Thursday
January 29, 2015

Posts by steve


Total # Posts: 28,475

Math
the period of cot(x) is pi. The amplitude and power make no difference. So, the general solutions are n*pi ± pi/3 for any integer n.
January 26, 2015

math
ummm... how about √(mx+b) ?? I suspect you have not posed the question completely.
January 26, 2015

Math
15 <= -k/4 + 9 6 <= -k/4 -24 >= k or, k <= -24 Just work it like an equation, remembering to switch directions whenever multiplying by a negative value.
January 26, 2015

math
since a square of side 10/√2 has half the area, each side needs to be shortened by at least by 10 - 10/√2
January 26, 2015

math
http://www.wolframalpha.com/input/?i=-16t^2+%2B+42t+%2B+3.75+%3E%3D+22
January 26, 2015

algebra. help!
No idea. I added the rows, but my results do not match any of the choices. Not even close. I'm missing something here.
January 26, 2015

algebra. help!
are these supposed to be vectors or matrices? In either case, I assume we are to add corresponding components. 3/4 - 5/3 = -11/12 2/3 + 4/2 = 8/3 So, I guess I'm not getting what it is you want.
January 26, 2015

math
Looks a lot like my work. But we'll let that go... Surely you can now solve the equation! If two numbers have a product of zero, one or the other must be zero. So, either x-12 = 0 --> x=12 x+1 = 0 --> x = -1 Clearly the solution is x=12. That is, the firework will ...
January 26, 2015

pre-algebra
clearly y cannot be 8.3. Multiply that by 6 and you get 50 6y+5 = 10 6y = 5 y = 5/6 y = 0.8333 4 = z/12-17 z/12 = 21 z = 21*12 = 252
January 26, 2015

math
first, do a google on special characters to find the ±√ symbols, which you can then copy and paste. All those words are just too ugly for words! You have y=2x^2-2x+1 and y=3x-5, so set them equal: 2x^2-2x+1 = 3x-5 2x^2-5x+6 = 0 The discriminant (b^2-4ac) is ...
January 26, 2015

math
use >= for greater than or equal <= for less than or equal
January 26, 2015

Science
h doesn't matter KE = 1/2 mv^2 = (1/2)(0.02)(2) = 0.02J all those words are just noise. v is 2 m/s, much easier to read.
January 26, 2015

math
if you mean sec^2 x - 1 = 3 then we can proceed to sec^2 x = 4 sec x = 2 or -2 sec pi/3 = 2, so using that as a reference angle in each quadrant, x = pi/3 or 2pi/3 or 4pi/3 or 5pi/3
January 26, 2015

Math
check the table. As x increases by 2, y increases by 7. So, the slope of the line is 7/2, making the only possible choices A and B. y = 7/2 x is 7 when x=2, but the table has y=8. So, we have to adjust things and get y = 7/2 x + 1 (A) If you check the other values, you will ...
January 26, 2015

Math
I can't quite parse your language. Do you mean y = √(bx)^-2 or some other arrangement? If that is what you meant, then b=0 will make the domain an empty set.
January 26, 2015

Math
Hmmm. y = 1 - 1/(2√(3x-6)) I get a horizontal asymptote at y=1, with the range (-∞,1)
January 26, 2015

physics
the height is y = 15t - 4.9t^2 So, solve for its vertex (max height), and t when y=0 and y=4 to answer the other questions.
January 26, 2015

Math
3.50 * 1.80 = 6.30
January 26, 2015

math
the slope of the line Ax+By+C=0 is -A/B so, check the pairs. #1 -3/4 vs -6/8 same, so parallel or identical since multiplying the 1st by 2 gives the 2nd exactly, they are in fact the same line. do the others in like wise.
January 26, 2015

Math
5(-11/5)^2 - 3(-11/5) + 9 5(121/25) + 33/5 + 9 605/25 + 165/25 + 225/25 995/25
January 26, 2015

Chemistry
Looks ok to me.
January 26, 2015

Science
#2B fission does not absorb light or heat. Gravity made the planets condense. The others look ok.
January 26, 2015

maths
write what you are given: p = h+7 4p+2h = 58 Now it's a cinch, right?
January 26, 2015

Physics
this is just practice converting to and from polar to rectangular coordinates. Convert each putt, add them up, and convert back: 3.32 @ N = <0,3.32> 1.63 @ SE = <1.153,-1.153> 0.703 @ SW = <-0.497,-0.497> add them up and you have <0.656,1.670> and that ...
January 26, 2015

physical sciences
if they act in the same direction, they add up to 12N if the act exactly opposite, the subtract to 2N in the direction of the original 7N force.
January 26, 2015

