# oobleck

Newest questions and responses by oobleck-
## Maths

If the bridge's length is x, then the train's engine has to move (x+100) meters to pull the last car across. So, since distance = speed * time, x+100 = 54000 * 12/3600

*posted on January 16, 2019* -
## Algebra repost

I like "n>4" for "a number is more than 4" But for "a number more than 4" I like 4+x

*posted on January 16, 2019* -
## Maths

That's cylindrical, not cylienderI called Anyway, if the wire is of length x cm, then you need the volumes to be equal: 14^2 * 10 = 0.4^2 * x now just find x.

*posted on January 16, 2019* -
## math

After the first transfer from A, P(B=3stars, 1heart) = 2/3 P(B=2stars, 2hearts) = 1/3 So, the probability of getting a start when drawing from B is 2/3 * 3/4 + 1/3 * 1/2 = 2/3

*posted on January 16, 2019* -
## Math

maybe. You are correct. But, maybe they wanted M' - everything which is not in M. In that case, (A).

*posted on January 16, 2019* -
## math

yeah, yeah. OK, that's fair, and I answered it (in terms of how many cards Kai has.) But, unless you start tossing in some actual numbers, don't expect a final numerical answer.

*posted on January 16, 2019* -
## math

clearly, the answer is 42. But that does not answer your question: how do you get it? Maybe you bounce on your head while spinning on a beach ball Maybe you study some math. Or maybe, just maybe, you ASK A REAL QUESTION!

*posted on January 16, 2019* -
## Mathematics

8/9 is correct, but 8/9 ≠ 1 1/9 !!! 1 1/9 = 10/9

*posted on January 16, 2019* -
## Math

If the two angles share a vertex (the middle letter) and one side (an outside letter) then they are adjacent.

*posted on January 16, 2019* -
## Algebra

There is a total of n*t man-days of labor. That is 56*7 = 392 So, your relationship is nt = 392 or, n = 392/t

*posted on January 15, 2019* -
## Math

10 3/7 + 18 2/7 That's just 10+18 + 3/7 + 2/7 28 + 5/7 or 28 5/7

*posted on January 15, 2019* -
## Mathematics

I assume you can draw the Venn diagram. If not google is your friend. If s passed science, then s+15 passed math. So, s + (s+15) - 12 = 60-7 now you can answer questions 2,3 For #4, 60-7 passed something; 12 passed both, so 60-7-12 passed one or the other,

*posted on January 15, 2019* -
## math

well, the projection of u onto v is (u.v)/|v| Then recall that v = |u|cosθ v/|v| and the orthogonal component of u is |u|sinθ w/|w| where w is orthogonal to v

*posted on January 15, 2019* -
## algebra

well, -3x+6y cannot be both 10 and -4, right? so, ...

*posted on January 15, 2019* -
## Math

all you need to work these is to recall that sin(ax) has period 2π/a sin(x-b) has a phase shift of b to the right. so, sin(ax-b) = sin(a(x - b/a)) has period 2π/a and a phase shift of b/a y = f(x)+k has a vertical shift of +k So, 1. y=sin(x+pi/2)

*posted on January 15, 2019* -
## Math

even multiples of 5 end in 0. So, you want numbers ending in 2 or 4 odd multiples of 5 end in 5, so you want numbers ending in 7 or 9 Now look at the list of even remainders when divided by 7: 1,3,5,8,10,12,15,17,19,22,24,26,29,31,33,36,38,40,43,45,47,...

*posted on January 15, 2019* -
## Math

google is your friend. You might start here: fac-staff.seattleu.edu/nirmalag/web/mpmathclub/6thMIC2012Cind.pdf

*posted on January 15, 2019* -
## Math

profit of 47.35-12.85, split 3 ways, right? (divided by 3)

*posted on January 15, 2019* -
## Math

that would be 16 days, right? 1/√2 * 1/√2 = 1/2

*posted on January 15, 2019* -
## math

do you mean the area under the line? If so, just draw the line, and you can see that it is ∫[0,2] 4-2x dx

*posted on January 15, 2019* -
## algebra

for multiplication, just expand out (ab^2 +3ab+8a^2)(-5ab^2) every term in the product will have some combination of powers of a and b, so it will still be a polynomial. same for addition and subtraction

