Friday
December 19, 2014

Posts by Steve


Total # Posts: 27,630

Algebra
can't be both. For floor, round down to next integer for ceiling, round up to next integer
December 12, 2014

Algebra
1 sometimes 0^0 is undefined 2 never 3 never 4 sometimes .3^1 < 1
December 12, 2014

Algebra
well, just solve 46 + .024x = 1558
December 12, 2014

Math
5r(13r+3s-5s^2) = 65r^2+15rs-25rs^2 -6s(13r+3s-5s^2) = -78rs-18s^2+30s^3 s^2(13r+3s-5s^2) = 13rs^2+3s^3-5s^4 Add them up to get 65r^2 - 63rs - 12rs^2 - 18s^2 + 33s^3 - 5s^4
December 12, 2014

geometry
google the number of segments determined by n points is and you will find many discussions of the topic. Find the one you like and use n=4.
December 12, 2014

Grade 9 Science
the orbit is not a circle, but an ellipse. The planet is not always exactly the same distance from the sun. Read up on Kepler's laws of planetary motion.
December 12, 2014

physics 1
This is just the same as figuring the time it takes for an object to fall 2cm on earth, except that the gravitation acceleration is not 9.81 m/s^2, but GM/r^2 where you have the values for G,M and r. Once you have that evaluated, s = 1/2 at^2 and you can just plug in s=0.02m ...
December 12, 2014

Calculus - Correction
Oops. The part from 0 to 0.0667 is not included, because it's all inside r=1. So, the real area is just 2∫[0.0667,π/2] 1/2 ((15sinθ)^2-1^2) dθ
December 12, 2014

Calculus
The area inside a polar curve is ∫1/2 r^2 dθ The circles intersect where 15sinθ = 1 θ = 0.0667 So, from 0 to 0.0667, we have r = 15sinθ From 0.0667 to π/2, we have to subtract the area inside r=1 from r=15sinθ, so the area is twice the area ...
December 12, 2014

calculus (check)
f(x) looks good No idea what F(n) is. If you mean the sequence of partial sums, it's just the normal sum formula for A.P.'s.
December 12, 2014

calculus (Series)
You just want the sum of the series where a = -2.02 d = -0.09 n = (-4 +2.02)/-.09 = 22 S22 = 22/2(-2.02 + -4) = -66.22
December 12, 2014

Calculus
You just want the sum of an arithmetic series where a = 4 d = 1/2 S28 = 28/2(2*4 + 27(1/2)) = 301
December 12, 2014

Math
That's what I get
December 12, 2014

Physics
Assume the heavier satellite is traveling in the +x direction. Conserve momentum, so the final velocity (xi+yj) is the solution to 1000*500i + 400*700(.707i+.707j) = (1000+700)(xi+yj) That will give the x- and y-components of the final velocity, which you can then express as ...
December 12, 2014

math
(n-2)180 / 360 = 4 So, find n to determine the number of sides, and that will let you find the angles.
December 12, 2014

algebra
I'd guess from previous posts that we want y > -5/3 x + 3 But what we are to do with it I don't know.
December 12, 2014

algebra 2
2√3+√27-√1/3 2√3+3√3-1/√3 5√3 - 1/√3 (5*3-1)/√3 14/√3 √1/2•(√8+√2) 1/√2 * 2√2 + 1/√2 * √2 2 + 1 3 √18-√3/√6 3√2 - √3/(√3√2) 3&#...
December 12, 2014

physics
BCE potential and kinetic energy depend on mass.
December 12, 2014

Geometry
tanθ = 1.89/50
December 12, 2014

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

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