Thursday
April 28, 2016

# Posts by Steve

Total # Posts: 39,993

Algebra
s^2 < πr^2 s < r√π
March 6, 2016

Algebra
pi r^2 < 1 r^2 < 1/π r < 1/√π dm
March 6, 2016

Algebra
s^2 = 36+12
March 6, 2016

Math
you have a right triangle. The two acute angles add to 90 degrees.
March 6, 2016

last 2 questions trig!!
use the law of cosines for two of the angles, then the 3rd angle is trivial. For angle A, 10^2 + 12^2 - 2*10*12cosA = 8^2 similarly for B or C For the boats, draw a diagram. Using the law of cosines, the distance d is found by d^2 = 36^2 + 62^2 - 2*36*62 cos128°
March 6, 2016

math 108 trig
cosx sin2x + sinx cosx - sinx = 0 cosx (2sinxcosx) + sinxcosx - sinx = 0 sinx(2cos^2x + cosx - 1) = 0 sinx(2cosx-1)(cosx+1) = 0 now it's easy, right? 3secx = 2tan^2x 3secx = 2(sec^2x-1) 2sec^2x - 3secx - 2 = 0 (2secx+1)(secx-2) ...
March 6, 2016

Algebra
If the faster painter takes x hours, then 1/x + 1/(x+5) = 1/6
March 6, 2016

Algebra
since time = distance/speed, 36/(20-s) + 22/(20+s) = 3
March 6, 2016

Gaussian Elimination
plug in your coefficients at the URL below to see all the details: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
March 6, 2016

trigonometry
draw the triangles in standard position. You will see that since sin = y/r cos = x/r tan = y/x, sinα = 1/6 cosα = √35/6 tanα = 1/√35 sinβ = 3/5 cosβ = -4/5 tanβ = 3/-4 = -3/4 Now just crank it out using your sum and double-angle ...
March 6, 2016

plz help trig!!!!!
I can't help with the drawing, so if that's a big problem, review your text and google stuff. Assuming that you drew vector v, then it should be clear that the components are x: 20 sin70° = 18.79 y: 20 cos70° = 6.84 similarly, w has components x: 10 sin60°...
March 6, 2016

statics counting methods
routes depend on connecting roads, but there are 8C3 = 56 ways to pick 3 from 8 items. There are, however, 8P3 = 336 different ways those 3 items can be arranged. The idea of 2.67 different routes is meaningless. What is a fraction of a route?
March 6, 2016

algebra
-17 + (-16)
March 6, 2016

Calculus, Really need help!
f(g) = √g = √(x^2+7) so, d/dx f(g(x)) = x/√(x^2+7) Or, using the chain rule, d/dx f(g) = df/dg * dg/dx = 1/2√g * 2x = x/√g = x/√(x^2+7)
March 6, 2016

Math: Algebra
original fraction: x/y new fraction: .9x / .5y = 1.8 x/y so, it increased by 80%
March 6, 2016

Algebra
after x days, we have lbs: 120 + 6x price: .80-.02x No idea about profit, since cost was not mentioned, but the income is certainly (120+6x)(.80-.02x) = -0.12x^2 + 2.4x + 96 That is just a parabola with vertex at (10,108)
March 6, 2016

physics
R = E/I = 6/8.6 = 0.70 ohms Now use the definition of resistivity to work it out.
March 6, 2016

trig exact vales
draw the triangle! adjacent/opposite = 4/1, so the hypotenuse is √17 now you can find sin, cos, and 2*sin*cos
March 6, 2016

math
since r=3 and s=5, h=4 v = 1/3 pi r^2 h = 1/3 pi * 9 * 4 = 12pi
March 6, 2016

math
one expression cannot describe all the measures of the triangle. However, x-7 + x + 3x+2 = 180
March 6, 2016

Algebra
ab = 64 a+b = 34
March 6, 2016

systems of linear equation
x = y-19 5(x+y) = 685
March 6, 2016

math
the discriminant must be non-negative. So, x^2-2kx+k^2 = 3+x x^2 - (2k+1)x + (k^2-3) = 0 the discriminant is (2k+1)^2 - 4(1)(k^2-3) = 4k^2+4k+1 - 4k^2+12 = 4k-11 so, 4k-11 >= 0 k >= 11/4 for k= 11/4, we have x^2 - 11/2 x + 121/16 = 3 + x x^2 - 13/2 x + 169/16 = 0 (x - 13...
March 6, 2016

you need the discriminant to be zero for equal real roots. So, 4-8p = 0 a quadratic with real coefficients cannot have two equal complex roots.
March 6, 2016