*posted on January 15, 2019* -
## math

well, the price must be 10+25, or a 250% increase 25 = 10*2.5

*posted on January 15, 2019* -
## Math

wait. you say that if there are 22 passengers, each ticket costs $60 but if there is one empty seat, each ticket costs $120? and if there are 2 empty seats, each ticket costs $180? I don't think so! But assuming that's so, let's go on, and you can fix it

*posted on January 15, 2019* -
## Calculus

xy = 800000 If the outer fence costs $c/m, then the inner fence costs $2c/m So, the total fence cost is x(2*c + 2c) + y*c so we want to minimize z = 4x + 2*800000/x dz/dx = 4 - 1600000/x^2 = 4(x^2-400000)/x^2 we want dz/dx=0 for a minimum, so x^2 = 400000

*posted on January 14, 2019* -
## algebra

w(3w-10) = 8 4*2 = 8 so, the width is 4 ft and the length is 3*4-10 = 2 (strange that the length is less than the width, but oh well...) Now, as it is very easy to find, using google, 1 meter is 3.28 feet, so 1 ft is 1/3.28 meter So, the width is 4/3.28 =

*posted on January 14, 2019* -
## algebra

check your post of 1:05 pm before reposting, eh?

*posted on January 14, 2019* -
## math

huh? $96 is 3/4 of her money, right? The coat cost 1/4 of her money, so its price was 1/3 of 96 = $2 or, since she started with $x, 3/4 x = 96 x = 128 The coat cost 128-96 = 32 since 32 is 1/4 of 128

*posted on January 14, 2019* -
## algebra

you know that area is length * width, right? Since the width is 12 less than twice the length, if the length is x, then the width is 2x-12 So, now you know that (2x-12)(x) = 270 2x^2 - 12x - 270 = 0 x^2 - 6x - 135 = 0 (x-15)(x+9) = 0 x = 15 so, the

*posted on January 14, 2019* -
## Math

The scale is 4" : 6'1" = 4" : 73" = 4:73 = 1:18.25

*posted on January 14, 2019* -
## math

to keep these straight, consider a horizontal slope (θ=0°) all the force is perpendicular to the plane, so clearly that component is F*cos0° So, for nonzero θ, the components of F are perpendicular: F cosθ parallel: F sinθ

*posted on January 14, 2019* -
## Geometry

not incorrect, but we usually try to simplify fractions, such as 3/9 = 1/3 4/1 = 4 etc. However, leaving it as -4/-1 does indicate just how you performed your calculation. I think your teacher (and probably an online answer key) would prefer just 4

*posted on January 14, 2019* -
## math

recall that for the point (x,y) sinθ = y/r cosθ = x/r tanθ = y/x So, for your two problems, If sinθ=7/13 and cosθ=12/13 find tan θ and cot θ Unfortunately, no angle θ has sinθ=7/13 and cosθ=12/13 since 7^2+12^2 ≠ 13^2 However, 5^2+12^2 = 13^2,

*posted on January 14, 2019* -
## Geometry

you are correct. Calculate the change in x and the change in y between the two points. The slope is y-change/x-change: (1-5)/(-3-(-2)) = -4/-1 = 4

*posted on January 14, 2019* -
## algebra

to find x, just equate the two values for y: 3x + 4 = -0.35x - 10 3.35x = -14 x = -4.179 (or, exactly, -1400/335 = -280/67)

*posted on January 14, 2019* -
## math

#3: the cross-product is the outsides = insides so, ...

*posted on January 14, 2019* -
## maths

Huh? Of course z lies on a circle! That's kind of vague. If z = x+iy, then (x,y), (y,-x), (1,0) are collinear See what you can do with that.

*posted on January 14, 2019* -
## maths

(k+w)(k+w^2) = w^3+kw^2+k^2w+k^3 = = (w^4-k^4)/(w-k) See where this takes you: https://www.wolframalpha.com/input/?i=sum(k%3D1..n)+(w%5E4-k%5E4)%2F(w-k)

*posted on January 14, 2019* -
## Chemistry

that's "presence" not "pressure" Figure how many moles of CaCO3 you have in 25g Now, looking at the reaction equation: CaCO3 + 2HCl = CaCl2 + H2O + CO2 you can see that each mole of CaCO3 produces one mole of CaCl2 ...

