Tuesday
September 1, 2015

Posts by steve


Total # Posts: 33,211

math
We are told that S12 = 135 S20-S12 = 210 S20 - 135 = 210 S20 = 345 Now, we know that S20 = 20/2 (2a+19d) S12 = 12/2 (2a+11d) So, we have 10(2a+19d) = 345 6(2a+11d) = 135 Solve that for d.
August 25, 2015

Math
when multiplying roots, take the root of the product. You then have 7throot( (11x/y^6) * (y^6/11x^8) ) = 7throot(1/x^7) = 1/x It would help if you showed your work...
August 25, 2015

Math
You did the right thing to get the numerator. Now just put it all over the common denominator: (3a+3b) / ab when you're solving equations, the cross-multiplying affects both sides of the equation. When just evaluating an expression, you need to remember why you are cross-...
August 25, 2015

math
get rid of the parentheses and rearrange things a bit: (y-2) + (z+3) + (x-3) y-2+z+3+x-3 x+y+z-2+3-3 But, you know that x+y+z = 26, so that gives you 26-2+3-3 24
August 25, 2015

maths
distance = speed * time = 5*90 = 450 km/hr speed = distance/time = 450/4 = 112.5 km/hr Or, you can reason like this: 4/5 the time means 5/4 the speed. 5/4 * 90 = 112.5
August 25, 2015

Red House Primary School
x/y = 2/3 (x-1)/(y+2) = 1/2 The original ratio was 8/12
August 25, 2015

TC
Assuming that the two parts share no common volume, then just add up the volumes, using the normal formulas: Clearly, the radius of the hemisphere (and the base of the cone) is 49-35=14cm So, the volume is just (1/2)(4/3)(pi)(14^3) + (1/3)(pi)(14^2)(35) = 4116 pi
August 25, 2015

math please help 9th grade
#1 (B) since 19 is not a perfect square, √19 is irrational. 18/3 is just 6, and 11/10000 is just a rational number. #2 (A) any repeating decimal is rational. #3 (B) ok. I can't say I like your syntax. Even if you can't figure out how to copy/paste special symbols...
August 25, 2015

Maths
1800 + 11*1500
August 25, 2015

Math
57/99 is 0.5757575757...
August 25, 2015

TC
If there are n means, then the common difference is (31-1)/(n+1) = 30/(n+1) The kth mean is 1+k*30/n So, you want [1+7*30/(n+1)]/[1+(n-1)*30/(n+1)] = 5/9 n = 14 Check: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31
August 25, 2015

Math
you are correct
August 25, 2015

math
-12 ÷ 3 x ( -8 + (-4)^2 - 6 ) + 2 -12 ÷ 3 x ( -8 + 16 - 6 ) + 2 -12 ÷ 3 x 2 + 2 -4 x 2 + 2 -8 + 2 -6
August 25, 2015

Maths
S8 = 5S4 r^8-1 = 5(r^4-1) r^8 - 5r^4 + 4 = 0 r^4 = 1 or 4 r = ±1 or ±√2 Clearly r=±1 does not work. For r=√2, we have 1,√2,2,2√2,4,4√2,8,8√2 S4 = 3+3√2 S8 = 15+15√2 and similarly for -√2
August 25, 2015

math
y = 75.00x
August 25, 2015

Bytco College
30.8g = 0.251 moles KClO3 You can see from the reaction 2KClO3 = 2KCl + 3O2 that 1.5 moles of O2 are released for every mole of KClO3. So, you have 0.377 moles of O2. You know that at STP 22.4 moles of a gas occupy 22.4L of volume. You can finish it off, right?
August 25, 2015

math
100 cos60°
August 25, 2015

math
total possible results: 36 ways to make 5: 14,23,32,41 So, p(5) = 4/36
August 25, 2015

Math
If the dimensions are x,y,z then we have x+y+z = 80 x = 2(y+z)-10 2y = z+6 Now just solve for z.
August 25, 2015

maths
So, did you draw the tree? Can't show you mine on this site.
August 25, 2015

