 6x^3 + 7x^2y - 16xy^2 + 10y^3
*October 27, 2014*

**algebra--1 question**

Just use >= for greater than or equal Your solution is correct. x < -3 or x >= 5
*October 27, 2014*

**algebra 2**

He only falls 1500 ft before the chute opens. So, change d to 1500 in the above solution and then rework the numbers.
*October 27, 2014*

**Calculus: need clarification to where the #'s go**

you have your formula: pv^1.4 = c, so you get v^1.4 dp/dt + 1.4pv^.4 dv/dt = 0 Now just plug in your numbers: (330^1.4)(-10) + (1.4)(330^.4)(79) dv/dt = 0 -33567.54 + 1125.02 dv/dt = 0 dv/dt = +29.84
*October 27, 2014*

**Calculus**

To find the rate of increase, note that the distance x after t hours is given by x^2 = (50+19t)^2 + (24t)^2 At 3 pm, t=3, and we have x^2 = 117^2 + 72^2 = 16633 x = 137.4 Now we have to find the derivative: 2x dx/dt = 38(50+19t)+48(24t) = 1874t + 1900 So, at t=3, we have 2(137...
*October 27, 2014*

**science-gen chem**

.969g CaCl2 = 0.00873 moles 1.111g KIO3 = 0.00519 moles Each mole of CaCl2 requires 2 moles of KIO3, so clearly the KIO3 is the limiting reagent. So, since each mole of KIO3 produces 1/2 mole of Ca(IO3)2, we get 0.00269 moles of Ca(IO3)2 = 1.051g
*October 27, 2014*

**Calculus - PLEASE HELP!**

3√(x^2+y^2) * (x + yy') = (x+yy')/√(x^2+y^2) + 1 x+yy'(3√(x^2+y^2) - 1/√(x^2+y^2) = 1 y' = (1/(3√(x^2+y^2) - 1/√(x^2+y^2) - x)/y y' = [x+√(x^2+y^2) - 3x(x^2+y^2)]/(y(3(x^2+y^2)-1)) So, we want either the numerator ...
*October 27, 2014*

**Calculus**

draw a diagram. Let the distance from the pole be x, and the shadow's length be s. Using similar triangles, we have s/6 = (x+s)/15 or, 5s = 2x+2s 3s = 2x so, ds/dt = 2/3 dx/dt plug and chug
*October 27, 2014*

**Calculus**

16/(x^2+16)^(3/2)
*October 27, 2014*

**Calculus**

dv/dt = 4pi r^2 dr/dt plug and chug
*October 27, 2014*

**Calculus**

using implicit derivatives, (x+2y)y'=2x-y (1+2y')y' + (x+2y)y" = 2-y' Now plug in the numbers: y'(3) = 2, so (1+4)(2) + (3)y" = 2-2 10+3y" = 0 y" = -10/3
*October 27, 2014*

**Math**

Now, if you meant x^2-31x+108 = 0 then (x-4)(x-27) = 0 x^x is a bit nastier
*October 27, 2014*

**Calculus**

df/dx = df/dg * dg/dx = g/√(g^2-4) * (3) = 3(3x-2)/√((3x-2)^2-4) = 3(3x-2)/√(9x^2-12x) at x=3, that's 3(7)/√45 = 21 / 3√5 = 7/√5
*October 27, 2014*

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