Sunday
March 29, 2015

Posts by steve


Total # Posts: 30,136

math
we all know that near x=0, sin(x) = x (or nearly) Since sin(pi-x) = sin(x), sin(pi-x) = pi-x
March 11, 2015

Trigonometry
just plug the numbers into the sum/difference formulas. Surely you can do that... Since both x and y are less than π/4 (why?), x+y is in QI. Since y > x, x-y is in QIV.
March 11, 2015

MATH
slope = tan 45°
March 11, 2015

math
As usual, 42
March 11, 2015

math
v = 4^3 = 64 ft^3 Now you can easily do (b), yeah?
March 10, 2015

math
x^2 + (x+7)^2 = 13^2 Looks like a 5-12-13 triangle to me.
March 10, 2015

Pre-Calculus(Trignometry)
Looks good to me.
March 10, 2015

Calculus
never come here expecting help "in a couple of minutes." you can't count on anyone's watching every post as it comes up. The first related question below is this exact problem, just with different numbers. Always be sure to check the related questions when ...
March 10, 2015

algebra
you have two points: (200,6) and (300,15) So, just use the two-point form of the line: y-6 = (9/100)(x-200)
March 10, 2015

Pre-Calculus
Because of symmetry, the vertex is midway between the roots: x = -13
March 10, 2015

Pre-Calculus
Looks good to me
March 10, 2015

Calculus
when the elevator is at height x, tanθ = (x-23)/15 so, sec^2θ dθ/dt = 1/15 dx/dt (1+tan^2θ) dθ/dt = 1/15 dx/dt (1 + ((x-23)/15)^2) dθ/dt = 1/15 dx/dt Now just plug and chug. You have x, and dx/dt=4 ...
March 10, 2015

calculus
3x^2+y^2 = 7 6x + 2yy' = 0 y' = -3x/y using implicit differentiation again, 6x + 2yy' = 0 6 + 2y'^2 + 2yy" = 0 y" = -(6+2y'^2)/2y = -(6+2(9x^2/y^2))/(2y) = -3(3x^2+y^2)/y^3 = -21/y^3 or, using the quotient rule, y' = -3x/y y" = ((-3)y...
March 10, 2015

Math
If you add up 22+18, that's 40. But, you counted the 6 who have both twice, so that leaves only 34. So, of the 50 students, 34 have shoes or boards, or both. So, 16 students have neither.
March 10, 2015

math
room: 8*6 = 48 carpet: 6*4 = 24
March 10, 2015

Math
(10+7)/(2+10+16+7)
March 10, 2015

Math
The letter C is not a closed shape. Is it not real?
March 10, 2015

Math
probably, but I'm not sure what you mean by "wider." All the graphs stretch out both directions infinitely far. However, (B) does so more slowly, so I guess you could say it's wider. See http://www.wolframalpha.com/input/?i=plot+y%3D3x^2%2B2%2C+y%3D3x^2%2B3%...
March 10, 2015

Math questions
3/4 = 18/24 5/6 = 20/24 8 3/4 = 8 18/24 = 7 42/24 7 42/24 - 5 20/24 = 2 22/24 = 2 11/12
March 10, 2015

math
4 1/2 yards is 4*36 + 18 = 162 inches She was left with 3 ft 8 in = 36+8 = 44 inches. I think now you can handle the rest, yeah?
March 10, 2015

Geometry
since volume scales as the cube of the linear scale, the new cone is scaled in every dimension to 3/4 the original cone. So, its volume is (3/4)^3 * 1920 = 810 Note that you don't need the height, just the relative scale factor. 1/3 pi r^2 h = 1920 1/3 pi (3/4 r)^2 (3/4 h...
March 10, 2015

Math
sorry, no Venn diagrams here.
March 10, 2015

algebra
If the digits are a and b, then we have a+b = 8 10b+a = 10a+b - 18
March 10, 2015

Arithmetic Progressions
a+d = 4a a = 10 10+d = 40 d = 30 S12 = 12/2 (2*10 + 11*30)
March 10, 2015

math
Trick question. At its highest point, the ball changes direction. It has to stop to do that. v = 0
March 10, 2015