Calculus
the distance z is found using z^2 = 1^2 + x^2 at x=5, z^2 = 26 z dz/dt = x dx/dt so at the moment in question √26 dz/dt = 5*400 note that z will be in mi/hr
August 25, 2015

MATH
(a+6)/a = 15/12 12(a+6) = 15a 12a+72 = 15a 3a = 72 a = 24 a/j = 12/9, so 24/j = 12/9 j = 18 So, if Andy gave Joe 9, he'd have 27
August 25, 2015

Physics
(8.5 m/s) / (3.6 m/s^2) = 2.36 s
August 25, 2015

Physics
constant speed means zero acceleration
August 25, 2015

oblique triangle trigonometry
you should be able to convince yourself that the area of a parallelogram with sides a and b, and angle θ is ab sinθ
August 25, 2015

oblique triangle trigonometry
as usual, draw a diagram and review your basic trig functions. sinθ = 5.45/58.36
August 25, 2015

Algebra
|t-68| <= 3.5 68-3.5 <= t <= 68+3.5 64.5 <= t <= 71.5
August 24, 2015

BHEKISISA
Probably not an English translator or transcriber ... I suggest you talk to your school counselor, rather than a bunch of strangers half a world away.
August 24, 2015

math
Assuming the usual carelessness with parentheses, I'll go with (34-5^2) / (5 * 2^2) (34-25) / (5*4) = 9/20
August 24, 2015

calculus
x+y = 10, so y = 10-x. p = xy^3 = x(10-x)^3 dp/dx = -2(10-x)^2(2x-5) p is max when x = 5/2
August 24, 2015

Science
yes
August 24, 2015

Science
if you're breathing the atmosphere, then it must.
August 24, 2015

trigonometric oblique triangle
assuming you meant 20°50' and not 20"50', draw the diagram, filling in the angles. Use the law of sines to find h: 40/sin61°10' = h/sin20°50'
August 24, 2015

trigonometric oblique triangle
Draw a diagram. T = top of pole B = bottom of pole S = tip of shadow Draw a horizontal line from S to intersect the pole at P. The height of the pole is BP+PT BP = 16 sin14° PS = 16 cos14° PT = PS tan20°
August 24, 2015

Math
because 1 is the multiplicative identity. 1*n = n for any value of n. Since the number is the same on both sides, the ? is 1. Or, you can do it the hard way: n * 6.273 = 6.273 Now divide everywhere by 6.273 n = 6.273/6.273 = 1
August 24, 2015

Trigonometry
You can see that the altitude of the planes makes no difference. If the earth is considered a sphere with a polar radius of 6357 km, then an arc of 3000 km subtends an angle of 3000/(2pi*6357) radians
August 24, 2015

Algebra
2m - nx = x + 4 2m - 4 = nx + x 2(m-2) = x(n+1) x = 2(m-2)/(n+1)
August 24, 2015

Algebra
why bother wit LaTex? Just type it in: Suppose A and B are digits for which the product of the two-digit numbers 2A and AB is 1971. Find A+B. 2A*AB = (20+A)(10A+B) = 1971 1971 = 3^3*73 So, its only two-digit factors are 27 and 73 A+B=10
August 24, 2015

geometry
area = 4 pi r^2 volume = 4/3 pi r^3 So, for any sphere, the area:volume ratio is 3/r However, I suspect that you garbled the question. Since area varies as the square of the diameter, if the diameters are in the ratio 3/4, area is in the ratio (3/4)^2 volume is in the ratio (3...
August 24, 2015

Math
If he invested $x in B, then just add up the interest: .04(x-8000) + .08x = 1360
August 24, 2015

math
just write the words in symbols. Ben ran 2 times as many laps as Ray. B = 2R Lee ran 3 laps L = 3 which is one-half of the number of laps that Ray ran. 3 = R/2 That leaves us with the equations B = 2R L = 3 L = R/2, so R = 2L B = 2R = 2(2L) = 2(2*3) = 12
August 24, 2015