Maths
Draw the diagram. If the height is h, note that h = 70tan63° - 70tan60°
March 6, 2016

math
I'd say one.
March 6, 2016

Let the vertex be (0,0) Then we have y = ax^2 y(84) = 24 so, find a.
March 6, 2016

math
3^-x = 4t 3^x = 1/(4t) Do you mean 4^(x-1) + 4^(x+1) -------------------- 17 * 12^x or some other grouping? All those words just cloud the issue. There's really no good way to mix the 3's and 4's as bases. I suspect a typo. Did you maybe mean 3^-x = 4^t ??
March 6, 2016

Pre-Calc
the fractions will be A/(x+8) + B/(x+5) A(x+5) + B(x+8) = 7 (A+B)x + (5A+8B) = 0x + 7 A+B = 0 5A+8B = 7 3B = 7 B = 7/3 A = -7/3 7/(x^2+13x+40) = (7/3)/(x+5) - (7/3)/(x+8))
March 6, 2016

Calc Derivatives
it's because y"=0 when x = -9/4 but y is undefined for x<0. check for +/- sign mistake
March 5, 2016

Math
well, 5*5 = 25
March 5, 2016

math
Add up the amounts of cocoa: (1/8)(300) + (1/16)x = (1/10)(300+x) x = 200 If the fractions seem confusing, note that the 1:7 ratio means there are 8 parts of ingredient, only 1 of which is cocoa.
March 5, 2016

science-math
As usual, this is not hard if you understand what is going on. The amount of alcohol is unchanged after adding water. So, if there are x liters of 18% solution, you have .18x = .12*10 x = 20/3 L of 18% alcohol, and 10/3 L of water Or, you can consider that you are reducing the...
March 5, 2016

Functions, graphs
for x > -1, both numerator and denominator are positive. ∫[0,√3] (x+1)/(1+x^2) dx = π/3 + ln(2) Good luck on this one if you haven't yet studied trig substitutions.
March 5, 2016

Maxima, Stationary Points
I'm surprised that Maxima gagged on a simple polynomial. I've used it very little, but I know it's been around for over forty years, and was way powerful back in the 70's. Maybe that pesky 88x term messes things up; otherwise it'd just be a cubic in x^2.
March 5, 2016

Math
the set where most of the values are distant from 22.6
March 5, 2016

Algebra
However, if we consider the sequence as 1/2 * 1/1, 1/2 * 1/3, 1/2 * 1/5 Tn = (1/2) * 1/(2n-1) T12 = (1/2)(1/23) = 1/46 There are other rules which would produce the given terms, but this is the easiest for me to see.
March 5, 2016

parabola
If we put the vertex at y=32.5, so that the arch lies on the x-axis, y = 32.5 - ax^2 so solve for x so that y(12.1) = 0 Now you can just shift that down so the vertex is at (0,0).
March 5, 2016

algebra or algebra1
just multiply the powers by 3, since (x^a)^b = x^(ab)
March 5, 2016

calculus
so, where do you get stuck? Surely your text discusses this topic.
March 5, 2016

Calculus
the area is just ∫[0,2π] y(t) dx/dt dt = ∫[0,2π] (Bsint+k)(-Asint) dt = ∫[0,2π] -ABsin^2(t) - kAsin(t) dt = (-AB/2)(t-sint cost) + kAcost [0,2π] = (AB/2 (2π) + kA) - (kA) = πAB This is true, of course, since the curves describe ...
March 4, 2016

Math
see Fidelis's post
March 4, 2016

Math
54/10000 = 27/5000
March 4, 2016

Algebra
probably because the 1/3 of 1/3 is a typo. If you discount the stuttering, you have x - (1/3)(72-x) ≥ 60 Solve that and see what you get. If it works, next time check the solution and see whether it interprets your problem correctly, instead of just blindly accepting the...
March 4, 2016

