Monday
August 3, 2015

Posts by Steve


Total # Posts: 32,562

math
Just apply the chain rule y=sec^3(2x)-3sec2x y' = 3 sec^2(2x) * sec(2x)tan(2x) * 2 - 3sec(2x)tan(2x)*2 = 6sec(2x)tan(2x) (sec^2(2x)-1) = 6sec(2x)tan^3(2x)
July 14, 2015

interoduction of aeronautical engineering
the volume of an ellipsoid with semi-axes a,b,c is 4/3 pi*abc Your semi-axes are just 23/2, 7 and 7. Plug and chug.
July 14, 2015

math
If there are x lbs of $6.50 coffee, then the rest (140-x) of $2.50 beans. So, add up the total cost of the various amounts: 6.50x + 2.50(140-x) = 5.07(140) Now just find x and then 140-x.
July 14, 2015

algebra
that's the same as y = 3x If that still doesn't ring a bell, then write it as y = 3x+0 Compare that to y = mx+b
July 14, 2015

Maths
one liter is 1000 cm^3 Since the base has an area of 50cm^2, it takes 50cm^3 to cover it to a depth of 1 cm. So, at 12000cm^3/min, the water level is rising at (12000cm^3/min)/50cm^2 = 240cm/min
July 14, 2015

Algebra
since 20% less effective each hour, that means that its effectiveness is 80% as much, and that repeats every hour. So, after x hours, the effectiveness is y = 0.8^x So, yes, it is exponential, and yes, it is decay. For B, since the initial dose is 200 mg, the amount left after...
July 13, 2015

Math
x/2 = 9th graders, leaving x/2 x/2 * 1/4 = x/8 = 8th graders, leaving x/2*3/4 = 3x/8 1/5 * 3x/8 = 7th graders, leaving 4/5*3x/8=3x/10 3x/10=12 = 6th graders. So, the team has 40 members. 20 9th graders 5 8th graders 3 7th graders 12 6th graders
July 13, 2015

math - eh?
I don't get it either. What comes after the equal sign?
July 13, 2015

math
just expand each product, and see whether all the terms are divisible by 6. For example, (2n+3)(3n+2) = 6n^2+13n+6 You can see that 13n is not necessarily divisible by 6. If you expand the others, you will see that one of them has all its terms multiples of 6.
July 13, 2015

math
The 1995th integer is 1994 more than the first one. so, x+1995+1994
July 13, 2015

math
q+n = 26 25q+5n = 10*1 + 16*10 25(26-n)+5n = 170 I expect you can take it from there, right?
July 13, 2015

Math
just put the words into symbols: B = 6 L = 2B T-B = L-T now start substituting B=6, so L=12 T-6 = L-T Now we know that L=12, so T-6 = 12-T 2T = 18 T = 9
July 13, 2015

computers (hacking)
google is your friend. I think you will find that (A) is what you want.
July 13, 2015

french
Just for starters, subjunctive is a mood, and infinitive is not. I expect you mean indicative. Just from my knowledge of Portuguese, I figure that 1 and 3 are indicative, and 2 is subjunctive. But, as Ms Sue says, our French expert will be glad to give feedback on your thoughts.
July 13, 2015

Geometry
If you draw a diagram, you can see that the apothem is just the altitude of a 30-60-90 right triangle with one side s/2. Recall that the sides of such a triangle are in the ratio 1:√3:2
July 13, 2015

Problem solving (point of intersection)
A: y=10x+40 B: y=20x
July 13, 2015

Chemistry
I'd say it is still nitrogen gas.
July 13, 2015

ENGLISH
The whole point of writing is communication. Improper spelling, grammar or punctuation makes it difficult or even impossible to understand. The person doing the writing has the responsibility to be clear. Do not make the reader struggle to figure out "what you mean."...
July 13, 2015

math
The two numbers are 70m and 70n, where m and n have no common factors. (70m)(70n) = 4900mn = 49000 = 4900*10 Thus, mn=10. So, m and n are 2 and 5, or 1 and 10.
July 13, 2015

Math
Think back on your days of learning multiplication, where if you are multiplying by a 3-digit number, you write down the partial answers, each row shifted over by one from the row above. That's all this is. We work with a base-10 system, so multiplying by a power of 10 ...
July 13, 2015

the ultimate run-on sentence
Why don't you repost it the way you received it?
July 13, 2015

algebra
There is a fixed cost. So, even if no bikes are produced, C(0) = 8000 Each bike costs 800 to make. So, for x bikes, that would be 800x. That means C(x) = 8000+800x How the heck did you arrive at f(x)=4800? That's a constant function. And who asked for f(x) anyway? We ...
July 12, 2015