Math
I'll do one, and you can do the other. You can check your work at wolframalpha.com x^3-x = x(x-1)(x+1) so we want A/x + B/(x-1) + C/(x+1) = (3x^2-7x-2)/(x^3-x) So, using the common denominator, we have A(x^2-1) + Bx(x+1) + Cx(x-1) = 3x^2-7x-2 (A+B+C)x^2 + (B-C)x - A = 3x^2...
March 10, 2015

Mathematics
well, just subtract 6√2 - 6 = 6(√2-1) On the other hand, if you're just asking about the nature of the difference, 6√2 is 6 times √2 6 is just 6 what is the difference between 6*3 and 6? same question, different numbers. Not sure just what is ...
March 10, 2015

maths
avg speed is total distance/total time time = distance/speed, so (100+200)/(100/40 + 200/60) = 360/7 km/hr
March 10, 2015

math
2*3*6 sinx*sinx cosx*cosx 36 sin^2(x) cos^2(x) or 9(2 sinx cosx)^2 9 sin^2(2x) 9/2 (1-cos(4x))
March 10, 2015

math
8 cubes of side 2 have surface 8(6*2^2) one cube of side 4 has surface 6*4^2
March 10, 2015

math
it appears you want 2^2010 + 2^2012 + 10 --------------------------- 2^2009 + 1 (2^2009*2 + 2^2009*8 + 10)/(2^2009+1) (2^2009*10 + 10)/(2^2009+1) 10(2^2009+1)/(2^2009+1) 10
March 10, 2015

trapezoidal method
there are many trapezoid rule calculators online, which explain the method and do the math.
March 10, 2015

College Algebra
if there is x at 10%, the remainder (12000-x) is at 3%. So, add up the interest: .10x + .03(12000-x) = .06(12000)
March 10, 2015

math
2 min = 8*15sec so, it will double 8 times. 10 * 2^8 = ?
March 10, 2015

Algebra 2
If you mean the nth term is -4 (1/3)^(n-1) then clearly you have a GP where a = -4 r = 1/3 The terms are -4, -4/3, -4/9, ... The sum is thus a/(1-r) = -4/(2/3) = -6
March 10, 2015

Geometry
75 at W20°S = <-70.48,-25.65> 125 at N10°W = <-21.71,123.10> Add them up to get the resultant: <-92.19,97.45> Now just convert that back to distance and heading.
March 10, 2015

Elective mathematics
since there is a common ratio, (2k-4)/(k-3) = (4k-3)/(2k-4) (2k-4)^2 = (4k-3)(k-3) 4k^2 - 16k + 16 = 4k^2 - 15k + 9 k = 7 Now just plug and chug.
March 10, 2015

Analytic geometry
I don't know what you mean by necessary, but the hyperbola is 9x^2+18x - 4y^2+8y = -41 9(x^2+2x+1) - 4(y^2-2y+1) = -41 + 9*1 - 4*1 9(x+1)^2 - 4(y-1)^2 = -36 or, 4(y-1)^2 - 9(x+1)^2 = 36 (y-1)^2/9 - (x+1)^2/4 = 1 That should tell you what you need to know.
March 10, 2015

Calculus
exponentials grow faster than any power. So, x^5/e^x -> 0 consider using l'Hospital's Rule. After 5 times, the limit is 120/e^x -> 0
March 10, 2015

math
Or, if the order is important, 5P3 = 5*4*3 = 60
March 10, 2015

math
5C3 = 5C2 = 5*4 / 1*2 = 10
March 10, 2015

Please Check My Math Answers. Thanks!
They all are correct. Good work.
March 10, 2015