Math
#1 ok #2 ok #3 Almost x^2-9 = (x+3)(x-3) divide by (x-3) and you are left with (x+3) #4 ok
January 26, 2015

physics
well, the height y = 1000 - 10.0t - 4.9t^2 just find t when y=0.
January 26, 2015

math
what's the trouble? You have two functions and want to know where they are equal. -x^2+15x = 4x-12 x^2-11x-12 = 0 (x-12)(x+1) = 0 I think you can take it from there, right?
January 26, 2015

Denumerator? :-)
I know what an enumerator does, but I'm not sure what a denumerator does . . . eliminate stuff?
January 26, 2015

math
we know that A+B+C=180°, and we see that A = 36.86° B = 67.38° So, C=75.76° Now you can use the law of sines to find the other two sides.
January 26, 2015

Math
4012/44 = 91.1 4982/44 = 113.2 So we know that the multiple is between 92 and 113 Since 4*3=12 and 4*8=32 are the only multiples that end in 2, we know that the other number is one of 93 98 103 108 113 44*93 = 4092 44*98 = 4312 44*103 = 4532 44*108 = 4752 44*113 = 4972 So, ...
January 26, 2015

College Algebra
Hmm. It's clear that x=0 works, but is there anything else? (2^x+1)(3^x+1) = 2^x + 3^x + 6^x + 1 so, (2^x+1)(3^x+1) +1-4^x + 1-9^x = 4 (1+2^x)(1+3^x) + (1+2^x)(1-2^x) + (1+3^x)(1-3^x) = 4 (1+2^x)(1+3^x+1-2^x) + (1+3^x)(1-3^x) = 4 I don't see anything dropping out. If ...
January 26, 2015

Mathematics
a line has constant gradient. A curve does not. Also, the gradient of a curve might even be discontinuous.
January 26, 2015

stats
you can play around with Z table stuff here: http://davidmlane.com/hyperstat/z_table.html
January 26, 2015

Statistics
try playing around here: http://davidmlane.com/hyperstat/z_table.html
January 26, 2015

Calc
This is also easy to see since cos(1/x) never exceeds 1. So, e^cos(1/x) never exceeds e. So, |e^cos(1/x)| <= e x e^cos(1/x) <= e*x -> 0 as x->0
January 25, 2015

Math
What you should do is read the problem carefully. It states that there are more than 50 marbles in the bag. So, what is the smallest multiple of 7 that is greater than 50? Must be 56.
January 25, 2015

phisics
mass * distance must be equal, so 18x = 36*0.45
January 25, 2015

Calculus
Since |(sin 1/x)| <= 1 |e^(sin 1/x)| <= e so x e^sin(1/x) <= x * e -> 0 as x->0
January 25, 2015

Physics (Classical)
using vectors, John's velocity is <0,-6.7> Mary's velocity is <-6.43,-9.53> Mary's velocity with respect to John is the difference between their velocities: <-6.43,-9.53> - <0,-6.7> = <-6.43,-2.83> Now just get the magnitude and ...
January 25, 2015

Math
840 * 2/3 = 560 840-560 = 280 half of 280 = 140 560+140 = 700
January 25, 2015

Algebra I
it lands when the height (y) is zero. So, just solve for x in -0.02x2 + 2.3x + 6 = 0 just use the quadratic formula.
January 25, 2015

math
(1 - 1/4 - 1/2(3/4))x = 800
January 25, 2015

algebra
you are correct if you meant [2(-2)-4(-3)]/(5-8)
January 25, 2015

Physics
First unify the units. 55.4 mi/hr = 24.8 m/s you know that the distance is given by s = 24.8t - 1/2 at^2 So, to stop in exactly 116 meters, we need 24.8t - 1/2 at^2 = 116 Now, we know that during that time, the speed reduces from 24.8 m/s to zero, so a = 24.8/t m/s^2 t = 24.8/...
January 25, 2015

Math
li spent $840 on vacation, She spent 2/3 of the amount on a train ticket and 1/2 of the remaining amount on food. How much did she spend on ticket and food altogether?
January 25, 2015

Math
sam travelled 1/4 of a journey by bus. he jogged 1/2 of the remaining distance and walked the rest of the way. If he walked 800 feet, what was the total distance he traveled?
January 25, 2015

Algebra 2 Applications
If you want to include the travel time of the sound, you have to look up the speed of sound in air. Let's say that is 343.2 m/s. So now, if the falling time is t, then we have 4.9t^2 = 343.2(3-t) t = 2.88 So, the balloon fell for only 2.88 seconds, making the distance 4.9*...
January 25, 2015

physics
well, you know that the height is y = 45t - 4.9t^2 Now just use that parabola to answer the questions.
January 25, 2015

math
If the four got amounts a,b,c,d respectively, then a = 2b b = 3c c = d/2 a+b+c+d = 840 a-d = 280
January 25, 2015

math
1day/L * 1000L/kL * 1year/365day = 1000/365 years.
January 25, 2015

math
since the denominator is not zero at t=2, just plug in t=2 to get the limit. The function is continuous at t=2. (2^44-9)/9
January 25, 2015

