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January 31, 2015

Posts by STEVE


Total # Posts: 28,511

Sequences
a10 = 6 + 9*8
December 12, 2014

Math
(13.69 + 3.96)/6
December 12, 2014

Math - Sooyong
vertical lines have no y-intercept horizontal lines have no x-intercept (unless these lines are in fact x=0 or y=0) #2 ok #3 also yes. Pick any point on the line (and there are an infinite number of points) and you can draw a perpendicular line through it.
December 11, 2014

Math
the minimum cable length occurs where f'(x) = 0 So, you need 2x/√(x^2+16) - 1 = 0 2x - √(x^2+16) = 0 2x = √(x^2+16) 4x^2 = x^2+16 3x^2 = 16 x = 4/√3 So, the minimum cable length is f(4/√3) = 10+4√3
December 11, 2014

Math
As usual, draw a diagram, and it is clear that f(x) = (10-x) + 2√(x^2+16) f'(x) = -1 + 2x/√(x^2+16) f"(x) = 32/(x^2+16)^3/2 Now the answers are easy to provide
December 11, 2014

algebra
When the car starts, the truck is 56/4 = 14 miles ahead. the car is going 8 mi/hr faster. So, how long will it take to make up the 14 miles? Add that to the 1/4 hr the truck already traveled.
December 11, 2014

Physics
300rev/min / (1/120 min) = 36000 rev/min^2 Now you can convert that to whatever units you like. Remember: 2pi radians/rev
December 11, 2014

math
2(w + 2w) = 72
December 11, 2014

math
xy=20 x+y = x + 20/x minimum occurs where x=2√5 (same as the problem for finding maximum area for a given perimeter: a square) So, pick two integers near √20. They would be 4 and 5, with sum=9 The only other sums are 1+20=21 2+10=12
December 11, 2014

Pre-Calc
Note that if you multiply on the left inside the radical, by (1-sinx)/(1-sinx), you have √((1-sinx)^2/(1-sin^2(x)) That should get you most of the way there, since √x^2 = |x|
December 11, 2014

trig
well, the perimeter is the sum of the sides, so 3n-4 + 3n+9 + 4n+5 = 114 10n = 104 Now it's easy to find n, and then figure the actual side lengths.
December 11, 2014

statistics finding the shaded region
enter your data here. http://davidmlane.com/hyperstat/z_table.html It's a great Z table site.
December 11, 2014

Algebra 2
well, note that f(x) = 5(x^3-2^3) = 5(x-2)(x^2+2x+4) That help?
December 11, 2014

statistics probability
P(-1.39<=Z<=1.69) = 0.8722 You can play around with Z table stuff at http://davidmlane.com/hyperstat/z_table.html
December 11, 2014

Math
If the mother's age is x, x/2 - 10 = 12 x = 44
December 11, 2014

maths
log_2(a) = 2log_4(a) = 3log_8(a) So, you have 2/(1/3 log_2(a)) - 4/log_2(a) = 1/(1/2 log_2(a)) 1/log_2(a) (6 - 4) = 2/log_2(a) 6-4 = 2 Or, recall that log_b(a) = 1/log_a(b) So, you have 2log_a(8) - 4log_a(2) = log_a(4) But, since 8=2^3 and 4=2^2, that means 6log_a(2) - 4log_a(...
December 11, 2014

algebra
log_8(2)+log_8(4x^2) = 1 1/3 + log_8(4) + log_8(x^2) = 1 1/3 + 2/3 + log_8(x^2) = 1 log_8(x^2) = 0 x^2 = 1 x = ±1 ln2 - ln(3x+2) = 1 ln (2/(3x+2)) = 1 2/(3x+2) = e 2/e = 3x+2 x = (2/e - 2)/3 = 2(1-e) / 3e ln(x-3) - ln(x-5) = ln 5 (x-3)/(x-5) = 5 x-3 = 5x-25 x = 11/2
December 11, 2014

algebra
well, clearly the spacing indicates -e^(-3.9n-1) -1 = -3 e^(-3.9n-1) = 2 -3.9n-1 = ln2 n = -(1+ln2)/3.9 Of course, I could be way off...
December 11, 2014

Math
since 36=6^2 its exponents are only half as big as powers of 6 to get to the same value. That is, log_36(n) = 1/2 log_6(n) So, 1/log_36(a) = 1/ (1/2 log_6(a)) = 2/log_6(a)
December 11, 2014

Algebra 2
remember the difference of cubes, and you see that you have (2x)^3 - (10y^2)^3 (2x-10y)((2x)^2+(2x)(10y^2)+(10y^2)^2) = 2(x-5y)(4x^2+20xy^2+100y^4) = 8(x-5y)(x^2+5xy^2+25y^2)
December 11, 2014