Math accelerated
Assuming a single blue tile between red tiles, we have the following table, for a single row of red tiles: R B 1 12 2 20 3 28 4 36 ... If the red tiles are laid out in a rectangular grid, then we have R B 1 12 2 20 4 34 ... So, decide on the layout of the red squares before ...
August 24, 2015

Maths
heading, not bearing. From Y, Z is on a bearing of S60E, so that is the plane's heading. 200 @ N45E = <141.42,141.42> z @ S60E = <.866z,-.50z> Since Z is directly east of X, you need 141.42 - 0.50z = 0 So, evaluate the distance z, and then the distance XZ will ...
August 24, 2015

Algebra
3^m + 2^n powers of 2: 2,4,8,16,32,64,128,256,512 powers of 3: 3,9,27,81,243,729 729+256 = 985 243+512 = 755 Looks like 985 is the winner
August 24, 2015

mathematics
x^(-1/3) * y^(1/3) - x^(2/3) * y^(-2/3) = (y^1/3 / x^1/3) * (x^2/3 / y^2/3) = (x^2/3 y^1/3) / (x^1/3 y^2/3) = x^1/3 / y^1/3 = (x/y)^(1/3)
August 24, 2015

Geometry
x^2+15^2 = (x+1)^2 x = 112 p = 15+112+113
August 24, 2015

math
1+5r = 5/3 5r = 2/3 r = 2/15 = 0.1333 = 13.3%
August 24, 2015

maths
after 1/10, 5/6 of the remainder is 5/6 * 9/10 = 45/60 = 3/4 so, x(1 - 1/10 - 3/4) = 1800 3/20 x = 1800 x = 12000
August 24, 2015

Algebra
Nope, 10 less than 30 is 30-10, not 10-30. So, you have 2n and then 15 less than that is 2n - 15 = 115
August 24, 2015

science
horizontal: 10/√2 + 9 = 16.07 vertical: 10/√2 = 7.07 total: √(16.07^2 + 7.07^2) = 17.56
August 24, 2015

math
right on.
August 24, 2015

Math
it would indeed.
August 24, 2015

Math
150 + n = -129 n = -129 - 150 = -279
August 24, 2015

Math
no, -27+8 = -19 Draw you number line. Note that - is to the left, + is to the right. Starting at 0, move 27 to the left, to -27. Then move 8 to the left from there, and you end up at -35.
August 24, 2015

English???
how is any of this related to the original subject of English?
August 24, 2015

algebra
Consider just the amount of anti-freeze present. If x quarts of 60% solution are drained and replaced with water (0% solution), then you have 0.60(25-x) + 0.00(x) = 0.40(25)
August 24, 2015

maths
C(5,3) = (5*4*3)/(1*2*3) = 10
August 24, 2015

Algebra
square both sides: (r1/r2)^2 = m2/m1 m1 = m2 / (r1/r2)^2 or m1 = m2*(r2/r1)^2
August 24, 2015

Math
you are correct on (a), so I guess you did know where to start, and after only 5 minutes of effort! So, that leaves 39/63 left to do, since 24+39 = 63
August 24, 2015

Word problems
clearly the vehicles met 110 miles from Midville. At 40mi/hr, it took the truck 1:22.5 to cover that distance. So, the vehicles met at 2:00 + 1:22.5 = 3:22.5 The car had only been going for 7.5 minutes, covering only 6.875 miles. So, the towns are 116.875 miles apart.
August 23, 2015

Math
x^2+1 --> 2^2+1 = 5 f(2) = 3, but that does not affect the limit.
August 23, 2015

Calculus
see related questions below.
August 23, 2015

Math
x y 1 3 3 17 6 38 10 66 check the slope between each two points: (17-3)/(3-1) = 14/2 = 7 (38-17)/(6-3) = 21/3 = 7 (66-38)/(10-6) = 28/4 = 7 Clearly the points lie on a line with slope 7. Since 7*1 = 7, but y(1) = 3, the rule must be y = 7x-4
August 23, 2015

math analysis
1/a + 2/a^2 = 0 a/a^2 + 2/a^2 = 0 (a+2)/a^2 = 0 a+2 = 0 a = -2 check: 1/-2 + 2/4 = -1/2 + 1/2 = 0
August 23, 2015

math
Your text explains Cramer's Rule, surely. Read it where it discusses taking determinants of coefficients. Or google cramers rule for lots of examples. Fo the first, D = |5 3| |2 1| = 5-6 = -1 Dx = |19 3| |7 1| = 19-21 = -2 x = Dx/D = 2 and similarly for the other parts
August 23, 2015