*posted on January 14, 2019* -
## math

yeah, yeah sorry that no one was here to tell you to, I don't know, substitute x=5 into the function? Geez, did you even read what they told you? PS don't forget that p(x) is in millions of $$$$

*posted on January 14, 2019* -
## Math

If the fast pump can fill it in x hours, then the slow pump takes x+5 hours. So, now you know that 1/x + 1/(x+5) = (1/2)/3 So just find x

*posted on January 14, 2019* -
## Math

hmmm. They have told you that if the list price is x, then the marked-down prices are D(x) = 0.80 * 0.90 = 0.72x H(x) = 0.75 * 0.85 = 0.6375x See what you can do with that...

*posted on January 14, 2019* -
## math

yeah, yeah sorry that no one was here to tell you to, I don't know, substitute x=5 into the function? Geez, did you even read what they told you? PS don't forget that p(x) is in millions of $$$$

*posted on January 14, 2019* -
## Trigonometry

recall that x' = x cosθ - y sinθ y' = x sinθ + y cosθ

*posted on January 14, 2019* -
## math

A) polynomial (quadratic, to be exact) B) solve -4x^2+20x-9 = 0 using the quadratic formula or factoring or completing the square.

*posted on January 14, 2019* -
## math

surely you recognize that this is a linear function. So, plot any two points (pick two values of x and calculate y) draw a line between the points and extend it both ways. That is the graph. If still unsure, google "linear function" or, what the heck,

*posted on January 14, 2019* -
## math

not any type I know not rational, polynomial,etc. whenever you see a function such as y(x) x (inside the parens) is the independent variable, y of x depends on x.

*posted on January 14, 2019* -
## Math

3^3 = 27 4^3 = 64 so, ...

*posted on January 13, 2019* -
## Chemistry

8/3 = 2^x * (4/3)^y (4/3)^y = 8/3 * 2^-x y ln 4/3 = ln(8/3) - x ln 2 y = (ln(8/3) - x ln2)/ln(4/3) ≈ (0.9808-0.6931x)/0.2877 = 3.4094 - 2.4094x

*posted on January 13, 2019* -
## Math

the domain for all rational functions is all reals, except where the denominator is zero. So, the domain here is all reals except x = 16/5 There is a horizontal asymptote at y=0, and there is a vertical asymptote there, positive on one side and negative on

*posted on January 13, 2019* -
## Math

10m = 1000cm so, there are 4*(1000/20) = 200 plants in all

*posted on January 13, 2019* -
## math

If he raised the price by x%, then if the cost was c, he sold it for c(1 + x/100) Then, after the 16% discount, his sales price was 5% above cost, so c(1 + x/100) * 0.84 = 1.05c Or, dividing by c, (1 + x/100) * 0.84 = 1.05 x = 25 So, he raised his price by

*posted on January 13, 2019* -
## algebra

the midpoint is at ((-1+4)/2,(5-3)/2) = (3/2,1)

*posted on January 13, 2019* -
## math

moving to the right means x is increasing. So, where do you have x'(t) > 0?

*posted on January 13, 2019* -
## calculus

while y'=1 at x=0, y(x) is discontinuous there. y(0) -> 0 on the left, y(0) = 1 on the right. Do the graph, and you can see that y is not differentiable at x=0 read the definition again.

*posted on January 13, 2019* -
## Calculus

each rectangle has width (9-1)/4 = 2 using left endpoints, that would mean you want 2(f(1)+f(3)+f(5)+f(7)) = 2(1+9+25+49)

*posted on January 13, 2019* -
## Math

recall that ln e = 1 so, lnx-1 = 0 when x=1 clearly, when x gets huge, lnx-1 is very close to lnx so the horizontal asymptote is just y = lnx/lnx = 1

*posted on January 12, 2019* -
## Math

If k=9, (x-3) / (x^2-6x+9) = (x-3)/(x-3)^2 = 1/(x-3) Not sure what you're after, but maybe this will help

*posted on January 12, 2019* -
## Algebra

Ooops my bad. If you swap first, solve for y you need to review how to find an inverse function. If y = 2x-3 to find f^-1, first swap variables x = 2y-3 then solve for y y = (x+3)/2 Or, you could solve for x and then swap y = 2x-3 y-3 = 2x (y-3)/2 = x x =

