Friday
April 25, 2014

Posts by Steve


Total # Posts: 21,980

math
well, since 1L = 1000 cm^3, ...

Algebra
(5x-5)/(10x^2-25x+15) = (x-1)(2x^2-5x+3) = (x-1) / (x-1)(2x-3) = 1/(2x-3) x=1 and x = 3/2 are excluded because you cannot divide by zero. (w^2+6w+9)/(2w^2-18) = (w+3)(w+3) / 2(w+3)(w-3) = (w+3) / 2(w-3) x = 3 and -3 are excluded: no division by zero allowed

mathh
because 1 2/3 * 2 = 3 1/3, which is less than 3 1/2 or, 1 2/3 = 5/3 = 10/6 3 1/2 = 3 3/6 = 21/6 and 10 is less than half of 21

math
3x + 2y = 100 a = xy = x(100-3x)/2 = (100x - 3x^2)/2 max area at x = 100/6 Note that the fencing is divided equally among widths and lengths for max area.

Math
original area: a = 1/3 pi r^2 h new area, using half the height is 1/3 pi r^2 (h/2) = (1/3 pi r^2 h)/2 = a/2

Geometry
that would be a good guess, if you want to find the distance, eh?

Geometry
the distance from end to end is twice the distance from midpoint to end. That should get you started. I assume you know how to get the distance between two points. . .

Algebra
if the stores are A and B, then S = {A,B} represents the stores. Now, if you want to represent the pets, then P1 = {{dog,cat,hamster},{dog,rabbit,fish}} Again, that is a set with two elements, each of which is a set describing the pets sold at that store. If all you want is to...

math
don't know, but according to Euler, V+F = E+2

Algebra
ok, but I'd clear the fractions to make it look nicer: 21x^2 + x - 10 = 0

Algebra
if a polynomial is factored and set to zero, as in (x-a)(x-b)(x-c) = 0 Thane any one of the factors can be zero. In fact, at least one of the factors must be zero. So, f(x) = 0 when x = a or b or c So, your quadratics can be factored as (x - 1/2)(x-(-10) = 0 (x - 1/2)(x+10) = ...

geometry
the center is at the midpoint of the diameter. So, just take the average of the end coordinates to get the center.

PRE-CALC
as you know, the rotation matrix is x' = x cosθ + y sinθ y' = -x sinθ + y cosθ You want the inverse matrix, which is the same as rotating (x',y') through -θ x = x' cosθ - y' sinθ y = x' sinθ + y' cosθ...

maths
The man is walking away, so the horizontal distance the end of the rope has moved at time t is 3t meters. Initially, there are 3 meters of rope from the free end to the pulley. So, at time t, the amount of rope from C to the man is c^2 = 3^2 + (3t)^2= 9(1+t^2) Now, the block m...

Math - PreCalc (12th Grade)
well, only 3 digits are up for grabs, and there are 10 choices for each one. So, what do you think?

math
just complete the squares as needed, and balance out what you had to change: x^2-2x+1 + y^2+2y+1 - 2 - (1+1) = 0 (x-1)^2 + (y+1)^2 = 4

math
pears: m mangoes: 2m peaches: m-10 .4m + .5(2m) + .8(m-10) = 102 m = 50

algebra
No factors over the integers. But, you do have (a-2b)^2 - 12b^2 as a difference of two squares, that'd be (a-2b + √12 b)(a-2b - √12 b) or (a-2(1-√3)b)(a-2(1+√3)b)

Math: Thinking Mathematically
the cables are attached at a height of 12 yards. The other leg of the right triangle is 9 yards. this is just a 3-4-5 triangle scaled up to 9-12-15. So, there are three 15-yard cables. convert that to feet and you're done.

algebra
no way any factorials could be involved in such a sum There are n terms, so we have na + 0+1+2+...+(n-1) We all know the sum of the first n-1 integers is (n-1)n/2, so the final sum is na + n(n-1)/2 = n(a+n-1)/2

math
I like 43/36, but we need a mixed number: 1 7/36

math
1080(.80)(1.08) = 933.12

math
just add the x's and y's: (2+1)x + (-5+1) y 3x - 4y

Math
I'm sure the user manual for the calculator has examples.

