Friday
August 22, 2014

Posts by steve


Total # Posts: 24,371

Calculus
Your function becomes less unwieldy if you note that if you divide top and bottom by cosx, you have y = (1/2 sin2x)/(sinx+cosx) All those nasty sec^2 and stuff go away and you have 2nd: wolframalpha.com is your friend. Enter 2nd derivative sinx/(1+tanx) and it pops right up. ...
June 16, 2014

Calculus
From what I can decipher from your cryptic use use of arcana (like A, II DC, Nr, etc.) your reasoning appears sound. I have a bit of trouble distinguishing between II DC and second DC. If they are the same, how can you check the sign of second DC without calculating it? If y&#...
June 16, 2014

physics
depends on the size of the umbrella.
June 16, 2014

math
The height y(t) is given by y(t) = h + vt - 16t^2 h + v - 16 = 148 h + 2v - 64 = 272 So, h=-8 v=172 y(t) = -8 + 172t - 16t^2 y(6) = 448
June 16, 2014

algebra
Since the population grew by a factor of 1.64 over 8 years, we have p = 4.2 * 1.64^(t/8) Since 1.64 = e^0.49 (call it e^.5), we have p = 4.2 * e^(t/16)
June 15, 2014

math
23% of wages is 14204.80 SS tax is 7658.24 FICA tax is 1791.04 so, subtract all those from her gross. Or, note that the total taxes add up to 38.3%, so just subtract that amount. Or not. You never really did ask a question.
June 15, 2014

Precalc
An equation is not a function. However, the definition of a function is usually written as an equation, as in f(x) = 2e^x - 7 But, that's really just a definition. An equation is usually something you have to solve for a particular value. For example, you might have to ...
June 15, 2014

calculus
Oops. The w(t) given above is the y-value of Janice's position. You also need to use the x-value, which I'm sure you can do.
June 15, 2014

calculus
If Janice is at (0,0) when t=0, then the wheel obeys w(t) = 20(1-cos(π/8 t)) The ball follows the parametric equations x(t) = -70 + 60cos60° t y(t) = 60sin60° t - 16t^2 I have no idea where point A is, but having the equations should make things amenable to solution.
June 15, 2014

maths
(x+y)/2 = 44 If x=12, then (12+y)/2 = 44 12+y = 88 y = 76
June 15, 2014

Algebra
we have x^2-2 where x <= 1 2x where x < 1 Not quite clear where you want to go with this. I suspect you really meant 2x where x < 1 x^2-2 where x >= 1 If so, then the graph is a line which stops at x=1, and a parabola from there on. There is a jump discontinuity at...
June 15, 2014

bearing and distance
Use the law of cosines. After t hours, the distance d between the vehicles is d^2 = (8t)^2 + (5t)^2 - 2(8t)(5t)cos70° because the angle between the bearings if 25+45 = 70° So, just plug in t=3 and solve for d. As for the bearing from q to p, just find the slope of the ...
June 14, 2014

math,bearing and distance
not sure what bearing "s30 degree of north" is.
June 14, 2014

Math
you can easily see that K = 18-C So, put that into the 2nd equation and you have 2(18-C)+4C = 50 36-2C+4C = 50 2C = 14 C = 7 So, K = 11
June 14, 2014

math
x^3+3x = x(x^2+3) = (a^2/3-a^-2/3)((a^2/3-a^-2/3)^2+3) = (a^2/3-a^-2/3)(a^4/3 + 1 + a^-4/3) Note we have the factorization of the difference of two cubes: = a^2 - a^-2
June 14, 2014

Another this math tho
ding ding -- we have a winner!
June 13, 2014

this math tho
well, does 3(-10)+54 = 18?
June 13, 2014

3 questions Math
Oops. The synthetic division site was http://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php
June 13, 2014

3 questions Math
#18 - did you try this at the syntehtic division site I gave you? You can see polynomial long division at calc101.com; click on the "long division" button. #19 If you meant 1/(2x + 14) - 9/(x + 7) = -6 then that's just 1/(2x+14) - 18/(2x+14) = -6 -17/(2x+14) = -6...
June 13, 2014

Algebra ll
take a visit to http://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php and enter your coefficients. It will show the calculation, and even explain it if needed. It's hard to do it here, due to browser formatting of html.
June 13, 2014

