Thursday
March 26, 2015

Posts by STEVE


Total # Posts: 30,068

Math
avg cost is c(x)/x = .1x + 36 + 90/x now just find x when dc/dx = 0.
March 9, 2015

Trigonometry
draw a diagram. Use the law of cosines, since you have two sides and the angle between them.
March 9, 2015

calc
the distance z between the ships after t hours, is given by z^2 = (150-35t)^2 + (30t)^2 at t=4, z=30√5 So, plug in your values, using 2z dz/dt = -70(150-35t) + 1800t
March 9, 2015

Precal
http://www.wolframalpha.com/input/?i=plot&a=*C.plot-_*Calculator.dflt-&a=FSelect_**Plot-.dflt-&f3=2x%5E2%2F((x-2)(x%2B4))&f=Plot.plotfunction%5Cu005f2x%5E2%2F((x-2)(x%2B4))&f4=x&f=Plot.plotvariable%5Cu005fx&f5=-6&f=Plot.plotlowerrange%5Cu005f-6&f6=6&f=Plot.plotupperrange_6&f7...
March 9, 2015

Functions - Please Help
the amplitude is (15.28-9.08)/2 = 3.1 Let's say Jun21 is day 172 Dec21 is day 355 The period is clearly 365 days, so y = 3.1cos(2π/365 (x-172)) Now just find x when y=13.5 and figure the dates.
March 9, 2015

math
f(z) clearly has poles of order 4 at z = 3 order 2 at z = ±√3 i
March 9, 2015

Trigonometry (Identities)
(cos-(sin-1))/(cos+(sin-1)) (cos-(sin-1))^2/(cos+(sin-1))(cos-(sin-1)) cos^2 - 2cos(sin-1) + (sin-1)^2 ------------------------------------- cos^2 - (sin-1)^2 cos^2 - 2sin*cos + 2cos + sin^2 - 2sin + 1 ----------------------------------------- cos^2 - sin^2 + 2sin - 1 2cos - ...
March 9, 2015

Maths
can't tell whether you mean 2^x - 1 or 2^(x-1) In either case, see http://www.wolframalpha.com/input/?i=plot+2^x-1%2C+2^%28x-1%29
March 8, 2015

math
the easy ones are (0,-10/3) and (2,0) Other than that, pick any value for x or y, and then calculate the other.
March 8, 2015

math
it's already two decimal places. If you mean two significant figures, then that is 7.4
March 8, 2015

maths
clearly zero
March 8, 2015

Ms Sue I need you MATH!
if the pool is circular, then pi r^2 = 25.75, so its radius r = 2.86 m. Adding a meter all around means its new area is pi * 4.86^2 = 74.20 m^2 So, the difference is 48.45 m^2 The volume of concrete is thus 4.845 m^3 If the pool is not round, adjust the figures to allow for ...
March 8, 2015

math
4y+8y+16 12y+16 4(3y+4)
March 8, 2015

Math ASAP
Since Sprint requires a 2-year (24-month) contract, for M months and m non-weekend minutes per month, that is (70-30) + 24(30+.029m) = 760 + .696m Verizon for 24 months with m non-network minutes minutes each, charges 24(28+.3m) = 672 + 7.2m All that stuff about weekend ...
March 7, 2015

Math 112
suppose 1/0 = x That means that 1 = 0*x But zero times anything is zero. There is no number x which can be defined as 1/0. 0! is useful because n! is a recursive definition. That is, n! = n * (n-1)! 3! = 3 * 2! 2! = 2 * 1! 1! = 1 * 0! But, n! is also defined as the product of ...
March 7, 2015

addmath A.P.
a = T1 = 3*1-2 d = T2-T1 = (3*2-2) - (3*1-2) = 3 T5 = 3*5-2
March 7, 2015

math
If you mean 1/x^2 e^-x dx, there is no integral using elementary functions. Maybe I misread it. http://www.wolframalpha.com/input/?i=integral+1%2Fx^2+e^-x+dx
March 7, 2015

math
If you graph it, you find that x = .19 or 1.28 so, now you can figure cos and tan
March 7, 2015