Math
looks like x^2 + 15x = 646 (x-19)(x+34) = 0 So, the dining room is 19x19 and the kitchen is 19x15 rectangular space is 19x34

Math
total notes: 7*4 + 8*3 = 52 total C's: 8 so, . . .

math
annual growth: 1.48 2.70 2.71 2.86 2.85 2.86 2.68 2.58 2.14 2.26 Average growth for past 2 years is 2.20, so I'd guess 316.05 million If you want to do a last-squares line, that'd be cool, too.

math
Total ways to top a sundae: 31 ways with nuts only: 1 I would have said 1/5, but that assumes that the sundae will have only one topping. But, if all possible ways to pick toppings are included, and equally likely, 1/31 is P(nuts)

math
y/2 = -3 + (2+y) y/2 = y-1 y = 2y-2 y = 2 so, x = 4

Algebra 1
any examples shown here will look just like the ones in your text. Why not post some specific type that is causing you difficulty? You can copy/paste the √ sign from here. √4 = 2 √8 = √(4*2) = √4√2 = 2√2

algebra
6n + 2b = 23.52 3n + 4b = 25.53 multiply the 1st equation by 2 and you have 12n + 4b = 47.04 3n + 4b = 25.53 now subtract to get 9n = 21.51 n = 2.39 Now you can get b

Math HELP!!!!!!!!
well, the max height is found at (6.25,625) So, as long as he's not too far away when he tries to leap over the building, yes, he'll make it (as long as the building is sufficiently narrow).

Calculus
∫2x e^-x dx = -2 e^-x (x+1) = -2(x+1)/e^x Now, e^x grows so much faster than x that the limit is zero as x -> ∞. That can be justified by using lHospital's Rule, to show that the limit is the same as -2/e^x -> 0 However, as x -> -∞ e^x grows very...

MATH HELP
to use factoring, get everything on one side of the equation. x^2 = -25 + 10x x^2 - 10x + 25 = 0 The only factors of 15 are 1,5,25 (x-5)(x-5) is what you want 2x^2 + 9x = 5 2x^2 + 9x - 5 = 0 you know that you will have (2x+?(x-?) or (2x-?)(x+?) since 9 = 10-1, I'd look at ...

Math- please help!!!
#1: 15p^7 - 14p^7 = ? #2: just collect like exponents (6-4)x^2 - (2+1)xy + (3+1)y^2

pre-calc - NO
log(a+b) is NOT log a + log b log(ab) = log a + log b 3-log(x+2)=5 log(x+2) = -2 assuming base 10, x+2 = 1/100 x = 1/100 - 2 = -1.99

math
75 or 175

ROCKS :D just want to make sure.
I'd say (A) The age difference is so small on a geological scale that the depth is not a good criterion.

math word problem
g = 2j-6 p = j+4 g+j+p = 54 22 gumdrops 14 jawbreakers 18 pops

math
just use the distributive law (m^2-2m+7)(3m+6) = m^2(3m+6) - 2m(3m+6) + 7(3m+6) = 3m^3 + 6m^2 - 6m^2 - 12m + 21m + 42 = 3m^3 + 9m + 42

Maths
if a and b are the times, since the speeds are in ratio 3/4, the times are related by a/b = 4/3 a = b+30 a = 120 b = 90

Math
$15 discount 15/40 = 37.5%

Math
B

MATHS
3/4 speed takes 4/3 the usual time. So, 4/3 x = x + 2.5 1/3 x = 2.5 x = 7.5

Calculus Help STEVE
oops. Well, if you got y', y" is just a bit down the road There are two ways to do it. First, use y' directly: y' = -2x^2 / 3y^2 by the quotient rule, y" = ((-4x)(3y^2) - (-2x^2)(6yy')] / 9y^4 = ((-12xy^2 + 12x^2y(-2x^2/3y^2)) / 9y^4 = -12xy(y - x(-2x...

math (check please)
1/3 * 9^2 * 4 = 108 good job

Math - Hmmm
taking a guess, we have 45/2 a^2 + 45b^2 = 90 a^2 + 2b^2 = 4 Can't think of any nonzero integers that will do the job.

math
a = pi d h = pi * 1.6 * 5.6

Physics
219 * (4.12/11.2)

Math: Please help
Well, if the 30th %ile is where 30% of the scores are less than that, then since there are 10 scores, and 3 are less than 113, I'd say you are correct. same for 200

Math
it's either gibberish or an equation.