Calculus
for x<0, |x| = -x. So, we have f(x) = (2x-1)/(-x-3) for x<0 (2x-1)/(x-3) for x>=0. Now you can easily find the limits, no? To confirm your answer, see http://www.wolframalpha.com/input/?i=%282x-1%29%2F+%28|x|+-3%29 and scroll down to where it describes the limits.
August 23, 2015

Math
it will take n years, where 1.08^n = 2
August 23, 2015

Calculus Typo
Oops. I messed up the length of the top base. It is 8/3 + 2*(8/3)cosθ So, the area is ((8/3) + 8/3 + 2*(8/3)cosθ)/2 * (8/3)sinθ = 32/9 (2sinθ + sin2θ) For max area we want cosθ + cos2θ = 0 2cos^2θ + cosθ - 1 = 0 (2cosθ-1)(cos&#...
August 23, 2015

Differential calculus
Let the sides be turned up through an angle θ. Then the depth of the gutter will be 8/3 sinθ, and the cross-section of the gutter will have area a = ((8/3) + 2*(8/3)cosθ)/2 * (8/3)sinθ = 32/9 (sinθ + sin2θ) for maximum area, we want da/dθ = 0...
August 23, 2015

Algebra 2
b = u+88 t = 5u b = t+40 Now just solve for u.
August 23, 2015

Maths
If you mean f(x+3) = 3x^2-x+4 then f(0) is where x+3 = 0, or x = -3 f(0) = 27+3+4 = 34
August 23, 2015

Algebra 2
These are the same kind. I'll do one. Do them by completing the square: 16x^2-96x+144+25y^2=400 16(x^2-6x+9) + 25y^2 = 400 16(x-3)^2 + 25y^2 = 400 Now divide by 400 and you have (x-3)^2/25 + y^2/16 = 1
August 23, 2015

Algebra 2 geometry
you know opposite pairs of sides are equal, so 2x-y = 7 x+y = 2 That help?
August 23, 2015

Calculus
2 <= f(x) <= x^2+2 clearly, lim f(x) = 2
August 23, 2015

math
if there is x in the CD account, then the rest (5000-x) is in the bond. So, just add up the interest: .04x + .07(5000-x) = 300
August 23, 2015

Maths
AP: x-4 = 32-x 2x=36 x=18 AP=4,18,32 GP: x/4 = 32/x x^2 = 128 x = ±√128 GP=4,√128,32 or 4,-√128,32
August 23, 2015

algebra
all look good to me.
August 23, 2015

Geometry - incomplete
Missing B.
August 23, 2015

math
#1. Do it as usual, but you will be solving for 1/x and 1/y. D = -1 Dx = -2 Dy = -3 So, 1/x = Dx/D = 2, 1/y = Dy/D = 3 x = 1/2, y = 1/3 Same thing, but you are solving for logx and logy: D = -5 Dx = -14 Dy = -3 logx = 14/5 logy = 3/5 x and y depend on the base of the logs.
August 23, 2015

calc
assuming the graph of acceleration is the line a = 6mt so, v = 3mt^2 + c v(0)=0, so c=0 x = mt^3 + c x(0) = 10, so c=10, and x(t) = mt^3 + 10 so, once you decide on m, you can figure x(6)
August 23, 2015

Math - eh?
probability of what?
August 23, 2015

sets
How many play both? If x, then 24+30-x = 38-4 x = 20 So, 4 play only hockey 10 play only netball 20 play both
August 23, 2015

algebraic equations
g = 9+s g+3 = 2(s+3) g+3 = 2(g-9+3) g+3 = 2g-12 g = 15
August 23, 2015