*posted on January 12, 2019* -
## Calculus

what? You cannot evaluate f(x) at x=2 and x=4? The height of the rectangles is f(2) = 2 - cos(2π) = 2-1 = 1 f(4) = 4 - cos(4π) = 4-1 = 3 Since the width of each rectangle is 2, the area a = 2*1 + 2*3 = 8 Now study your text's examples again, and it

*posted on January 12, 2019* -
## Math

for any x, the slope of the tangent line is h'(x) First, simplify things by noting that e^-lnx = 1/e^lnx = 1/x h'(x) = cos(1/x) * -1/x^2 h'(1/π) = -π^2 cos(π) = π^2

*posted on January 12, 2019* -
## Calculus

Or, more conventionally (I think) f(x) = ∫[0,x] arctan(t) dt By the 2nd FTC, f'(x) = arctan(x) so, f'(0.5) = arctan(0.5) ≈ 0.46

*posted on January 12, 2019* -
## Algebra

First, make sure you have typed things correctly. What you have written is gibberish. So, I shall go with g(x) = -4/(-x-3) + 1 First of all, what's with all those - signs? Oh, well ... swap variables and solve for x: h(x) = 4/(x-1) - 3 = (7-3x)/(x-1) By

*posted on January 12, 2019* -
## Calculus

recall that e^lnx = x. So, e^(2lnx) = (e^lnx)^2 = x^2 So, you just want ∫x^2 + e^(2x) = 1/3 x^3 + 1/2 e^(2x) + C

*posted on January 12, 2019* -
## Calculus

use two rectangles on [1,5] means they both have width 2. So, the 2 subintervals are [1,3] and [3,5] The midpoints are thus at x=2,4 So, take f(2) and f(4) for the heights. Your approximation is just the sum of those two rectangles.

*posted on January 12, 2019* -
## math

if each book cost x, then total cost = 16x if each book sold for that same amount, total revenue = 30x 30/16 = 1.875 or 87.5% gain Not sure whether I interpreted your meaning correctly It's kinda vague

*posted on January 12, 2019* -
## Maths

you just need to think on these a bit. a boy and a girl can be chosen in 5*4=20 ways Once chosen, they count as a single person with 7 others, so there are 20*7! ways to arrange them now use the same logic, deciding how many ways 2 boys/girls can be chosen

*posted on January 12, 2019* -
## Science

M = moles/liter So, for your solution, 2.0mole/0.4L = 5.0M

*posted on January 12, 2019* -
## Math

the solution to the system is a point. Not much of a graph. Since the two graphs have different slopes, the two lines must intersect -- in exactly one point.

*posted on January 11, 2019* -
## math

unless it's equilateral or equiangular it's not regular

*posted on January 11, 2019* -
## Math

6/5 divided by blank equals 6 or, (6/5)/x = 6 now multiply by x: 6/5 = 6x now multiply by 1/6 6/5 * 1/6 = x 1/5 = x

*posted on January 11, 2019* -
## Math

looks like you should have been studying instead of waiting for someone to do them for you. Still, maybe what I showed you will help.

*posted on January 11, 2019* -
## Math

#1 Note that x+3y=4 can be rewritten as 4x=-12y+16 so both lines are the same, so C #2 Y=5x+7 can be written as 3y-15x=21 So, the two lines are parallel: D #3 x-2y=6 is 3x-6y=18 So, it's the same line: C #4 y-7x=-14 is 7y-49x=-98 so, D Looks like you need

*posted on January 11, 2019* -
## math

just as a general rule, you divide one quantity by another. Suppose you have a product which sells for $52.17 for 9 boxes. The unit rate is $/box, so you divide $52.17/9box = 52.17/9 $/box = $5.80/box or, say you go 23 miles in 3 minutes, and you want your

*posted on January 11, 2019* -
## Math

why 2 halves?