Math
looks like 2160 pi to me.
March 7, 2015

Math
V = pi r^2 h also, there are 5 tanks, not just 1. So, we need 5 * pi * 36 * 12 = 2160 pi ft^3
March 7, 2015

algebra - Oops
3/4 = h/15 This assumes that she is 5 feet up the ladder, or 4 feet closer along the ground. If she is in fact 5 feet closer along the ground, then the original answer is good. The wording of the problem is unclear.
March 7, 2015

algebra
Assuming that she is 5 feet along the ladder, then using similar triangles, 3/5 = h/15
March 7, 2015

math
They said the speed of the bus is x. time = distance/speed. So, 280/x = 280/(x+20) + 7/6
March 7, 2015

physics
since all the velocities are constant, the only force acting on the skaters is gravity. (neglecting friction, as usual)
March 7, 2015

Math - Oops
x = 15000√3 = 25981 4/3 * 0.0384 = -15000/25981^2 dx/dt dx/dt = -2304 ft/s My bad.
March 7, 2015

Math
As far as I can tell, the time of day makes no difference. So, as usual, draw a diagram. If the plane is at distance x from the spot directly overhead, its speed is dx/dt, and tanθ = 15000/x sec^2θ dθ/dt = -15000/x^2 dx/dt when θ = 30°, secθ = 2/&#...
March 7, 2015

Math
1/R = 1/R1 + 1/R2 -1/R^2 dR/dt = -1/R1^2 dR1/dt - 1/R2^2 dR2/dt using the two given resistances, 1/R = 1/3 + 1/4 = 7/12 (7/12)^2 dR/dt = (1/3)^2(.04) + (1/4)^2(-.03) dR/dt = 37/4900 = 0.0076
March 7, 2015

indian ridian ridge
1/∛x = x^(-1/3) (x^(-1/3))^-6 = x^((-1/3)(-6)) = x^2
March 7, 2015

maths
104 = 8*13 96 = 8*12 That should help
March 7, 2015

Maths
3d = 3-192 = -189 d = -63 192;129;66;3
March 7, 2015

physics
Draw a diagram. You have a 3-4-5 triangle. well, 60-80-100, but it's the same ratio of sides.
March 7, 2015

Math
Looks good to me
March 7, 2015

math
If the price was p, then 1800000/(p-4000) = 1800000/p +5 p = 40000 so, at $4000 each he could buy 45 at 3600 each, he could buy 50 he sold 48 computers for 1800000 * 1.15 . . .
March 7, 2015

math
see related questions below
March 7, 2015

math
I'll use h for height, because l for length looks like the number 1. the surface area is two semi-circular ends: 2*(πr^2/2) = πr^2 the rectangular cut surface: 2rh the curved surface: πrh Now just plug and chug
March 7, 2015

math
T = A+(B-A)/2 = (A+B)/2 B = 2T-A
March 7, 2015

math
If KN=x, and Z has speed b-20 Z flew for 3.5 hr B flew for 1.5 hr (b-20)(3.5) = 340+x b(1.5) = x (b-20)(3.5) = 340+b(1.5) 2b = 340+70 b = 205 check: K is 307.5 KM west of N So, K is 647.5 km west of G 647.5/185 = 3.5 307.5/205 = 1.5
March 6, 2015

math
clearly, 23 is not the largest. If it is the smallest, then 23 + 23+d + (23+d)+d = 180 3d + 69 = 180 3d = 111 d = 37 and the angles are 23,60,97
March 6, 2015

math
s(t)equals = 5cos(t) minus- sin(3t) ??? why all the words? Just write s(t) = 5cos(t) - sin(3t) v(t) = -5sin(t) - 3cos(3t) a(t) = -5cos(t) + 9sin(3t) a(π) = -5(-1) + 9(0) = 5 you are correct.
March 6, 2015

SAT Math
those two terms are 6 apart, so their difference is 6*4 = 24
March 6, 2015

Math
after a couple of others just like this, do you have some work of your own to show?
March 6, 2015

Pre-Calc.
just set y=0. x = ±3 So, the vertices are at (±3,0) You know that it has to be y=0, because if x=0, -y^2/4 = 1, meaning y^2 has to be negative.
March 6, 2015