Algebra
just find when the two are equal: 16x+150 = -x^2+60x-10 x^2 - 44x + 160 = 0 (x-40)(x-4) = 0 Now the answer should be clear.
June 13, 2014

algerbra
try something like this: http://www.wolframalpha.com/input/?i=3x%2By+%3C%3D+5 you can type in many different things, and it will show you the solution
June 13, 2014

algebra 2
B(t) rose by 32
June 13, 2014

Algebra (Factoring)
2(x^4-5x^2-36) 2(x^2+4)(x^2-9) 2(x^2+4)(x-3)(x+3)
June 13, 2014

Algebra
x/5 = 40/1.6 x/150 = 1.6/40 solve for x
June 13, 2014

Math
99 action means 55 horror, for a total of 154 films in 7 days. That's 22 films/day on average.
June 13, 2014

geometry
Assuming the sun rises at 6 am and sets at 6 pm, then at 9 am it is 45° above the horizon. That means a 147cm person will cast a 147cm shadow.
June 13, 2014

science
total mass of H2SO4 is 98 So, figure the % mass of each of the elements: H2 = 2 S = 32 O4 = 64
June 13, 2014

Math
since √x is not real for x < 0, we need 5y+1 >= 0 y >= -1/5 3y-5 >= 0 y >= 5/3 So, we need y >= 5/3 for the domain Now proceed to solve: √(5y+1) - √(3y-5) = 2 5y+1 - 2√[(5y+1)(3y-5)] + 3y-5 = 4 8y - 8 = 2√[(5y+1)(3y-5)] (4y-4)^2...
June 12, 2014

maths
This is just a work problem in disguise. Together the cars must cover a distance. 1/x = 1/4 + 1/6 = 5/12 x = 12/5 Check. Say the distance is 120 miles In 2.4 hours, the car covers 2.4/4 = 0.6 the distance. In 2.4 hours, the van covers 2.4/6 = .4 the distance. ok
June 12, 2014

math
you can order n things in n! ways. 24! = 6.2 * 10^23
June 12, 2014

Math
v = pi r^2 h So, just plug in r=3.7m and h = 2.4m
June 12, 2014

MATH
as you know, the derivative of e^u = e^u u' So, ∫e^u du = e^u Here, u = -x, so du = -dx You thus have ∫e^u (-du) = -∫e^u du = -e^u = -e^-x
June 12, 2014

Algebra
no way to tell
June 12, 2014

Algebra
If the first takes x hours, 1/x + 1/(x+5) + 1/(3x) = 1/(9/4) x = 4 So, the 3 pipes require 4,9,12 hours.
June 12, 2014

Arithmetic
1/3 of the marbles are green. So, 1/3 of at least 54 are green. How many is that?
June 12, 2014

whole number
1219 - 32 - 24 = ?
June 12, 2014

Science(electric circuits)
hmmm. The current in each parallel path may be different. That's a pretty open question, with no context.
June 12, 2014

englewood
total income,state,city tax is 6% 6% of 215 = 12.90 So, total deductions are 15.16+29.33+12.90 = 57.39 Net income is thus 215.00-57.39 = $157.61 Who says we are not taxed enough?
June 12, 2014

science-chemistry
.00565*450 = 2.54g of NaCl So, how many moles is that?
June 12, 2014

Math
I'm having a little trouble visualizing the angles in question. If we label the boats A and B and the dock D, which angles are we talking about?
June 12, 2014

Intro to Algebra
the area of a trapezoid is (b+B)h/2. Since we have 4 trapezoids with bases 5 and 6, the total area is 4(5+6)h/2 = 22h ft^2 paint costs $10/33ft^2 = .3030 $/ft^2 cost of $40 means 132 ft^2 22h = 132, so h=6 ft
June 12, 2014

Math
8^m 3^m = 24^m 576 = 24^2, so 24^(2(m-4)) = 24^m 2(m-4) = m 2m-8 = m m = 8
June 12, 2014

math - ouch
Good catch, Reiny - I was a bit sloppy.
June 12, 2014

math
cos3x = cos2x we need 3(x+2m*pi) = 2(x+2n*pi) for some m and n. Some playing around will get you x = 0,2/5 pi, 4/5 pi or, in degrees, x = 0,144,288
June 12, 2014

math
Facts as presented: g+p+c = 100 21g+8p+3c=600 since c = 100-(g+p), 21g+8p+3(100-g-p) = 600 21g+8p+300-3g-3p = 600 18g+5p = 300 Since 5p = 300-18g, g must be a multiple of 5. But, since g is even, it must be 10,20,30,... If g=10, p=24 If g=20, 18g=360, so any number g>10 ...
June 12, 2014

intro to computer
B - nothing is free
June 12, 2014

Math please help!!
just plug and chug, using the quotient rule (2^x ln2 - e^x)(2^x+e^x) - (2^x-e^x)(2^x ln2 + e^x) --------------------------------------------------------------- (2^x+e^x)^2 You can simplify that to 2^(x+1) e^x (ln2 - 1) / (2^x+e^x)^2
June 11, 2014

math
90ft * 7ft * (1/2 oz/ft^2) = 90*7*(1/2) oz Note how the ft^2 cancel out, just leaving oz in the result. Watch the units, and they will help you decide how to multiply or divide the ratios.
June 11, 2014

