Tuesday
September 1, 2015

Posts by Steve


Total # Posts: 33,198

Math
4*1500 + 12*2*120
July 17, 2015

algebra 2
recall that the sides of a 30-60-90 triangle are in the ratio 1:√3:2 You have a side of 200ft opposite the 30° angle, so it is the shortest side.
July 17, 2015

maths
31+x = 4(1+x)
July 17, 2015

maths
t=tens digit u=units digit t+u = 7 10u+t = 4(10t+u)-3
July 17, 2015

geometry
Two ways you can do this. Since ABC is similar to DEF, and DF/AC = 4/3, the other two sides are also 4/3 as big, making them each 16. So, the perimeter of DEF is 8+16+16=40 Or, since the scale factor is 4/3, the perimeter of DEF is 4/3 that of ABC. ABC's perimeter is 6+12+...
July 16, 2015

Math
this isn't so hard 7^2+5*7 = 49+35 = 84 < 100 8^2+5*8 = 64+40 = 104 > 100 So, any x, 8 or above, will satisfy the inequality. If any of your choices is less than 8 (or so), it won't work. Of course, if x is negative, there are other possibilities.
July 16, 2015

maths
1 dollar is 100 cents, so 4x dollars is 400x cents now add things up
July 16, 2015

careers
I am always amused by all you students who say what you're studying, and wondering what you can do with it. Seems to me like you're better off figuring out what you want to do, and then picking classes to help you prepare for that. In any case, your school counselor is...
July 16, 2015

math
b + b+5 = 49
July 16, 2015

math
just add up the value of the parts. They have to sum to the value of the whole. 8.00(20) + 6.00x = 7.00(20+x) Actually, this one is easy -- since 7.00 is the average of 6 and 8, you need equal amounts of the two kinds.
July 16, 2015

Algebra 2
what you have is a geometric series, with a = 20 r = 1/2 S2 = 20(1-r^2)/(1-r) S12 = 20(1-r^12)/1-r sigma(3,12) = S12-S2 = 20[(1-r^12)/(1-r) - (1-r^2)/(1-r)] = 20/(1-r) ((1-r^12)-(1-r^2)) = 5115/512
July 15, 2015

algebra
175e^5k = 181 so, k = .00674 P = 175 e^(.00674t) Now plug in t=25.
July 15, 2015

Math
r/80 = .20
July 15, 2015

Math
slope = ∆y/∆x = (2-14)/(10-2)
July 15, 2015

Calculus
(a+b)^4 is NOT a^4+b^4
July 15, 2015

Calculus
y=(x+λ)^4/(x^4+λ^4) y' = 4(x+λ)^3(x^4+λ^4) - (x+λ)^4(4x^3) ----------------------------------------- (x^4+λ^4)^2 = (4λ)(λ+x)^3(λ^3-x^3) -------------------------- (x^4+λ^4)^2
July 15, 2015

Math
and then multiply that by 4, since the square has 4 sides.
July 15, 2015

Math
or, since the ratio of lb/$ is constant, .99/3 = x/2
July 15, 2015

math
correct, but x is only halfway up the cliff . . .
July 15, 2015

Math
3.00 + 1.06(30/300 * 14.55)
July 15, 2015

Calculus
5th root of x^3 is (x^3)^1/5 = x^(3*1/5), not x^(3+1/5) So, you start out with y = x^(-1/2) - x^(-3/5) Now just use the power rule, to get y' = (-1/2)x^(-3/2) - (-3/5)x^(-8/5) If you insist on combining the fractions, then you wind up with 6 - 5x^(1/10...
July 15, 2015

algebra
The general solution to the quartic equation is very involved. Read the wikipedia article. This cannot seriously be a homework problem.
July 15, 2015

math
Let P be the base of the perpendicular from A, and Q the base of the perpendicular from B. APD is a 30-40-50 right triangle. So, CD=30, making AP=30 and QD=10. Triangle CQB thus has height 40 and leg CQ=50. So, tan(BCD) = 4/5
July 15, 2015

Math
factor it to get -16t(t-6) That should help
July 15, 2015

Math
C = T-S-H
July 15, 2015

Math
3*30 + (210-3*23)*.22
July 14, 2015

math
The mean is 20 + x/5 For that to be an integer, x must be a multiple of 5. The mean must be greater than 4, since the mean of 3,4,5,8 is already 4. For the mean to be 5, x=5 Also, the mode is 5 And the median is 5.
July 14, 2015

trig
Review what the grade is. It just means that tanθ = 0.1
July 14, 2015

Math
Sorry - not much TeX here. It appears that you mean H(x) = 120000*1.20^(1/2 x) That means that H grows by 20% every 2 years. But, if we want an annual rate, then we have to realize that this is the same as H(x) = 120000*(√1.2)^x √1.2 = 1.095 So, we wind up with H(x...
July 14, 2015

math
n is between 651 and 749 The last digit is between 0 and 4 Looks like we can choose from 650,652,654,...730,732,734
July 14, 2015

algebra
(fg-8)(f^2g^2 + 8fg + 64) This is just the difference of two cubes: (fg)^3 - 8^3 Recall that (a^3-b^3) = (a-b)(a^2+ab+b^2) You have a = fg b = 8
July 14, 2015

algebra
jeez - just plug in x=2! (4*2-2)^2 = 6^2 = 36 16*4-16*2+4 = 36
July 14, 2015

algebra
just square the binomial: (5m^2+7)^2 = 25m^4+70m^2+49
July 14, 2015

Sj
There are two branches: +√x and -√x Just pick one branch of the graph.
July 14, 2015

Maths
Of the 15 balls, 14 remain. P(red) = 2/7 means there are 4 red balls out of 14. So, the lost ball is red.
July 14, 2015

algebra
√(x^2+y^2+100x+2500)-√(x^2+y^2-100x+2500) = 60 (x^2+y^2+100x+2500)-2√((x^2+y^2+100x+2500)(x^2+y^2-100x+2500))+(x^2+y^2-100x+2500) = 3600 2(x^2+y^2+2500) - 2√(x^4+2x^2y^2+y^4-5000x^2+5000y^2+6250000) = 3600 √(x^4+2x^2y^2+y^4-5000x^2+5000y^2+6250000...
July 14, 2015

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

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