Middle School Math
Not at all. 3g+5 = 17 3g+5-5 = 17-5 3g = 12 3g/3 = 12/3 g = 4 I'd be interested to see how you arrived at -20.
December 11, 2014

math
If the ratio is 2:3, then games won = 2/5 of 120 = 48 So, games lost is 3/5 of 120 = 72 The correct proportion would be x/120 = 3/5 Consider. If the ratio is 2:3, the won/lost = 2/3 won = 2/3 lost lost+won=120 lost + 2/3 lost = 120 5/3 lost = 120 lost = 120 * 3/5 = 72
December 11, 2014

math show work please
You just need 2^(t/7) = 3 (t/7) log2 = log3 t = 7log3/log2 = 11.1 hours
December 11, 2014

algebra
that would be the cost per ride, since the only thing that changes is the number of rides.
December 11, 2014

Math
You are correct. 4 was indeed the solution to the equation, but you correctly went on to realize that that meant the actual price was $8/mug. Good work. Still, just plugging x=4 into the equation would have given the same answer for the income, since that accounted for the ...
December 11, 2014

Math
It would surely help if you showed how you got there. What you provide is not much help. If x is the number of price increases, then we have price p = 6.00 + 0.50x quantity sold q = 200 - 10x revenue is price * quantity, so r(x) = (6.00 + 0.50x)(200-10x) = 1200+40x-5x^2 This ...
December 11, 2014

Math
no, the amplitude is the coefficient out front: 37 You know the amplitude of sin(x) is 1 5 in this case isn't really anything. It might look like a phase shift, but it's not even that. And you still have a typo, since there's no t anywhere on the right side. You ...
December 11, 2014

Trig
so, since when is 1/2 pi not the same as pi/2?
December 11, 2014

Math
diameter is 35, so radius is 17.5 -- that is the amplitude of f(t) f(t) is like 17.5 sin(t) Since the max height is 50, that means the axle is at 50-17.5 = 32.5 f(t) is like 17.5 sin(t) + 32.5 The period of sin(kt) is 2pi/k, so we need 2pi/k = 13 k = 2pi/13 f(t) = 17.5 sin(2pi...
December 11, 2014

Algebra
well, just plug in the numbers and see whether it's true. 5(-2) - 2(-1) + 1 > 0 -10 + 2 + 1 > 0 -7 > 0
December 11, 2014

Math
since the range of sin(x) is [-1,1] that is the domain of sin^-1(x).
December 11, 2014

Math
In no way! 3/12 = 25% 50% is 6/12 !
December 10, 2014

Math
there were 12 plants in all 3 had no fertilizer. 3/12 had no fertilizer. Is C your final answer? ...
December 10, 2014

trigonometry
A. 4.5/x = tan 25° B. 4.5/x = sin 25°
December 10, 2014

math
121 = 7+2x
December 10, 2014

Math 6th grade
3 1/4 = 15/4 pizzas each person got 1/4 * 15/4 = 15/16 of a pizza Joe ate 1/4 of his portion, so he ate 1/4 * 15/16 = 15/64 of a pizza Extra credit: who stole the other 3/4 of a pizza? No one buys 3 1/4 pizzas!!
December 10, 2014

Math
Actually, since -(-(-x)) = -x we have |-x| = -x which is true for all x <= 0 Still the correct answer, though.
December 10, 2014

Math solve the equation
7x = 72 7x/7 = 72/7 x = 72/7 9p = 30 p = 30/9 or 10/3
December 10, 2014

German
yes, but it is incorrect. das Kind ein Kind no "eine" allowed. And, since Kind is a noun, it is always capitalized. Now, with adjectives, following a definite article, they are all ending in e. Otherwise, they are inflected by gender: das kleine Kind ein kleines Kind...
December 10, 2014

Algebra2
I'd be interested in seeing your work. I get (h-6)/150 = tan 46.2° (h-6)/150 = 1.04 h-6 = 156.42 h = 162.42
December 10, 2014

Algebra2
If the height is h, then (h-6)/150 = tan 46.2°
December 10, 2014

pre-algebra
5n >= 300*1.25 + 500 5n >= 375+500 n >= 175
December 10, 2014

Calculus
y = e^-x^2 y" = (4x^2-2)e^-x^2 y"=0 when x = ±√2 y(±√2) = e^-2 = 1/e^2 = 1/e^a Looks like a=2
December 10, 2014

math
The first train travels 16(6 37/60) = 96 592/60 = 105 13/15 min = 105'52" or 1 hr 45 min 52 sec do the other similarly
December 10, 2014

Math
y' = 7x^3+28x^2-63x-252 = 7(x+4)(x+3)(x-3) Now things should be easy. You know y is increasing when y' > 0...
December 10, 2014