Calculus Help
6x^2 + 9y^2 y' = 0 y' = -2x^2 / 3y^2

Calc Help :(((((
I figure it's y = ln (x+√(9+x^2)) y' = 1/(x+√(9+x^2)) (1 + x/√(9+x^2)) = 1/√(9+x^2) y" = -x/(9+x^2)^(3/2)

math 1 question pls help!!!!!
Ah - Damon is correct - I missed "similar"

math 1 question pls help!!!!!
since the length and height are not changed, the volume is 1/2 as much as before. 120 is correct.

Calculus Help Please!!!
f(θ) = arcsin(√sin9θ) since d/dx arcsin(x) = 1/√(1-x^2), f'(θ) = 1/√(1-sin9θ) * 9cos9θ/2√sin9θ = 9cos9θ / 2√(sin9θ)√(1-sin9θ) nasty, but that's how it is

CALCULUS HELP
r = f(g(h(x)) r'(x) = f'(g(h(x))) g'(h(x)) h'(x) r'(1) = f'(g(h(1))) g'(h(1)) h'(1) = f'(g(4)) g'(4) (3) = f'(5) (5)(3) = (7)(5)(3) = 105

Calculus Help Please!!!
y = secx y' = secx tanx at x = pi/6, y' = 2/√3 * 1/√3 = 2/3 so, now we have a point and a slope, so the line is y - 2/√3 = 2/3 (x-pi/6) http://www.wolframalpha.com/input/?i=plot+y%3Dsec%28x%29+and+y+%3D+2%2F3+%28x-pi%2F6%29+%2B+++2%2F%E2%88%9A3

Calculus :(
y' = -d sin(t) + 2t sin(t) + t^2 cos(t)

Math - PreCalc (12th Grade)
as with any arithmetic progression, Sk = k/2(a1 + ak) = k/2(1+5k-4) = k/2(5k-3) Sk+ak+1 = k(5k-3)/2 + 5k-4+1 (D) Don't forget your algebra I just because you're in pre-calc now.

Math - PreCalc (12th Grade)
ok so far, though they already told you that f(2)=3 because the point (2,3) is on the graph. As you know, the slope at any point (x,y) on the graph is 2x+2 So, the slope at x=2 is 6 Though, if this is pre-calc, how do you know the slope of the tangent to a curve? That's ac...

Algebra
visit calc101.com and click on the link for long division. You can see all the details and play around with other polynomials.

Math - PreCalc (12th Grade)
yes, that would be correct.

Math - PreCalc (12th Grade)
You are correct; you cannot divide by zero. So, f(x) is not defined for x=4. However, for any other value of x, f(x) = (x-4)(x+4)/(x-4) = (x+4) So, if you define f(4) = 8, then f(x) = x+4 for all values of x, and is now continuous.

Math (check answers)
A only has 4 faces, 4 vertices, 6 edges D has 5 faces, 5 vertices, 8 edges

Math
I think you mean ±3√3 The two solutions are √27 and -√27 But, √27 = √(9*3) = √9√3 = 3√3

Math
a quadratic always has two solutions.

Math - PreCalc (12th Grade)
I guess, though product is also involved lim(2x) = 2 * lim(x) But I guess C is closest.

Math - PreCalc (12th Grade)
D If for no other reason, the sum of nth powers will be a polynomial of degree n+1.

Probability
#3 ok #4 There are 3 odd numbers out of 6. P(odd) = 1/2 #5 ok #6 what happened to the coin? (A) #7 ok #8 ok

Math (check answers)
correct

Multiple Choice HELP!
B

math
nothing to solve. There is no equation. Now, if you just want to simplify the expressions, you wind up with -3+n and 23+N

Math HELP!! Who can solve??
If I tell you that 2x = 10 how do you find x? You just divide by 2 on both sides of the equation, so you wind up with x all alone. Similarly, if you have D = 2zv and you want to find v, just recognize that D = (2z)v and you want to divide by the 2z to get v by itself. Thus, D/...