Algebra
I assume you mean 1/(1-2x) + 6x/(1+2x) = 3 the common denominator is (1-2x)(1+2x), so we get (x ≠ ±1/2) (1+2x) + 6x(1-2x) = (1-2x)(1+2x) 8x^2 - 8x = 0 8x(x-8) = 0 I expect you can take it from there, right?
January 25, 2015

Calculus
as you figured, the time t is t = (300-x)/(160) + √(800^2 + x^2)/70 dt/dx = 160x - 70√(800^2 + x^2) ----------------------------- 70*160√(800^2 + x^2) dt/dx=0 when 160x = 70√(800^2 + x^2) 25600x^2 = 56000000 + 4900x^2 x = 389.23 Hmm. Not what I had ...
January 25, 2015

Maths
x(t) = 0 if the object is at rest where it started. Don't you think you need to specify a bit more abut the situation?
January 25, 2015

maths
I think you have left something out. An = An-1 + 96
January 25, 2015

math
No, it would be y >= x+3 You have to include the number of female birds. There are at least three more males than that.
January 25, 2015

math
these are just simple polynomial addition, subtraction and multiplication. (f*g)(x) = f(x)*g(x) = (x+4)(3x+2) and the same for the other operators.
January 25, 2015

Math
tan π/4 = 1, so 4x = π/4 (1/√2,1/√2) period = π/4 x = π/16 + n(π/4) for the second, you just have cscx =0 or secx = 2 and proceed as above
January 25, 2015

maths
you know that the difference between terms is constant, so (4x+5)-(x) = (10x-5)-(4x+5) now just solve for x.
January 25, 2015

math function2
A) 18-6 = 12 seconds B) no idea of the radius. You give no indication of the height of the wheel, or where the platform is in relation to the axle. C) no can do. All we know is that h(t) = A + Bsin(pi/6 t + C)
January 25, 2015

Algebra Ques23
I can't imagine the math class where you have exercises in trigonometry, algebra, calculus, and such a simple question as this. Also, I get tired of your homework dumps with no effort on your part.
January 25, 2015

Trig 4
no. They are just ratios in a right triangle. Review your text, where I'm sure it is explained clearly. Google is your friend.
January 25, 2015

physics
clearly, the resultant is max if they act in exactly the same direction. So, what do you think?
January 25, 2015

Mathematics (Vector) (ENGG1410)
they are just ellipses parallel to the xy plane.
January 25, 2015

College Trigonometry
You can also read the excellent article on "trajectory" in wikipedia, where these equations are derived.
January 25, 2015

Math
you don't need to sum the series. It doubles 8 times in 24 hours, so the population is 40*2^8. You'd only need the sum if a new population, double the old one, was added every 3 hours. The runner problem is just the same. Every day you multiply the distance by 1.1 So, ...
January 24, 2015

math
just use the quadratic formula.
January 24, 2015

maths
Think of the hexagon as six equilateral triangles. The altitude of each triangle is 24. So, the side of each triangle (equal to the sides of the hexagon are) 48/√3
January 24, 2015

Trigonometry
No idea which angle sigma is, but I'll assume it's C, since otherwise you'd probably have used alpha. sinA/a = sinC/c so, sinA/28.1 = .4617/52.8 sinA = .2457 A = 14.2° or 165.3° Now you can find B and b.
January 24, 2015

Algebra Rearrangement
it's a quadratic in x: rx^2-tx-h = 0 use the quadratic formula to find the value(s) of x.
January 24, 2015

math
(c ¢)/(1 lb) * (a oz) * (1 lb)/(16 oz) = ac/16 ¢
January 24, 2015

math
1/(9+3+1)
January 24, 2015

Geometry
Pick up a real cube and draw a 3x3 grid one each face. Fill in the grids on 3 faces with R and 3 with B. The very center cubelet has no painted faces. Now count the others and total up the various color combinations. Make sure that it makes no difference how the two colors are...
January 24, 2015

Pre Calculus
Review the idea of reference angles, which are always in QI. sin 0.0135 = 0.0135 That is the angle in QI. But sin is negative in QIII and QIV. So we have π+0.0135 and 2π-0.0135 cot 0.351 = 2.731 But, cot is negative in QII and QIV, so we have π-0.351 and 2π...
January 24, 2015