Math
well, the vertex is at t = -b/2a = 72/32 = 9/4 So, find s(9/4)
July 12, 2015

math
well, it's a square with side=1 . . .
July 12, 2015

math
one of the factors will be (x-50). What is that when x=50?
July 12, 2015

math
You have to remember that (a-b)(a+b) = a^2-b^2 You have a denominator of x+√7 So, if you multiply top and bottom by x-√7, you have 2√7 (x-√7) --------------------- (x+√7)(x-√7) 2√7 x - 2√7√7 -------------------- (x)^2 - (&#...
July 12, 2015

GREATER TOMMOROW
a+ar = 6 ar^4 + ar^7 = 288 a(1+r) = 6 ar^4(1+r^3) = 288 1+r^3 = (1+r)(1-r+r^2), so r^4 * a(1+r)(1-r+r^2) = 288 6r^4(1-r+r^2) = 288 r^4(1-r+r^2) = 48 We probably want r an integer, so try to see what factors we have of 48 48 = 1*48 48 = 16*3 - bingo r = 2 so, a = 2 The sequence...
July 12, 2015

Calculus
g'(x) ≈ ∆g/∆x = [g(x+h)-g(x)]/h So, just pick a small h, and figure [g(π/2 + h)-g(π/2)]/h = [cos(π/2 + h)-cos(π/2)]/h = [(cos(π/2)cos(h) - sin(π/2)sin(h)-cos(π/2)]/h = -sin(h)/h So, pick any value of h close to zero, and...
July 12, 2015

math
In both cases, the slope is -5/8, so either the lines are identical, or they are parallel. Pick a point on one line, and see whether it is also on the other line. If y=0, then for line 1, x = -1 for line 2, x = -14 So, the lines do not intersect.
July 12, 2015

Physics
According to your formula, I get ∆T = ∆L/L * K I assume that the coefficient is set up to produce °C or °K (which are really the same thing). ∆T = (.0734cm)/(50cm) * (1.9x10^-5) = 2.789x10^-8 Now, somehow that does not seem right. That would mean that...
July 12, 2015

math
d = p-2 d = 3x p-2 = 3x p = 3x+2 So, after 10 seconds, Lee has run 10x meters Pat has run 10(3x+2) = 30x+20 So, Pat is 20x+20 meters ahead of Lee
July 12, 2015

math
recall how to factor the sum of two cubes ...
July 12, 2015

math
None -- two odd numbers always have an even sum.
July 12, 2015

mathematics
s+6 = 2(a+6) a+s = 42 Sena is 30
July 12, 2015

Physics
I guess that depends on what he wants to happen.
July 12, 2015

mathematics
see the answer given to taiwo below. Double it.
July 12, 2015

math
stop wasting our time with these stupid lottery questions.
July 12, 2015

math
or, try this to start out x+y = 2tan x-y = 2sin x^2-y^2 = (x+y)(x-y) = 4tan sin = 4sin^2/cos Saves having to expand those pesky squared binomials.
July 12, 2015

math - take 2
Looks like I used some different angles last time. I hope both methods produce the same answer!!
July 11, 2015

math
This one takes some drawing. Let's label the near lighthouse A, and the far one B. The ship began at P, and ended up at Q. It helps to draw a line due north from Q. A bit of analysis shows that PQ = 20 mi ∠BPQ = 95° ∠PBQ = 30° We want the distance QB, ...
July 11, 2015

Algebra
well, geez. Plug in t=8 and do the, uh, math!
July 11, 2015

math
just a little nudge can usually help.
July 11, 2015

math
x = y-8 2y = 4x Now do a little substitution for y, and you can easily find x.
July 11, 2015

math circle geometrics
draw a radius perpendicular to the chord. If the center of the circle is O, the chord is AB, and the midpoint of the chord is P, then you have a right triangle where the leg OP is 5, and the hypotenuse (the radius) is 7. So, PA=PB is half the chord length.
July 11, 2015

math probability
answered in a related question below.
July 11, 2015

physics
the x-velocity is 43.4/1.8 = 24.111 m/s so, the ball is hit at an angle θ such that cosθ = 24.111/26, so θ = 21.97° So, the y-velocity is 26sin21.97° = 9.73 m/s. The height of the ball is y = 9.73t - 4.9t^2 So, when caught after 1.8 seconds, y(1.8) = 1.638
July 11, 2015

MTH 156
you know the perimeter is 2(length+width) So, f(1,8) = 2(1+8) = 2(9) = 18 and so on for the others. To produce an output of 16, all you need is two numbers that add up to 8.
July 10, 2015

Math
since (x^a)^b = x^(ab) (√3)^2 = 3 So, if √3 = 3^a, (3^a)^2 = 3^(2a) = 3^1 So, 2a=1 √3 = 3^(1/2) The nth root of x is x^(1/n)
July 10, 2015

Maths
Oops. The 4th term is C(6,3)
July 10, 2015

Maths
The (x^3)(1/x)^3 term will be constant. That is the 4th term of the expansion. So, what is C(6,4)?
July 10, 2015

