Thursday
April 17, 2014

Posts by Steve


Total # Posts: 21,714

Math
2x + (90-x) = 96

Algebra
I hope the selections include 3/16 (1±√33)

Algebra
1/7 (3±√30)

math word problems
a = b/2 b = 4c a+c = 648 so, b/2 + b/4 = 648 3/4 b = 648 b = 648 * 4/3 = 864

trigonometry
(84-8)/x = tan 60° Now just solve for x

probability math question
10 marbles 8 not blue what do you think?

math
minimize 2(xy + xy/4 + y^2/4) subject to xy(y/4) >= 231 x=5.29 y=13.22 h=3.30

Calcules
Hmm. I got v = 5.29 x 13.22 x 3.30 = 230.78 a = 262.12

algebra
the reflection takes (x,y) -> (x,-y) so, g(x) = -f(x)

physics
velocity changed by 20m/s in 10s. So that means an average acceleration of (20m/s)/(10s) = (20/10) m/s^2 = 2 m/s^2 That is, every second, the velocity increased by 2 m/s, thus going from 0 to 20 in 10 seconds.

PreCalc PLEASE HELP
a8 = a1*r^7, so r^7 = 100/(25/32) = 3200/25 an amusing little sequence, no?

PreCalc PLEASE HELP
62500*1.05^6 = 83755.98

math
x^(5/2)

science
well, you've done the words. CuCO3 -> CuO + CO2 or CuCO3(s) -> CuO(s) + CO2(g) You can put a ∆ over the arrow to show addition of heat

chemistry
looks like 32 g of O2, no?

Statistics
99% = µ±2.576 std

Chemistry - incomplete?
Wow. Since none of the elements in the product are included among the reactants, there's a lot of room to play around. I think there's something missing here.

Basic Spanish
generally this site works to answer specific questions. There is a wealth of online resources at your google fingertips. Or at your local used bookstore or library.

Maths
3,500,000 + 48,800 = 3,548,800

College Math
AB has direction (-3,4,1) BC has direction (0,-2,6) CD has direction (3,-4,-1) DA has direction (0,-2,6) So, AB || CD and BC || AD since the sides are parallel in pairs, they must have the same lengths in pairs (I trust you can verify this). the area is just |(b-a)x(d-a)| wher...

math
just substitute and evaluate g(x) = x^2-x, so g(g) = g^2-g = (x^2-x)^2 - (x^2-x) g(f) = f^2-f = (2x-1)^2 - (2x-1) f(x) = 2x-1, so f(g) = 2g-1 = 2(x^2-x)-1 f(f) = 2f-1 = 2(2x-1)-1 expand those out if you desire.

math
what's the trouble? Just substitute and evaluate: g(x) = x^2-1, so g(g) = g^2-1 = (x^2-1)^2-1 g(f) = f^2-1 = (1-3x)^2-1

Math
DINNER SINNER SINTER SIFTER SOFTER ... COFFER COFFEE I guess not. Maybe you can come up with something better, but that's the method.

Math
equate the y's to eliminate them: -x+3 = x^2+1 x^2+x-2 = 0 (x+2)(x-1) = 0 ...

Calculus Help Please!!!
6x^2 + 9y^2 y' = 0 y' = -2x^2 / 3y^2 now for y", do it again: 12x + 18y (y')^2 + 9y^2 y" = 0 y" = -2(2x+3y(y')^2) / 3y^2 Now just substitute in y' and you're done Or, you can use the quotient rule on y': y' = -2/3 (x^2 / y^2) y&qu...

math
75 is 25% off from 100 75 is 12% off from 85 It is unclear just what you have in mind.

Calculus
If the length (parallel to the river) is y, 2x+y = 100 a = xy = x(100-2x) = 100x-2x^2 max a at x = 100/4 = 25 So, the yard is 25x50 As usual, max area when the fence is divided equally among lengths and widths.

Calculus
According to my knowledge of physics, s(t) = 135t - 16t^2 Anyway, average velocity = total.distance/total.time So, that would be (s(3)-s(1))/(3-1)

precal - go with Reiny
good work; I missed out on that one!

precal
you have 2sin2x = 1 so, sin2x = 1/2 2x = pi/6 + 2n*pi x = pi/12 + n*pi = pi/12, 13pi/12

physics
since all the sticks are the same size and mass, the center is just the average of all the (x,y) midpoints: (0,(.32+1.32)/2) ((.33+1.33)/2,0) (.64/2,.768/2) so, the center of mass is at ((0+(.33+1.33)/2+.64/2)/3,((.32+1.32)/2+0+.768/2)/3) = (0.383,0.401)

Algebra
Good work, but if x = 2.43, the border is only half that wide, if it surrounds the entire picture. I guess in this case it does not.

Algebra
since you give no idea on the available space, that's hard to say. However, a border of 2.43 inches around a 5x7 photo will occupy an area of (5+2*2.43)(7+2*2.43) = 116.94 in^2, which is more than twice as big as the photo.

Math
w^2 + 16w = 465 w = 15

Math
the max will occur at x = 11.2/.8 = 14

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

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