Maths
If the breadth is b, then you can find it by solving 2(b + b+25) = 430
August 23, 2015

unda geometry
If you do not understand the integral equations, you have a long way to go, namely calculus. Go pick up any 1st-year calculus book, and somewhere in its index you will find how to determine the centroid of a curved area. Google will also help, with many examples, but unless ...
August 23, 2015

centroid
Just use the formula. The x-coordinate is ∫[0,3] xy dx = ∫[0,3] x^3+x dx ------------------------------------- ∫[0,3] y dx = ∫[0,3] x^2+1 dx ∫[0,3] x^3+x dx ------------------- ∫[0,3] x^2+1 dx Then do the same for y, using x = √(y-1) ...
August 23, 2015

calculus: don't even no where to start from need help plz
that is correct. No matter what value you pick for x, 2x+4x=6x.
August 23, 2015

calculus: don't even no where to start from need help plz
just good old chain rule stuff If y = arctan(u), y' = 1/(1+u^2) u' = 1/(1+(1/x^2)^2) (-2/x^3) = -2x/(1+x^4) y = 3z^2 * z^2 = 3z^4 y' = 12z^3 Seems too easy. Maybe I misread the problem y = x^x lny = x lnx 1/y y' = lnx + 1 y' = x^x (1+lnx) I find it ...
August 23, 2015

Math
you got the center right, so the equation must be (x+3)^2/a^2 - (y-2)^2/b^2 = 1 Since a=2, and (-6,4) is on the graph, so 9/4 - 4/b^2 = 1 b^2 = 16/5 (x+3)^2/4 - (y-2)^2/(16/5) = 1 As you can see, it works: http://www.wolframalpha.com/input/?i=plot+%28x%2B3%29^2%2F4+-+%28y-2%29...
August 23, 2015

Algebra
just solve for L in 2π√(L/32) = 16.9 √(L/32) = 16.9/2π = 2.69 L/32 = 7.23 L = 231.51
August 23, 2015

maths
n/d = 3/2 (n+3)/(d-2) = 9/4 n/d = 15/10
August 23, 2015

maths
n/d = 3/2 (n+3)/(d-3) = 9/4 I don't get two integer values for n and d. Typo?
August 23, 2015

Calculus
If you look at the graphs at http://www.wolframalpha.com/input/?i=plot+x*sin%281%2Fx%29%2C|x|%2C-|x| it's easy to see the squeeze. for x>=0, x = |x| and |sin(1/x)| <= 1 so, |x sin(1/x)| <= |x| x sin(1/x) is squeezed in between the |x| lines. So, while f(0) does ...
August 23, 2015

maths - incomplete
I think you are missing some info here.
August 22, 2015

Math
I'll go out on a limb here and assume you meant (√2x)/9.81= √((300+x)^2+60^2)/150 square both sides and you have (roughly) 4x/96 = (x^2+600x+93600)/22500 2x^2-675x+187200 = 0 that has no real roots. So, if I got it wrong, fix it and solve using the same method...
August 22, 2015

Calculus
√(x+3) --> √(1+3) = √4 = 2 lim 1/x --> 1/7 how did you come up with your bizarre values?
August 22, 2015

Algebra
you cannot factor x^2+1 plug in some numbers and you will see quickly that (x+1)(x+1) ≠ x^2+1 If you allow complex numbers, then x^2+1 = (x+i)(x-i)
August 22, 2015

Math - eh?
I can't figure out what you mean by take 2 1/2 from the height from both sides and 2 cm from one side
August 22, 2015

Math I am lost!
sounds like the time difference between trips was 2 minutes (1/30 hr). Since time=distance/speed, d/30 - d/60 = 1/30 d = 2
August 22, 2015

Calculus 1
period: 4.7, so 2π/k = 4.7 k = 2π/4.7 y = sin(2π/4.7 t) average: 5.3, so y = 5.3 + sin(2π/4.7 t) brightness varies by ±0.35 y = 5.3 + 0.35 sin(2π/4.7 t) (Assume that at t = 0 the brightness of the star is 5.3 and that it is increasing.) No phase...
August 22, 2015

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