Math
r = 2j+3 r-3 = 4(j-3) 2j+3-3=4j-12 j=6 in 10 years, Joe will be 16
July 10, 2015

maths,integration
v = 4-t s = 4t - 1/2 t^2 + c s(0) = 5, so c=5, and s(t) = 4t - 1/2 t^2 + 5
July 10, 2015

Algebra
with interest rate r, continuous compounding for t years results in a growth factor of e^rt. So, you want e^5r = 4 r = ln4/5 = .277, or 27.7% Which formula were you using to get 11% ?
July 10, 2015

Maths
answered in related questions below.
July 10, 2015

math
you have two pairs of equal sides. So, the two sides you have are half the perimeter.
July 10, 2015

precal
There are lots of good Riemann Sum online calculators. This one is easy, though. The interval widths are 0.5, so all you have to do is evaluate 0.5(f(.5)+f(1.0)+...+f(3.0))
July 9, 2015

math
d$ = 100d¢ You want to convert dollars to whistles: 100d¢ * (w whistles)/c¢ = 100dw/c whistles The easiest way to do this kind of thing is to treat it as a conversion from one unit to another. You can always multiply by 1 without changing anything. Since w ...
July 9, 2015

math
The common denominator of all those fractions is 120. So, say there are 120 members Then 45 are R, 75 are D Also, 80 are men, so 48 are Dm. That leaves 75-48=23 Dw So, 23/120 are Dw
July 9, 2015

math
.08c = .12d 2c = 3d so, c+d = 3/2 d+d = 5/2 d or c + 2/3 c = 5/3 c Not sure what your choices are...
July 9, 2015

Calculus Partial Derivatives
ignoring all the stuff with F and f, I assume you meant y = f(x+at) + f(x-at) ∂y/∂t= f'(w)∂w/dt + f'(v)∂v/dt = a(f'(w)-f'(v)) ∂2y/∂t2 = a(f"(w)∂w/∂t - f"(v)∂v/∂t) = a^2(f"(w)+f"(v))
July 9, 2015

chemistry
14.8/.917 g
July 9, 2015

Math
1 and 2 3 is false, since √2.25 = 1.5 is a radical that is not a whole number, but is not irrational
July 9, 2015

Math
whole natural excludes zero integers include negatives rational includes integers and fractions
July 9, 2015

Algebra
By the way, 2x^3 sqrt(10/x) is also correct. So, good work, I think.
July 9, 2015

Algebra
If you'll allow one more step, 2x^2 sqrt(10x)
July 9, 2015

math
If the committee is really 3 men, then Mary can't be on it at all. I suspect you meant 3 people. In that case, if either John or Mary is on the committee, then there are only 13 other people to pick for the other two seats. That gives us Committees with John: 13P2 = 156 ...
July 9, 2015

math
100-999
July 9, 2015

Mathematics
So, did you actually check your answer? tx=180 means ty=144 So, total time for X is 180+80=260 total time for Y is 144+80 = 224 distance from A of X to meeting place is L/260*80 distance from B of Y to meeting place is L/224*80 Add those up and you do not get L. Your mistake ...
July 9, 2015

Physics
work = force * distance, so assuming European conventions, where the ground floor is floor zero, work = 60*9.8*10 * 3*12 Joules power = work/time, so p = work/12 Watts
July 9, 2015

Math
70+W <= 150
July 9, 2015

Algebra
Since time=distance/speed, if his speed is s and the current's is c, then 15/(s+c) = 15/(s-c)-5 15/(2s+c) = 15/(2s-c)-1 Now just solve for s and c.
July 9, 2015

mathematics
I think you mean she sold 16 boxes, since she only had three different types. t+h+c = 16 40t+50h+60c = 800 That's not enough to completely specify a solution, but it will get you to t = c h = 2(8-c) So, clearly c<=8. If we start listing the possibilities, we get c,t h 8...
July 9, 2015

math
a) the shortest sides are in the ratio 8/3 b) so are the perimeters.
July 9, 2015

math
just multiply 13 by 21/15, the scaling ratio.
July 9, 2015

Physics
since a = 2.7 m/s^2, at t=4.2, v=11.34m/s Then its acceleration drops to (13.0-11.34)/5 = 0.332 m/s^2 So, starting at t=4.2, x = -108 + 0.332t + 0.166 t^2 At 5.7s after the first phase, then x = -100.7
July 9, 2015

math
what should be added to 4 to get 6? 6-4, or 2. Same here. you need to add (-2/15) - (2/3 + 3/5) So, use the common denominator of 15 to work with the fractions.
July 8, 2015

math
The common denominator is 63, so you have 54/63 - 126/63 - 49/63 + 57/63 ...
July 8, 2015

maths
Not much to this one. 1/10 = 7/70 ...
July 8, 2015

maths
I'll assume you meant 1/(x+1)+1/(x+2)= 2/(x+10) Putting all over a common denominator, the numerator becomes (x+2)(x+10) + (x+1)(x+10) = 2(x+1)(x+2) 2x^2+23x+30 = 2x^2+6x+4 I expect you can take it from there, eh? Just beware spurious roots that might make any of the ...
July 8, 2015