Math
The domain is the set of first numbers of the pairs: {0,-2,2,1,-5} the range is the set of second numbers: {2,4,8,6,0} Looks like D to me.
March 6, 2015

math, physics
the initial velocity is 60 ft/s s = 60t - 1/2 at^2 So, a = 3 ft/s^2 60/3 = 20 seconds I wouldn't call that a sudden stop!
March 6, 2015

MaTH
meet 1: 7'46" meet 2: 7'46" - 42" = 7'04" next meet the reduction was 2*42 = 84 seconds meet 3: 7'04" - 84" = 5'40"
March 6, 2015

math
(i) 50(0.035) + 30(0.0475) = 3.175 (ii) 3.175/(50+30) = 0.03968 = 3.97% .035x + .0475(50-x) >= 0.04*50 x <= 30 That is, with 30kg from A and 20kg from B, the result is exactly 4% fat Since A's content is less than 4%, using any more of A will reduce the result below ...
March 6, 2015

College Algebra
y = x^2-13x+36 clearly the y-intercept is (0,36) y = x^2 - 13x + (13/2)^2 + 36 - (13/2)^2 y = (x - 13/2)^2 - 25/4 So, the vertex is at (13/2,-25/4) y = x^2-13x+36 y = (x-4)(x-9) The x-intercepts are at (0,4),(0,9) The coefficient of x^2 is positive, so it opens up. (C) No idea...
March 6, 2015

algebra
12t^2 + 17t - 40 = 0 (4t-5)(3t+8) = 0 t = 5/4 or -8/3
March 6, 2015

Pre-Calc.
you have to complete the squares. Rearrange things a bit and you have x^2+6x + 4y^2-8y = -9 x^2+6x + 4(y^2-2y) = -9 Now complete the squares, and be sure to make the same changes to both sides of the equation: x^2+6x+9 + 4(y^2-2y+1) = -9+9+4 (x+3)^2 + 4(y-1)^2 = 4 (x+3)^2/4...
March 6, 2015

algebra
F = Av^2/400 v^2 = 400F/A v = 20√(F/A)
March 6, 2015

calculus
if the base has width 2x, then the area is a = 2xy = 2x(27-x^2) = 54x - 2x^3 da/dx = 54 - 6x^2 = 6(9-x^2) da/dx=0 when x=3 So, the rectangle is 6 by 18 with area=108
March 6, 2015

Math Check
#1 C #2 B 4x + 2z = 10, so z = 5-2x That gives 2x + y - 3(5-2x) = 4 -2x + 3y - 13(5-2x) = -8 or 8x + y = 19 24x + 3y = 57 so, y = 19-8x That is, whatever x you choose, y and z can be found.
March 6, 2015

Pre-Calc
as you know, the hyperbola x^2/a^2 - y^2/b^2 = 1 has asymptotes of y = ± b/a x You have a=2, b=1, so the asymptotes have slope ±1/2. Also, your hyperbola is shifted, so its center is not at (0,0). Thus, your asymptotes are y-2 = 1/2 (x+1) y-2 = -1/2 (x+1) or, y...
March 6, 2015

College Algebra
4x+y-5=0 has slope -4 So, now you have a point and a slope: y-3 = -4(x-3)
March 6, 2015

College Algebra
just plug and chug. No mysteries here: f(g(2)) = f(1) = 0 g(f(-1)) = g(4) = 3 f(2)-g(3) = 1-2 = -1 f(-1)*g(-2) = 4(-3) = -12 f(x)/g(x) = (x-1)^2 / (x-1) = x-1 for x≠1
March 6, 2015

Math
sorry, bub. No diagrams here.
March 6, 2015

Math
the horizontal sections are the same shape as the base of the pyramid, but of different sizes. What do you think of the vertical sections? As with the cube, I assume the vertical sections are parallel to a side of the base.
March 6, 2015

Maths
come on, guy. For the first equation, pick any two values. Make them easy ones. y=-1, x=4 x=-3, y=4 So, plot (4,-1) and (-3,4) and draw the line. Do the same for the other one.
March 6, 2015