Geometry
The sides are a b=a+12 c=b+24 d=c+36 So, a+b+c+d = 136 a+b+c+c+36 = 136 a+b+2c = 100 a+b+2(b+24) = 100 a+b+2b+48 = 100 a+3b = 52 a+3(a+12) = 52 4a+36 = 52 4a = 16 a = 4 So, the sides are 4,16,40,76
June 11, 2014

Math
if the dept head makes x, then x + 3x = 290000 4x = 290000 x = 72500
June 11, 2014

Algebra
learn to recognize common Pythagorean triples in right triangles. The simplest is 3-4-5. This is just double that, or 6-8-10. The rope is 10 feet long. Or, you can do the algebra, using r^2 = 6^2+8^2 and solve for r.
June 11, 2014

hindi
सर्वाधिक लोकप्रिय में से एक था बकवास कविता का ल&#...
June 11, 2014

Math
C = 2πr, so r = C/2π A = πr^2 = π(C/2π)^2 = C^2/4π In this case, A = 16^2/12 = 21.3
June 11, 2014

hct
evidently the volume of iron is 26.44-25.40 = 1.04 mL. So, the density is 8.2g/1.04mL = 7.88 g/mL
June 11, 2014

Algebra
D/B = 27/16 for all strings. So, For the longer string, D/64 = 27/16 Now just solve for D
June 11, 2014

Math help!
f = secx^cotx log f = cotx * log secx 1/f f' = (-csc^2 x * log secx) + (cotx * secx*tanx/secx) f' = secx^cotx (1 - csc^2(x) log secx)
June 11, 2014

trig
While this might appear to be an exercise in half-angle or double-angle formulas, it is really just a check to see whether you remember your basic trig definitions: cscθ = 1/sinθ and secθ = 1/cosθ You happen to be using θ/2, but the principle holds. so...
June 11, 2014

Math
You were right as far as you went. But, you didn't use the rest of the information they gave you. a+b+c = 22 But what else do we know? If a is the short side (assuming it is indeed an odd integer), then b=a+2 (next odd integer) c=2a (twice as big) So, substituting in the ...
June 11, 2014

Algebra/I hope this is the last time.
why all the embedded words and weird unbalanced parentheses? Just list the points: (0,4) (1,5) (2,6) How ever did you get (2,1)? (-10,-6) (-5,-1) (-4,0) and many more
June 11, 2014

Math
You know that cosθ = x/r In QII, x < 0 and y > 0, so we know x = -2 r = 3 so, y = √5 Now you know that sinθ = √5/3 and you now can easily figure sinθ * tanθ
June 11, 2014

math (cant figure it out)
correct: C(7,2) = 7*6 / 2 = 21
June 11, 2014

Algebra
We already went through f(3/2) and f(b) with f(x) = x^2+2. I answered early this morning, and you said thank you 4 hours ago. Why are you asking for those again? You got f(3/2) correct then. Why are you now not sure? At any rate, just substitute in the value wherever x appears...
June 11, 2014

Math (check answer plz)
I assume you mean 9C4 9C4! = 0 Anyway, 9C4 = 9!/(5!4!) = 9*8*7*6 / 4*2*3*1 = 126 9P4 = 9!/5! = 9*8*7*6 = 3024
June 11, 2014

statistics
since 84+16=100, it appears that 84 have taken politics 16 have taken history 0 have taken both 100 have taken at least one of the subjects.
June 11, 2014

algebra/Steve or Damon help
f(3/2) = (3/2)^2 + 2 = 9/4 + 2 = 4.25 f(b) = b^2+2 how did you get zero?
June 11, 2014

math
r^3 = 3375 r = 15 Now just use S4 = 32.5 to find the cheapest price. I suspect a typo, since $32.5 is such a small number.
June 10, 2014

math
after each step, there is 0.9 as much alcohol as before. So, after 7 steps, the amount of alcohol is 10*0.9^7 = 4.78 liters.
June 10, 2014