Math
It appears that the chopped piece fell 4 feet. So, the tree was 4+7=11 feet tall.
January 24, 2015

physics
the height of the falling stone is 6.82-8.8t-4.9t^2 the height of the stone thrown upward is 8.8t - 4.9t^2 So, when do they meet? At t=0.3875 Now plug that into either function to get the height at that time. http://www.wolframalpha.com/input/?i=solve+6.82-8.8t-4.9t^2++%3D++8....
January 24, 2015

physical
√((300+400/√2)^2+(400/√2)^2)
January 24, 2015

maths
34.67*10^-6 pN/m^2 * 1.0197*10^17 lb/pN * 2.59*10^6m^2/mi^2 = 9.16*10^18 lb/mi^2
January 24, 2015

Set Question 1
Since A∩(BC) = A∩B ∪ A∩C, your first step is (X ∪ Y ∪ Z)∩X ∪ (X ∪ Y ∪ Z)∩(Y∩Z) and now break down each of those similarly. Just review your basic set properties. Recall that X∪X = X∩X = X
January 24, 2015

Trignometery
As usual, draw a diagram. If we label Kappy=K Blue UFO=B Red UFO=R KR = 42 tan64° + 42 tan 12° UV = 42(sec 12°)
January 24, 2015

Algebra
39,916,799 http://www.wolframalpha.com/input/?i=sum+n*n!+for+n%3D1+to+10
January 24, 2015

Geometry
the tangent at P has slope x/(2a) So, the normal line is y-ap^2 = p/(2a) (x-2ap) y = p/(2a)(x-2ap)+ap^2 So, where does that line intersect y = x^2/(4a) ? p/(2a)(x-2ap)+ap^2 = x^2/4a (1/4a)x^2 - p/(2a)x + p^2(1-a) = 0 Now just solve that for x and figure y. One solution better ...
January 24, 2015

math
no idea. where did you leave off? Just start with 8 and keep adding 3
January 24, 2015

Math
1A reflection in the x-axis changes the sign of y. parent: x^3 flip over x: -x^3 raise 2: -x^3+2 2C y becomes taller, which has the equivalent effect of making the graph look narrower. parent: x^2 shift right (x-2)^2 flip over x: -(x-2)^2 stretch up (make narrower): 3(x-2)^2 ...
January 24, 2015

math
If the rectangle's dimensions are x and y, and the square is side s, then 2x+2y = 4s 2(x+y) = 96 x = s-4 2(x+y) = 2x+2y = 4s = 96 so, s = 24 x = s-4 = 20, so y = 28 2xy = 2*20*28 = 1120
January 24, 2015

math
If the cardboard has side x, the volume is (x-8)^2*4 = 324 Now it is clear what x is.
January 24, 2015

algebra
(x - 1/5)^2
January 23, 2015

Maths
a = 4 d = 11 n = (368-4)/7 + 1 = 53 S53 = 53/2 (4+368) = ?
January 23, 2015

algebra
Using feet for all measurements, we have 18 * 3/4 * length = 4*27*4 length = 32 ft
January 23, 2015

algebra
2.50(5/4) + 5.50(3/4) = x(5/4 + 3/4) x = $3.625
January 23, 2015

applied math
width is 10*12 = 120 inches So, it takes 120/4 widths Since the wall is an exact number of widths, we just need to figure the length to find the rolls. 10*12*4 = 480 in long so, we need 480/(20*12) = 2 rolls Makes sense, since each roll does 2 strips, and we need 4 strips.
January 23, 2015

algebra
I get 0.808
January 23, 2015

Math
P = (8,-3) The slope of PQ is ∆y/∆x = (3/(7-x)-(-3))/(x-8) = (3+3(7-x))/((7-x)(x-8)) = (24-3x)/((7-x)(x-8)) You have provided no data about Q or the desired slope, but just plug in the numbers you have.
January 23, 2015

math
using the two-point form of a line, you have (p-59) = (42-59)/(50-32) * (q-32) Now just rearrange that into p = 1/18 (1606-17q)
January 23, 2015

Algebra 1
You know two things: g+s = 425 g = s+25
January 23, 2015

college algebra
just solve for t in 16t^2 = 128
January 23, 2015

Math
you have a right triangle with legs 4 and 6. The hypotenuse is thus 2√13. I don't see any good choices.
January 23, 2015

math
you have the line intersecting when kx^2-5x+2 = -3x+4 kx^2-2x-2 = 0 Now recall the discriminant, d=b^2-4ac If d>0 there are two roots If d=0, there is one root If d<0 there are no real roots. The discriminant of your equation is 4+8k I expect you can determine when that ...
January 23, 2015

Math
if it takes t seconds to flip it once, then the actual flipping will take 10,000*t or 100,000*t seconds. There are 86,400 seconds in a day, if that helps.
January 23, 2015

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