Maths
c'mon. Can you plot points? Plot two points for each equation. Connect the pairs into lines. See where the lines intersect.
March 6, 2015

math
see http://www.wolframalpha.com/input/?i=plot+x-y%2F3%3D2%2C+x-5y%3D0+ or use the graphing utility of your choice. See where the lines intersect.
March 6, 2015

math
ar^5 - ar^2 = 3(ar^6-ar^5) r^3-1 = 3r^4 - 3r^3 3r^4 - 4r^3 + 1 = 0 The only real root of this equation is r=1. Is there a typo? Can you find an error I made?
March 6, 2015

Pre-calc/trig
Both a and b are not truly periodic, since the oscillation gradually has lower and lower amplitude. But, all other things being equal, I'd say the pendulum keeps its amplitude much better than the ball, so I'd have to go with (a) Even (c), if the plane is always on ...
March 6, 2015

Math
using substitution, z = -3, so 3y-8(-3) = -9 3y = -33 y = -11 so, x-(-11)+2(-3) = 22 x+11-6 = 22 x = 17 So the solution is (17,-11,-3) The other is not quite so simple, but since z = 1-2x-4y, we have x-2y-3(1-2x-4y) = 2 x+y-(1-2x-4y) = -1 or, 7x+10y = 5 3x+5y = 0 So, since 5y...
March 6, 2015

Pre-Calculus
the vertices are at the ends of the major axis, and the covertices are on the minor axis. So, since 25 > 4, the vertices are on the y-axis. when x=0, y=5 when y=0, x=2 So, the vertices are at (0,±5) the covertices are at (±2,0) Looks like you need to review ...
March 6, 2015

College Algebra
the two-point form is y-3 = (-4-3)/(4-1) (x-1) and you can massage that into what you need.
March 6, 2015

College Algebra
just use the distance formula: d = √((-1-2)^2 + (-1-3)^2) = √(9+16) = 5
March 6, 2015

College Algebra
the domain is all reals except where the denominator is zero. see more information at http://www.wolframalpha.com/input/?i=%28x%2B4%29%2F%28x^2-1%29
March 6, 2015

calculus
#1 I think you have a typo here. Since the r = d/2, the radius always grows half as fast as the diameter. #2 If the base is x from the wall, and the top is y in height, then you have x^2+y^2 = 25^2 so, 2x dx/dt + 2y dy/dt = 0 or, getting rid of the 2's, x dx/dt + y dy/dt...
March 6, 2015

College Algebra
since body/snout is constant, body/3.5 = 7/2
March 6, 2015

College Algebra
680(1+.04/12)^(12*17)
March 6, 2015

Business Math GBM 200
cost is 300*.24 = 72.00 desired end revenue is 72*2 = 144.00 But only 79% = 237 lbs get sold $144/237lb = .6076 = $0.61/lb
March 6, 2015

Physics
how long does it take to fall 0.75m? 4.9t^2 = 0.75 the speed is 2/t m/s I don't think the above answer is correct.
March 6, 2015

MATHS
Looks to me as though there are in fact many possible solutions. Maybe the "correct" one is the smallest total. Nope. 1244 +125 ------- 1369
March 6, 2015

o level mathematics
Draw your Venn diagram. The intersection of all 3 circles is 2 The other 3 numbers are placed outside any intersections. So, that means we have accounted for 20 of the 35 students. The other 15 can play any combination of two of the games, or just one game. So, there could be ...
March 6, 2015

AHOOOGAAH! HOMEWORK DUMP!
...
March 6, 2015

computer programming
you're going to have to explain those lengths a bit better than that.
March 5, 2015

Pre-Calc
sinB/b = sinA/a so, sinB = 108*sin21°/76 = 0.50925 so, B = 30.6° or 149.4° Since A+B+C = 180, that means C is 128.4° or 9.6° So, since c/sinC = a/sinA there are two choices for c, as well.
March 5, 2015

Math
assume an infinite number of hops. In practice, of course, the ball stops earlier than that, but you have a geometric progression where a = 20 r = 4/5 So, the initial drop is 20, and each bounce is a round trip 4/5 as high as the one before, so the total distance after n hops ...
March 5, 2015

maths
12% off means 88% of the price. So, .88p = 1.21c p = 1.375c so, the marked price is 37.5% above cost
March 5, 2015

math
c+p+s = 100 .5c + 2p + 5s = 100 There are lots of answers, as long as there are an even number of chicks (so you have whole dollars for their cost) For example, getting the most sheep possible, you have 2 chicks, 4 pigs, 19 sheep Now, you can start converting each pig into 4 ...
March 5, 2015

