Thursday
April 2, 2015

Posts by Steve


Total # Posts: 30,258

Calculus 1
f(x)=3 sin x+ln(5x) f'(x) = 3 cosx + 1/x Note that ln(5x) = ln5 + lnx So, the ln5 is just a constant, with zero derivative Of course, you could use the chain rule, so d/dx ln(5x) = (1/5x)*5 = 5/5x = 1/x
March 11, 2015

Math
(1+0.013)^n = 2 n = log2/log1.013 ...
March 11, 2015

Pre Algebra
zero
March 11, 2015

Calc
Use <= for less than or equal. a(t) = cos(t)-sin(t) v(t) = sin(t)+cos(t) + c v(0)=1, so c=0 v=0 when sin(t)+cos(t)=0. That is, sin(t) = -cos(t) sin(t)=cos(t) when t=π/4, so using that as a reference angle, that makes t = 3π/4 or 11π/4 Only 11π/4 is ...
March 11, 2015

Math
First, I doubt that 960t-5t is correct. If you meant v=960-5t, then clearly 960 is its maximum speed, whence it slowed down. If you meant v=960t-5t^2, that's a bit more interesting. Then the maximum speed is at t=96, and v(96) = 46080 But, if we stop counting at t=10, then...
March 11, 2015

Ap calc
a = 12t-6 v = 6t^2-6t+c v(0)=3, so c=3, and v = 6t^2-6t+3 s = 2t^3-3t^2+3t+c Since we assume zero distance at t=0, c=0. s(2) = 2*8 - 3*4 + 3*2 = 10
March 11, 2015

math
If the interior angle is x, then the sum of the other two interior angles is also x. Since they add up to 180, x=90. Also, since the sum of an interior angle and its adjacent exterior angle is a straight line, they sum to 180. So, the largest interior angle has the smallest ...
March 11, 2015

math
see the 1st related question below
March 11, 2015

Algebra
a = 49/10 b = 14/9 The reciprocal of b/a is a/b (49/10)/(14/9) = 49/10 * 9/14 = 441/140 = 63/20
March 11, 2015

math
4x + 5x = 90 x=10 The angles are 40 and 50 The smaller is increased by 10% from 40 to 44 So, the larger is decreased by 4 to 46. 4 is 8% of 50
March 11, 2015

math
If you meant that Logan is twice as old as Lindsay, then you are correct in setting it up as you did. Your solution, however, is bogus. x-5 + 2x-5 = 30 3x - 10 = 30 3x = 40 x = 40/3 No joy there. If it should have read Logan is 2 years older than Lindsay, then the equation is...
March 11, 2015

math
h/800 = sin 15°
March 11, 2015

physics
just see when the distances are equal: 120km/hr = 100/3 m/s, so 100/3 t = 2.5/2 t^2 t = 80/3 Now I expect you can handle the rest . . .
March 11, 2015

Algebra please explain
each year the boat is worth .85 as much as it was 92000*.85^10 = 18112.45 You are correct. I assume you were guessing between A and C, since the other two are clearly unreasonable.
March 11, 2015

important maths ques
As usual, draw a diagram. If you draw a line through the center, perpendicular to the chords, you cut them in half. The radius is the hypotenuse of two right triangles. One has a leg of 5, and the other has a leg of 12. So, 5^2 + 12^2 = r^2 12^2 + (17-x)^2 = r^2 5^2 + x^2 = 12...
March 11, 2015

maths please help and explain
2logx + 1 = log900 since 1 = log10, 2logx + log10 = log900 log x^2 + log10 = log900 log(10x^2) = log 900 10x^2 = 900 x^2 = 90 x = √90 3log(x-2) = 4.714 log(x-2)^3 = 4.714 (x-2)^3 = 51760.68 x-2 = 37.268 x = 39.268 16^(x-3) = 8^(2x+1) since 16 = 2^4 and 8 = 2^3, 2^(4(x-3...
March 11, 2015

MATHS
this is just like your last problem with the fruits. Try writing down in algebra what they told you. Come back if you get stuck, but show how far you got.
March 11, 2015

maths
What info did they give? d+p+a = 1134 .75d = a+252 p-96 = a+252 Now you can solve for the amounts.
March 11, 2015

Maths
Quite an interesting result, new to me. I see you have a typo. This problem is discussed here: http://math.stackexchange.com/questions/364002/prove-that-tan-1-fracyzxr-tan-1-fraczxyr-tan-1-fracxy
March 11, 2015

math
without trying to go into any existential discussion, let's just say that it is usually written as 1/4 I suspect there is more than that to your question . . .
March 11, 2015

math
or, if the slope is vertical, there's no derivative there. y = ∛x
March 11, 2015

math
not so. consider y = |x| Any time there's a cusp, or pointy place, on the graph, f is continuous, but since the slope changes instantly from one value to another, it is not differentiable there.
March 11, 2015

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

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