Math
x+y=30 25x+30y=810
June 10, 2014

Algebra II
correct
June 10, 2014

math
S3 = 1(1-r^3)/(1-r) = 157 1+r+r^2 = 157 r^2+r-156 = 0 (r-12)(r+13) = 0 r = 12 or -13 So, the GPs are 1,12,144,... 1,-13,169,...
June 10, 2014

high school algrebra 1
for p people, the cost c is c = 25 + 18p the cost per person is 25/p + 18
June 10, 2014

math (cant figure it out)
a cube has 6 faces, so the theoretical probability is 1/6, not 1/30! (B) Why would you divide 120 by the number of spots that show? Would P(5) be 1/24?
June 10, 2014

math
h/75 = tan 62
June 10, 2014

Algebra 1
#1 ok #3 .701 = 0.7 to the nearest tenth. Your rounding doesn't have any tenths!
June 10, 2014

Algebra 1
#1 you cannot divide by zero. So, when the denominator is zero, that value of x must be excluded. So, what is x when 3x-6=0? #2 ok #3 use the quadratic formula for this one. #4 Nope. 4^0 = 1 2^-3 = 1/2^3 = 1/8 So, 1 - 1/8 = 7/8 You calculated 4^0 - 2^3 #5 correct. So why did ...
June 10, 2014

algebra 2
Starting from February, after m months, he has 40m dollars. So, when does 40m = 320? m=8 So, what's 8 months after February?
June 10, 2014

Math
20 cows 70 animals so, 20/70
June 10, 2014

Math - incomplete
Reiny went through this for you once. Now, maybe if you say which side of STU is b, we can make some headway.
June 10, 2014

Algebra 1
You did not factor correctly. x^2-4x+4 = (x-2)(x-2) If that's what you got, then you clearly don't understand what it means. x-2 = 0 when x=2, not -2.
June 10, 2014

averages
8(x+2) = 8x-24+y 8x+16 = 8x-24+y 40 = y It doesn't matter what the average age is. Replacing a 24-year-old by a 40-year-old adds 16 years to the total ages, raising the average by 2.
June 10, 2014

physics
72t + 1/2 at^2 = 70 72 + at = 54 so, a = -16.2 m/s^2 applied for t=10/9 seconds
June 10, 2014

maths
42
June 10, 2014

algebra
since g(3) = 2, g^-1(2) = 3 since h(-4) = 1, h^-1(1) = -4 (h*h^-1)(-7) = h(7)*h^-1(-7) = (-5)*(-8) = 40 If you meant (h◦h^-1)(-7) then that would be -7, since by definition (h◦h^-1)(x) = x.
June 10, 2014

Math
y = 2cos(3x+135) cos(kx) has period 2pi/k, so y has period 2pi/3. The 135 is just a phase shift, and does not affect the period.
June 10, 2014

check answer
correct.
June 9, 2014

Geometry
since area grows as r^2, the area grows by (1/2)^2 = 1/4
June 9, 2014

Goemetry
PQ has length √(2^2+15^2) = √229 P'Q' has length 4 times that.
June 9, 2014

math (check answer plz)
Repeating an experiment naturally gives rise to experimental probability. Since no experiment is described, the probability must be theoretical only. So, (C).
June 9, 2014

math
the clue is that (x+3) divides the volume. So, a little checking shows that the volume v = (x+3)(x-7)(x+9) so, if x+3=15, x=12 and the box is 15x5x21
June 9, 2014

math
surely you have the formula for the period of a pendulum of length L (and small amplitude): T = 2π √(L/g) Now just plug in your numbers.
June 9, 2014

Math
-.05t + 300 = 182 Now just solve for t.
June 9, 2014

Calculus
we just did one of these x(t) = 3t^2 - 18t + c Now just figure x(6)-x(0)
June 9, 2014

Maths
The max occurs when x = -b/2a = 5/4, and is indeed 65/8 wolframalpha.com confirms this: http://www.wolframalpha.com/input/?i=-2x^2%2B5x%2B5
June 9, 2014

Maths
done earlier, and you were correct.
June 9, 2014

Algebra
m = miles g = gallons m = 20g
June 9, 2014

math *check*
6 possible outcomes only 1 is a 5 So, theoretical P(5) = 1/6 You rolled 12 times, so that's B: experimentation. Evidently the die was heavily loaded.
June 9, 2014

Math
Correct. Reiny missed the -2x^2. Even experts trip over the details sometimes.
June 9, 2014

Calculus
Oops. Flipped a minus sign f(3) = 9-27+c = -18+c total change is thus -18
June 9, 2014

Algebra
just solve for x in 2771x/(100-x) = 36000 x = 92.85%
June 9, 2014

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