Directions
Face North, and turn 70° eastward. Due east is N90°E NE is N45°E
March 5, 2015

math
the more negative the balance, the greater the debt.
March 5, 2015

math
3 1/3 = 10/3 1 1/4 = 5/4 10/3 * 5/4 = 50/12 = 25/6 = 4 1/6 miles
March 5, 2015

Calculus
dx/dt = (2-x)√(1-x) dx/(2-x)√(1-x) = dt Note that 2-x = 1 + 1-x = 1 + √(1-x)^2 2 arctan √(1-x) = t + c √(1-x) = tan(t/2 + c) = tan(t/2) + c 1-x = (tan(t/2) + c)^2 x = 1 - (tan(t/2)+c)^2
March 5, 2015

Calculus
what, have you forgotten your algebra I? y' = (y^2 + y^2 cosx)^2 y' = y^4 (1+cosx)^2 y'/y^4 = (1+cosx)^2 dy/y^4 = (1+cosx)^2 dx -1/3 y^-3 = 1/4 (6x+8sinx+sin2x) + c y = -∛(4/(3(6x+8sinx+sin2x) + c))
March 5, 2015

algebra
y = x^2-2x-8 = x^2-2x+1 - 9 = (x-1)^2 - 9
March 5, 2015

math 5th grade
8/(10+8) this assumes the socks feel identical, and they are stacked in a messy pile.
March 5, 2015

math
evidently you have not spent the intervening time studying the problems. #1 A flat rate is just that: a constant amount, say $25 A commission is a certain amount, say $50 for every sale. So, for x sales, he would earn 50x so, his total earnings are 25 + 50x #3 is just like #1...
March 5, 2015

math
If (x) = -2 and (y) = 2, then everything is false.
March 5, 2015

math
I assume (x) means |x| = absolute value? well, you have |x| = 2 |y| = 2 Looks like (c) is false. Can't tell with (a), since "1 (y)" eludes me.
March 5, 2015

Math
2x+y = 2400 so, y = 2400-2x a = xy = x(2400-2x) = 2400x-2x^2 That is just a parabola, with vertex at x=600 So, the field is 600 x 1200 As usual, these problems achieve maximum area when the perimeter is divided equally among lengths and widths.
March 5, 2015

Math
If the rectangle has width 2x, then the area is a = 2xy = 2x(12-x^2) da/dx = 24 - 6x^2 = 6(4-x^2) da/dx=0 when x=2 So, the largest area is 4(12-2^2) = 32
March 5, 2015

Math
how about 100 and 100 99*101 = 9999 100*100 = 10,000
March 5, 2015

Acceleration
SInce 1 mi = 1,6 km, 1 mi/hr/s = 1.61km/hr/s So, 23.3 mi/hr/s = 37.5 km/hr/s So, now you can compare them.
March 5, 2015

math - typos
Holy crap! Is ! the NOT operator? If so, we have !(!((5-10)*(4-(9/2)) > 60) has unbalanced parentheses (((5*7)/(4/(5+3)))=15)) has unbalanced parentheses In both cases there are not enough ('s Better go over it and make sure things balance out
March 5, 2015

math: algebra
so, who asked anything about the volume?
March 5, 2015

math: algebra
Drop an altitude from the vertex to the center of the base. Now draw a line from there to the center of a side of the base. Seen from the side, you now have a right triangle with legs 4 and 22. The hypotenuse is the slant height of the pyramid, and thus the altitude of one of ...
March 5, 2015

Math
there is only one statement, and it is true. why?
March 5, 2015

Physics
speed = wavelength*frequency So, if speed doubles you know nothing about the frequency. If the wavelength is unchanged, then the frequency doubles. But, if the wavelength doubles, the frequency remains unchanged.
March 5, 2015

Math (Asap)
aw, shucks... <scuff scuff>
March 5, 2015

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