Friday
April 18, 2014

Posts by steve


Total # Posts: 21,747

homonyms
Give Writeacher her due, ok? Her wisdom is as dew on the lily. Or, if you're a Scottish laddie, defend her honor with your sgian dubh!

homonyms
I knew that. It's not new to me.

math
Did you try checking to see whether the equation balances with that value? As it happens, it does.

Linear Equations
Depends on the method. For substitution, it could be 2025a + 45(1.81-324a)/18 = =1.39 For elimination, it could be 4050a+90b = -2.78 1620a+90b = 9.05 For any method it could be to reduce the size of the coefficients: 45a+b = -1.39/45 18a+b = 18.1/18

Math
z1 z2 = (4*3)cis(7π/6+π/3) = 12cis(3π/2)

Calc Help :(((((
Hmmm. Are you sure you're reading it right? Remember that log(1/3) = -log(3)

Math
same as theta=45°, or y=x Actually, it's y=x rotated by 180°, but it's still the same line. Recall that tan 225° = 1 = y/x

Math
in QIV, cosθ = 3/5 sinθ = -4/5 and you know that sin2θ = 2sinθ cosθ So, plug and chug

Geometry
you're kidding, right? The definition of a square specifies that all 4 sides are equal. That's what equilateral means. In a rectangle, such as a book, a desk top, a door, etc. the sides are not all equal. So, no for rectangles.

Math
well, you have the formula sin(u)+sin(v) = 2 sin (u+v)/2 cos (u-v)/2 So plug in u=3x and v=x

algebra
since time = distance/speed, she has been running 5.6km*1000m/km / 3.4m/s = 1647 seconds or 27:27

Math - PreCalc (12th Grade)
since sec^2 = 1+tan^2, (x/.2)^2 = (y/-.25)^2 + 1 25x^2 - 16y^2 = 1 Looks like A to me

Math - PreCalc (12th Grade)
C(7,5) = C(7,2) = 7*6 / 1*2 = 21

PRE-CALC
That would be the number of points where the denominator is zero. The denominator is (x + 2)(x − 5) so, what do you think?

Math - PreCalc (12th Grade)
or, to see the foci plotted, http://www.wolframalpha.com/input/?i=foci+of+%28y-2%29^2%2F9+-+%28x-2%29^2%2F16+%3D+1

Math - PreCalc (12th Grade)
there are lots of them, depending on the eccentricity. Recall that an hyperbola with equation y^2/a^2 - x^2/b^2 = 1 has vertices at (0,±a) and foci at (0,±c) where c = ae and e>1 is the eccentricity. Also, recall that c^2 = a^2 + b^2 Here, we have the center o...

Math
assuming no amputees, there are 12 too many legs to be all ducks. So, 6 of the animals had 2 extra legs each. 8 ducks and 6 cows or, more algebraically, if there are d ducks and c cows, d+c = 14 2d+4c = 40 now solve for d and c.

mathematics
correct 6*11 + 7*11 = (6+7)*11 = 143

statistics
the central 80% of the Z table lies within µ ± 1.282σ So, plug in your numbers You can play around with Z table stuff at this excellent site: http://davidmlane.com/hyperstat/z_table.html

Trig - sum and difference formulas
the important identity here is cos(A+B) = cosAcosB - sinAsinB So, it looks like you have cos(6x+x) = cos 7x You also know that sin(A+B) = sinAcosB + cosAsinB so, sin(90+x) = sin90cosx + cos90sinx = 1*cosx = 0*sinx = cosx Do lots of these, since they will come in handy later on.

mathematics
(x+3)(x+6)-2(x+1) x(x+6) + 3(x+6) - 2(x+1) x^2+6x + 3x+18 - 2x-2 x^2 + 7x + 16

mathematics
-x(x-1) - (-4)(x-1) + 5(3x)(2x+1) - 5(1)(2x+1) -x^2+x + 4x-4 + 30x^2+15x - 10x-5 29x^2 + 10x - 9

PreCal
0 < -9x / x(1-x^2) x=0 is not in the domain. Excluding that, we have 0 < -9/(1-x) If the quotient is positive, 1-x < 0 x > 1

Math
dunno. Is 6^2 - 4(-7)(3) positive? The discriminant will always tell you.

Gr 10 math - finding slopes in shapes
correct. -3/-4 = (-1)(3) / (-1)(4) = 3/4 The -1's cancel out

calculus
Assuming an initial position of zero, s(t) = 5/2 t^2 for 0<=t<1 so, at t=1, s = 5/2 Now, using the 2nd function, s(t) = 5/2 + 4t^(3/2) - log(t) solve that for s(t) = 4

Calculus
use implicit differentiation: x/2 + y/8 y' = 0 y' = -4x/y

Algebra
The second equation is y = 2(x^2-1)^2 so, -2(x^2-1) = 2(x^2-1)^2 so, x^2-1=0 is a solution, meaning x = ±1 Otherwise, divide by 2(x^2-1) to get -1 = (x^2-1) x = 0 So, the solutions are -1,0,1 View the graphs at http://www.wolframalpha.com/input/?i=solve+y%3D-2%28x^2-1%2...

math
man, ya gotta check your answer. It does not fit the first equation. y = x-3, so x + 3(x-3) = 6 4x = 15 x = 15/4 y = 3/4

Math
If you rearrange things a bit, you get x - 6y = 2 3x - 18y = 4 which is the same as x - 6y = 2 x - 6y = 4/3 The lines are parallel, so there is no intersection, and no solution to the equations. Your answer fits the 2nd equation, but not the first.

Algebra
subtract the equations to get 2x^2 - x = 1 2x^2-x-1 = 0 (2x+1)(x-1) = 0 x = -1/2 or 1 so, y^2 = 11/2 or 4

Trig
sinx = 2cosx tanx = 2 tanx > 0 in QI or QIII, so there are two values for x. Verify this at http://www.wolframalpha.com/input/?i=solve+sinx+%3D+2cosx

Math -Quadratics Help!
#1 I assume you can find the intersection of two lines. In this case, that is at (1,1/4). The line 5x+7y+3=0 has slope -5/7, so now we have a point and a slope, and the desired solution is y - 1/4 = -5/7 (x-1) #2 y=3x-5 has slope 3, so the angle it makes with the x-axis is arc...

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).

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