Physics
the only equation you really need is d=vt, or t=d/v. That gives you 114t = 79t+36 35t=36 t = 36/35 That's how long it takes B to overtake A. In that time, A travels 79*36/35 = 81.26 km You can think of this another way by noting that B is traveling 35 km/hr faster than A. ...
July 8, 2015

algebra 1
-72-4x^2+8x^3-36x Geez, have you never noticed that polynomials are generally written in descending powers? Much preferred would be 8x^3-4x^2-36x-72 Using synthetic division, this is easy, or you can visit calc101.com, click on the long division button and then enter your ...
July 8, 2015

math (algebra)
If x passed, then the rest (36-x) failed. So, adding up all the grades, we have 78x + 60(36-x) = 71*36 This is just a mixture problem in other guise.
July 8, 2015

Math
6720/56 = 120 So, you have nPr = nCr * 5! That means that r=5. Review the definitions of nPr and nCr to see why this is so.
July 8, 2015

Calculus
I first thought of x^2+1, but f(-1) = 2. So, next, 2x^2+1 f(x) = x^2+1 for x in (-5,-1)U(-1,1) 3 for x = -1 2 for x > 1 I think this fits the bill.
July 8, 2015

math (algebra)
or, note that x^32-1 = (x^16+1)(x^16-1) = (x^16+1)(x^8+1)(x^8-1) ... and if you keep expanding the differences of squares, you wind up with (x-1) at the end.
July 8, 2015

Calculus
for the 2nd part, if a function is differentiable, it is continuous. Hence it has a limit at every point.
July 8, 2015

math
clearly on the nth day you win 5^n dollars. So, what's 5^11? Send me my 10% commission check, ok?
July 8, 2015

algebra
it takes t seconds to fall 125 ft, where -16t^2 = -15 Now, the velocity is just -32t. or, in one operation, -32√(15/16)
July 8, 2015

Computer Programming
odd - you know how to do multiplication. Do a division in the same way. Just copy the multiply routine, and replace * with /. Be sure to watch out for division by zero.
July 8, 2015

Computer Programming
looks pretty good so far. But your best help is your IDE, or the javac error messages. If there are no compile errors, then just run your code and see what it produces. It looks like you are getting a handle on things. Just keep poking around to find code snippets that do what...
July 8, 2015

algebra 2
you want the total area, less the pool, to be 105. So, that means that the border has width x, where (6+2x)(10+2x)-(6)(10) = 105 x = 5/2 ft or 2'6"
July 8, 2015

algebra
There are 7 octaves, plus an extra A,B,C A) Since there are 8 A keys, there are 8C5=56 ways to pick them. For the G keys, there are only 7C5 = 21 choices. For any key, consider it like this. Pick a key from the 1st octave. Now there are fewer octaves to pick the other 4 keys. ...
July 8, 2015

science
recall F=ma? m = F/a now just divide.
July 8, 2015

Maths
Good work, but you had to use a different function. Poorly set problem...
July 8, 2015

Calculus
If you got a single value for an interval, it doesn't look good for the kid. y = 4x-6arctan(x) y' = 4 - 6/(x^2+1) = (4x^2-1)/(x^2+1) y" = 12x/(1+x^2)^2 You are correct with what you got. But, what do you have when y" = 0? An inflection point. That's where...
July 7, 2015

Maths
(1+x)^(1/5) = 1^(1/5) + (1/5)/1! x + (1/5)(-4/5)/2! x^2 + (1/5)(-4/5)(-9/5)/3! x^3 = 1 + x/5 - 2x^2/25 + 6x^3/125 Using the series, we have a problem. It only converges when |x| < 1. I think what you really want to do is find (x-1)^(1/5), using x=32. Then you have x^(1/5...
July 7, 2015

Maths
if x ml of 100% alcohol are added, then you want .15(400) + 1.00x = .32(400+x)
July 7, 2015

Triginometry
Metro: 45tan56° Gammapro: 45(tan56°+tan24°) It always helps in these problems to draw a diagram. Then you can see which sides of the triangle you have, and so which trig functions to use. Of course, it also helps to review your trig functions, and study the similar...
July 7, 2015

Math
again, use tan. he adjacent leg in each case is 7.4 be sure to add 1.8 to the answers, since that's how high the observation point is.
July 7, 2015

Math
the height is just 25(tan33°+tan55°)
July 7, 2015

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