Algebra
even-root radicals have domain only positive reals, since even powers of all numbers are positive odd powers can be negative or positive, so odd-root radicals have domain all reals.
December 10, 2014

Math
80/x + 80/(x+10) (80(x+10)+80x) / x(x+10) (160x+800) / x(x+10)
December 10, 2014

Pre-Calc/Trig...
by definition, ln(e^x) = x e^(lnx) = x ln and e^ are inverse operations. Just as cos(arccos(x)) = x √(x^2) = x a*(x/a) = x a+(x-a) = x So, ln e^4.3 = 4.3 e^(ln 4.3) = 4.3
December 10, 2014

Math
hint: -9x^2-55x+56 = (7+x)(8-9x)
December 10, 2014

Math
you are correct
December 10, 2014

math
h√-1
December 10, 2014

Math
5.815 < 6.021
December 10, 2014

calculus
s(t)=250-3t+9t^2+2t^3 v(t) = -3+18t+6t^2 a(t) = 18+12t plug in t=0 for initial values. the other questions are just normal ideas. What do you get?
December 9, 2014

Math
factors: 1,2,3,6,7,14,21,42 So, which add to -19? 2-21
December 9, 2014

help asap
well, find the slopes of AC and BD. If their product is -1, they are perpendicular.
December 9, 2014

math
17(2+3) = 17(5) = ?
December 9, 2014

AP Calc
a = pi d^2 when a=3, d^2 = 3/pi v = pi/6 d^3 dv/dt = pi/2 d^2 dd/dt So, -pi/18 = pi/2 (3/pi) dd/dt dd/dt = -pi/27 in/min
December 9, 2014

Calculus- Tangent Line
looks good to me. Of course, it would help to know just what the curve was ...
December 9, 2014

Math
x^2+4x = x(x+3) 2x^2+13x+15 = (2x+3)(x+5) x^2-16 = (x-4)(x+4) So, what you have is x(x+4)(x+5) ------------------ (2x+3)(x+5)(x+4)(x-4) That leaves you with x / (2x+3)(x-4)
December 9, 2014

Math
72x^7
December 9, 2014

Statistics
10P4 = 10*9*8*7
December 9, 2014

fuctions and statistics
you can always multiply by 1 without changing anything. You know that 1 ft = 0.3048 m That means that 1ft/0.3048m = 1 0.3048m/1ft = 1 Now, you want to convert feet to meters, so just multiply by the "correct" representation of 1, so that the units cancel out as you ...
December 9, 2014

English
They look ok to me. And yes, "according to" is ok, as well. I guess you are all "set" now, eh?
December 9, 2014

English
#2 is correct, except for the typo. I'd never use "the" in this case. However, it is correct to say He must have been late for the bus. A bus is a specific vehicle, but "school" is a more vague entity, implying education and other activities, and not ...
December 9, 2014

Physical Science
All oxygen boils at -183 C, but I have no idea what temperature your oxygen is at.
December 9, 2014

math(5th grade)
zero, if the school is north of his home.
December 9, 2014

Calculus
well, you remember that inflection is where y" = 0 concave up when y" > 0 For y" I get 2 times your answer, but that doesn't change its properties. y' = 2cosx(sinx+1) y" = -sinx + cos^2x - sin^2x = -sinx + 1 - 2sin^2x = -(2sinx-1)(sinx+1) Note ...
December 9, 2014

Calculus
the line has slope 2/3 So, the normal needs slope -3/2 3x^2-4y^2=8 6x - 8yy' = 0 y' = 3x/4y So, we need 3x/4y = -3/2 y = -x/2 3x^2-4(-x/2)^2 = 8 3x^2-x^2 = 8 x = ±2 y = ∓1 So, we want lines through (2,-1) and (-2,1) with slope -3/2 y-1 = -3/2 (x+2) y+1 = -...
December 9, 2014

Calculus
I suspect a typo. Why the ^1 ? At x=0, you have (1+0)^1/0 = 1/0 = +∞
December 9, 2014

Math
g(x) --> -6x^2/5x^2 = -6/5
December 9, 2014

Math (Word Problem into formula)
To start with, there is 1 kg of tin. After adding x kg of tin, then we have c(x) = (x+1)/(x+6)
December 8, 2014

algebra
the first thing is your sloppy typing. a/b - c/d is NOT (a-b)/(c-d)
December 8, 2014

geometry
18ft8in = 224in So, one side is 56in area = 56^2 in^2 Now convert that to ft^2
December 8, 2014

GEOMETRY
T(3+4),(5-4) = T7,1
December 8, 2014

Calculus
Hmmm. Not surprising, since you have not posed a question ...
December 8, 2014

geometry
you need to note that one pace is one yard. Now the instructions should make sense, since 15 paces is halfway from 3rd base to 2nd.
December 8, 2014

geometry
the stride is one yard. So, the bases are 30 paces apart. 15 paces is halfway between the bases, along the baseline. Then move back 3 paces from the baseline. Done.
December 8, 2014