calculus
I think you missed a t in the denominator ∫ 1/(t^2-5t) dt = 1/5 log((5-t)/t) the definite integral is log(6)/5

Math help understand
or, you can look at it like this. The bus makes up 195km in 3 hours, so it is going 195/3 = 65 km/hr faster than the bike. 15+65 = 80 km/hr

geometry
if two of the points are a diameter apart, the triangle is a right triangle. So, given that the first two points are on the same semi-circle, which they must be, then we want the probability that the third point is on the same semi-circle. If it is not, then the triangle will ...

math question (CHECK)
I get 1536

Math
a = j/2 a + j = 12 If all you want is the sum of their ages, it doesn't matter what a and j are.

ama
if the ladder reaches up h feet, sinθ = h/10 cosθ dθ/dt = 1/10 dh/dt You know θ and dh/dt, so solve for dθ/dt.

math
1/6, 1/4, 2/5, 6/11, 4/7, 5/8, 2/3, 15/22, 7/9, 9/10

geometry - typo
Read what you wrote. That's a might small fence.

Math
Hmmm. Once you have an equation for the line, which you have, there's no need to interpolate. You can just plug in 550 for x. Now, if you don't have a function, but just data points, then you need to interpolate. That is, use the slope between two points to estimate an...

MATH (check please)
Hmm. I got 285.7 typo?

math algebra
(w^2-x)(w^2-x)

Math
as it says, base 4. 16 = 4^2 the base is raised to the power.

math help!
well, since f(1) = f(5), the vertex is at x=3, midway between. So, y = a(x-3)^2 + k Now plug in your points to get a and k: 3-k = 4a k = 3-4a y = a(x-3)^2 + 3-4a Unfortunately, since all we have is two points, there's no way to determine exactly where the vertex is. It is ...

trig
tan(kx) has period pi/k, since x grows k times faster. So, I think you have a typo. It should be 3tan3x = 3 tan3x=1 now, you know that tan pi/4 = 1, so 3x = pi/4, and x = pi/12. Now, tan(3x) has period pi/3. 2tanx-2 = 0 tanx = 1 Since tan pi/4 = 1, tan (pi/4 + pi) = tan 5pi/4 ...

trig
as you said, sin and cos have period of 2pi and tan has period pi. That's how you know.

math
1-1/3 = 2/3 2/5 * 2/3 = 4/15 1 - 1/3 - 4/15 = 6/15 = 2/5 so, you want 2/5 x = 600

math
18 + (18+w) = 36+w

algebra: functions
f/52

math
cot -220 = 1.19 what, your calculator doesn't do tan x in degrees? cot x = 1/tan x

Math (algebra)
C(r) = .11(2pi r^2) + .06(2pi rh) since pi r^2 h = 500, h = 500/(pi r^2) C(r) = .11(2pi r^2) + .06(2pi r(500/pi r^2)) C(r) = .22 pi r^2 + 60/r For C to be a minimum, C'(r) = .44pi r - 60/r^2 = 0 .44pi r^3 - 60 = 0 r^3 = 60/.44pi r = 3.51

Math
vertical angles are always equal.

Math
the wall, ground, and ladder form a righ triangle, with the ladder as hypotenuse, so, x^2 + 4^2 = 12^2 supplementary angles add up to 180 degrees. So, x + 3x+2 = 180 one angle is x, the other is 3x+2. Solve for x, and you're almost there.

math help
Think of a regular hexagon. All the angles are 120°. Now, think of pressing down on the top, keeping the top and bottom sides parallel. The two side angles will decrease, and the other four angles will increase. Stop when the side angles have become acute.

maths
5^(logx) + x^(log5) = 50 Note that log(5^logx)) = logx * log5 log(x^log5)) = log5 * logx So, the two are equal. That means 2*5^logx = 50 5^logx = 25 = 5^2 logx = 2 x = b^2 where logs are base b. So, if natural logs, x = e^2 if common logs, x = 10^2 = 100 check (common logs): 5...

College Math
74 are taking something 36+52 = 88, so 14 are taking both. So, 22 are taking biology only 22/200 = .11 is P(biology only)

MATH QUIZ PLS HELP!!!
#6 baffles me. Pyramids don't have a radius. All the others look ok, as long as #5 wants the volume.

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