Math
7/8 * pi * 7^2
March 10, 2015

precalculus
ln2 + lny - ln(2y) ln(2 * y / (2y)) ln(1) 0 If I misread the cryptic 2lN then fix it and follow the rules to get the right answer.
March 9, 2015

precalculus
decrease of 1.8% is a remaining portion of 98.2% So, the population after t years is 89000 * 0.982^t now just find t when the function = 50000
March 9, 2015

math
it is the set of products, where each value in each pair is an element of the set described above, with no duplications: {7*8,...9*11}
March 9, 2015

math
hard to say, without knowing the relationship of the angles. In a triangle? Between parallel lines?
March 9, 2015

precalc
x^2+3x-10 = (x+5)(x-2) x^2-8x+15 = (x-5)(x-3) So, you want (x+5)(x-2) / (x-5)(x-3) * R = (x-2)/(x-3) So, you have R = (x-2)/(x-3) * (x-5)(x-3) / (x+5)(x-2) R = (x-5)/(x+5)
March 9, 2015

3rd grade fraction
you sure there are 15 coins?
March 9, 2015

Vectors
The vector equation for the line is r(t) = x(t) i + y(t) j = (-2-t)i + (4+2t)j r(0) = -2i+4j r(t) = -2i+4j + t(-i+2j)
March 9, 2015

math
π(2.4^2-2.2^2)cm^2*350cm * 10g/cm^3 = 10.12 kg
March 9, 2015

MATH
40mm * 25mm * 2mm = 2000mm^3 2000mm^3 * .0005 oz/mm^3 = 1 oz now, why you tell us about a bar of soap and then about the weight of gold, I have no clue...
March 9, 2015

Algebra 1
since y=2x-1, 2x + 2(2x-1) = 22 6x = 24 x = 4 so, y = 2x-1 = 7 one solution.
March 9, 2015

Math
you want two partitions of 36 that multiply to between 300 and 350 18x18 = 324 17x19 = 323 16x20 = 320 15x21 = 315 14x22 = 308
March 9, 2015

Trig verifying identities
oops. That is csc^2(x) - 1 = cot^2(x)
March 9, 2015

Trig verifying identities
sec(pi/2 - x) = csc x sec^2(x) - 1 = cot^2(x) remember that the co- in cosine, cotan, cosec means the complementary angle. cos(x) = sin(pi/2 - x) and so on
March 9, 2015

preCal help please
can't figure what you want. 5√-3 / (√5-√3) ? multiply top and bottom by √5+√3
March 9, 2015

Math
all you have is the difference. You need one more piece of information. normal - storm > 121
March 9, 2015

Math help and check
1 and 2 are ok 3 is eponential as in (1,2) (2,4) (3,8) (4,16) ... where the common ratio is 2 y = 2^x
March 9, 2015

Math
correct 80 < t or t > 80
March 9, 2015

FRACTIONS (simplify)
2m^2-8 = 2(m-2)(m+2) so, that is the common denominator. You end up with (m+2)(m-2)(m+2) - m(2)(m-2) + 2m^2-m^3 ---------------------------------------- 2(m-2)(m+2) m^3+2m^2-4m-8 - (2m^2-4m) + (2m^2-m^3) ---------------------------------------- 2(m-2)(m+2) 2m^2-8 ------------ ...
March 9, 2015

PreCal
(√2 + 1)/i (√2 + 1)i/i^2 -(√2 + 1)i
March 9, 2015

Calculus 2
no, that is point-slope form. To me, it's just as good as the slop-intercept form, since it contains all the necessary info. For this kind of problem, you have a point on the curve, and the slope of the tangent. The point-slope form is ideal. x = tcost dx/dt = cost - tsint...
March 9, 2015

MATH
1.8E-5 = 18E-6 so, sqrt will be √18 E -3 You can do that by hand, or just do some estimating 4^2 = 16 4.2^2 = 17.64 4.3^2 = 18.49 So, you can see it is between 4.3 and 4.3
March 9, 2015

geometry
no diagram. more data.
March 9, 2015

math
v = pi r^2 h = 100pi h dv/dt = 100pi dh/dt Now just plug in your numbers to get dv/dt. Note that it does not matter what the height is. Since the cylinder has a constant radius, its volume is directly proportional to its height.
March 9, 2015

math
the magnitude is clearly √(16^2+18^2) now just figure the angle. Draw a diagram.
March 9, 2015

math
just use the product rule v = x^2 h dv/dt = 2xh dx/dt + x^2 dh/dt Now just plug in the given values.
March 9, 2015

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

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