Calculus
naturally, since that is the formula for the sum of a G.P.
December 8, 2014

Calculus
The sum is 1/(2^i) = 1/2^1 + 1/2^2 + 1/2^3 + ... = 1/2 + 1/4 + 1/8 + ... You will recognize that as a geometric series, with S = (1/2)/(1 - 1/2) = 1
December 8, 2014

Algebra 2
See the graph at http://www.wolframalpha.com/input/?i=solve+x^2+-+3x+%3D+1
December 8, 2014

Algebra 2
well, 5*2 = 8+2
December 8, 2014

Algebra 2
x^2-2x-35 = 0 Well, the factors of 35 are 5 and 7. They differ by 2, so ...
December 8, 2014

Math Help
all correct. good work.
December 8, 2014

Fraction
13 = 12 8/8 minus 7 5/8 equals 5 3/8
December 8, 2014

calculus
if the dimensions for metal and wood are m and w, then we know that cost = 2(10w+20m)=400 area = m*w = m(200-20m)/10 = 20m-2m^2 This is just a parabola with its vertex at m=5 So, the maximum area is with dimensions metal=5 ft wood=10 ft
December 8, 2014

12 Math
log_2(36)^3 = 3log_2(36) = 3(2+log_2(9)) = 6+6log_2(3) Not sure where you want to go from there. Now, if you meant log(32), that is 5, so log_2(32^3) would be 15.
December 8, 2014

College Algebra
DRS says there are 2 or 0 positive roots 1 negative root RZT says look for roots among ±1,5,7,35 Synthetic division using easy values first says f(x) = (x-1)(x^2-2x-35) I think you can probably take it from there, ok?
December 8, 2014

Linear Algebra
maximize r = 500x + 750y + 1000z subject to x+y+z <= 30 x/2 + y + 2z <= 3*8 The answer from the above constraints may in fact not allow for proper distribution among operating rooms, so watch out for that.
December 8, 2014

math
The bottom is +289
December 8, 2014

Math
what do you mean simplify? You can distribute the fraction, and you get -15/20.5 = 0.73 so you could write -.73x^2 - 2.20x - 1.65 but that's only approximate. SO, again, what do you mean by "simplify"? I will note that x^2+3x+2.25 = (x+1.5)^2 if that helps You ...
December 8, 2014

Math
12x^12/4x^3 = 3x^9 x^8/24x^6 = x^2/24 3x^9 * 24/x^2 = 72x^7
December 8, 2014

Homeschool
each 1.5 cm represents 3m So, how many times bigger is 8 than 1.5? There will be that many 3m lengths. So, the real length is 8/1.5 * 3
December 8, 2014

trig
you can't solve it. It's just a function definition. But, the graph is at http://www.wolframalpha.com/input/?i=r+%3D+3%281-sin%CE%B8%29 Now, if you want to see its equation in rectangular coordinates, r = 3 - 3sinθ r^2 = 3r - 3r sinθ x^2+y^2 = 3r - 3x x^2+y^2...
December 8, 2014

math
40*40 = 1600 So, the cost is (800/9)*25 + 800*2.50
December 8, 2014

math
if $x at 8%, then the rest (8000-x) is at 12%. So, .08x + .12(8000-x) = 650 Now do the math.
December 8, 2014

Algebra 2
clearly there are (2y^2+6)/(y^2-1) notebooks. So, plug in y=3 to find how many.
December 8, 2014

Math
you get the y-intercept when x=0 You get the x-intercept when y=0. So, 1/6 x^4 - 2x^2 + 4 = 0 x^4 - 12x^2 + 24 = 0 x^2 = (12±4√3)/2 = 6±2√3 So, take each of those values and get its ± square roots.
December 8, 2014

fundamental to programing
read x,y,z if (x<y & x<z) {print x} else if (y<x & y<z) {print y} else {print z}
December 8, 2014

Math (TRIG)
Review the equation for a hyperbola in polar coordinates. #2 Hint: sec^2 = 1 + tan^2 #3 y = 500 sin70° t - 16t^2 Solve for t when y=0 to find the time in flight The x-velocity is constant at 700 cos70° So using the time from step 1, distance = speed * time
December 8, 2014

Trig (math)
#1 in polar form, -1+√3i = (2,2π/3) So, the two square roots of that are (√2,π/3) and (√2,4π/3) #2,#3 just plug in x = r cosθ y = r sinθ #4 8x - 7y = -10 7y - 8x = 10 7r sinθ - 8r cosθ = 10 r = 10/(7sinθ-8cosθ)
December 8, 2014

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