*posted on January 11, 2019* -
## Physics

he said to divide the time into 3.0m That is, divide the 3.0m by time, giving m/s

*posted on January 10, 2019* -
## Geometry

actually, 2+7=9 -5 is 7 units below y=2

*posted on January 10, 2019* -
## math

not so. I'll show you how to find the answer. Using the formula for the nth term of an AP, you know that a+6d = 2(a+2d) 4/2 (2a+3d) = 16 Now you can find a and d, so you just need to know how many terms there are. If there are k terms, then a+(k-1)d = 72

*posted on January 10, 2019* -
## Probability

P(A or B) = P(A)+P(B)-P(A and B) = 1/13 + 1/4 - 1/13 * 1/4 = 4/13

*posted on January 10, 2019* -
## Math

10-x >= 3

*posted on January 10, 2019* -
## Math

you can do it in a few ways. One way is to see how many small cubes fit in each dimension 1/2 = 6/12 3/4 = 9/12 so, the block can hold 6*6*9 = 324 small cubes Or, 1/2 * 1/2 * 3/4 = 3/16 m^3 scale that by a factor of 12 and the volume scales by a factor of

*posted on January 10, 2019* -
## math

6.50 each is 6.50/1 right? "each" means the unit rate!

*posted on January 10, 2019* -
## Math

wow I did mess that up! The derivative is 2cos(x^3) * -sin(x^3) * 3x^2 = -6x^2 cos(x^3) sin(x^3) or, as Reiny put it.

*posted on January 10, 2019* -
## Algebra 2

substitution: z = -19-2x+3y so use that to get 5x+y-(-19-2x+3y) = -7 -x+6y-(-19-2x+3y) = 35 or 7x-2y = -26 x+3y = 16 Now you have x = 16-3y, so that gives 7(16-3y)-2y = -26 -23y = -138 y = 6 so, x=16-3y = 16-3*6 = -2 so, z = -19-2x+3y = -19-2(-2)+3*6 = 3

*posted on January 10, 2019* -
## math

well, they must all add up to 360, right? so add up those three and subtract that sum from 360

*posted on January 10, 2019* -
## Algebra

correct, though it usually called "distributive"

*posted on January 10, 2019* -
## algebra

well, first, draw the triangle! it is easy to find the area, since the base is a vertical line. Now it should be clear that one inequality is x > 1 Now determine the equations of the other two sides, and decide whether y is above or below each line.

*posted on January 10, 2019* -
## Math

the limit exists, and it is in fact the derivative

*posted on January 10, 2019* -
## calculus

using the product rule, dp/dt * v^1.3 + p*1.3 v^0.3 dv/dt = 0 so, I guess you could say that (dp/dt)/(dv/dt) = -1.3p/v or, by rearranging the 1st equation, p = kv^-1.3 dp/dt = -1.3kv^-2.3 dv/dt (dp/dt)/(dv/dt) = -1.3k/v^2.3

*posted on January 10, 2019* -
## Math

come on sin(π/2) = 1. So, k=π/2 so, f(x) = sin(π/2 x) for x>1 That way the limit on both left and right is f(x) = 1

*posted on January 10, 2019* -
## Math

the derivative of u^2 is 2u u' the derivative of cos(u) is -sin(u) u' so, with u=x^3, the derivative of cos^2(x^3), using the power rule as well, is 2cos(3x^2) * -sin(3x^2) * 6x

*posted on January 10, 2019* -
## Math

at x=1, x^2 = 1 so, you need at x=1, sin(k) = 1 so where is sin(k) equal to 1?

*posted on January 10, 2019* -
## math

if they made only large and medium, then 291-5 = 286 mediums seems kinda lop-sided to me.

*posted on January 10, 2019* -
## algebra

not sure I know what a "literal equation" is. Care to elaborate?

*posted on January 10, 2019* -
## Math

clearly, that will be 4 * 1 1/2 = 4 4/2 = 6 gallons

*posted on January 9, 2019* -
## Math

no figure to look at. Sorry

*posted on January 9, 2019* -
## Math

except for the lx part, this is just algebra I 3 + ln (4x) = 4 ln(4x) = 1 Now, get rid of the ln by doing its inverse: e^ 4x = e^1 x = e/4

*posted on January 9, 2019* -
## Math

No idea where angle 4 is, but you need to recall that vertical angles are congruent alternate int/exterior angles are congruent adjacent angles are supplementary etc. Time to review your theorems on parallel lines and their transversals

*posted on January 9, 2019* -
## Math

A(t) = 497*(1/2)^(t/38) You can see that when t grows by 38, you multiply again by 1/2 now plug in t=4

*posted on January 9, 2019* -
## Technology

No. Old vacuum-tube machines filled whole rooms The silicon chip enable miniaturization.

*posted on January 9, 2019*