Math Algebra Intermediate
I guess you could go on and make it ay(1-ay)(1+(ay)+(ay)^2+(ay)^3+(ay)^4) Not sure that's much better ...
March 4, 2016

Discrete Math (function and similar triangles)
sounds reasonable. Or, you can pair up values in (0,1) with values of f(x) = 10/x
March 4, 2016

Calculus
well, what is the rate of growth from x=a to x=b ? 2000b^4 / 2000a^4 = (b/a)^4 same for 200x^4
March 4, 2016

math
(1+cosx)/sinx + sinx/(1+cosx) = (1+cosx)^2 + sin^2x ------------------------ sinx(1+cosx) 1+2cosx+cos^2x+sin^2x ------------------------- sinx(1+cosx) = (2+2cosx)/(sinx(1+cosx)) = 2/sinx so, does 2/sinx = 1 have any solutions?
March 4, 2016

Math
right. So what you want is 1 minus that.
March 4, 2016

Math
well, what is the probability that no white ball is drawn?
March 4, 2016

math and algebra
I assume you know how to draw the number line. You show no numbers, but surely you can place them in the appropriate places...
March 4, 2016

Damon is, as usual right in these matters. I forgot to factor in the added mass.
March 4, 2016

physics
Since F=ma, the heavier cart has 1/3 the acceleration, so its velocity will be 1/3 that of the smaller cart. KE = 1/2 mv^2, so if you have 1/3 v instead of v, the KE will be 1/9 as big. So, K=20J for the larger cart.
March 4, 2016

math
so, did you actually use the value(s) and see whether they worked? Being able to check your answer is just as important as getting it in the first place! if the perimeters are equal, then 4(3x-2) = 2(x-2 + 2x+5) 4(3x-2) = 2(3x+3) 2(3x-2) = 3x+3 6x-4 = 3x+3 3x = 7 x = 7/3
March 4, 2016

math help pls pls pls
the final price is tax added to the discount price, so c(p(t)) = 1.06*0.85t = 0.918t Read the text carefully. They actually gave the formula to you : c(p)
March 4, 2016

math
Note that √(1-cos^2x) = sinx tanx = sinx/cosx Now it should be clear
March 4, 2016

Trig
2cos4x + √3 = 0 cos4x = -√3/2 4x = 5π/6 or 7π/6 x = 5π/24 or 7π/24 period is 2π/4 = π/2, so all solutions are 5π/24 + kπ/2 or 7π/24 + kπ/2 So, for all solutions in [0,2π) we have 5π/24, 17π/24, 29&#...
March 4, 2016

Math
Sn: 2 is a factor of n2 + 7n n is either even or odd. If n is even, n=2k n^2 + 7n = (2k)^2 + 7(2k) = 4k^2 + 14k = 2(2k^2 + 7k) 2 is a factor If n is odd, n=2k+1 n^2 + 7n = (2k+1)^2 + 7(2k+1) = 4k^2+4k+1 + 14k+7 = 4k^2+18k+8 = 2(2k^2+9k+4) 2 is a factor So, Sn is true
March 4, 2016

Geometry ??
E = 2(1/4) - 3(1/4) = -1/4
March 4, 2016

Math
rounding to nearest 1/100th % is 181/13.58 = 13.3284 = 1332.84% rounding to nearest 1/100th is 13.33 = 1333%
March 4, 2016

Math
To show that it is true for any n, use your knowledge of some sums (k=1 to n): sum(1) = n sum(k) = n(n+1)/2 Now just simplify 3*sum(k) - sum(1)
March 4, 2016

Math
#1 you did the area:volume ratio. It asked for volume:area. So, flip all your fractions. #2 why did you choose cylinder? What makes it "best"? #3 justify using your criteria. You might want to consider rapid cooling or prolonged chilling effect.
March 4, 2016

snowmobiles/science
no idea -- what do you already have?
March 4, 2016

math
you know that summing from 1 to n: sum(1) = n sum(n) = n(n+1)/2 so, sum(3n-1) = 3sum(n)-sim(1) = 3n(n+1)/2 - n = (3n^2+3n-2n)/2 = (3n^2+n)/2 = n(3n+1)/2
March 4, 2016

Math
You want to minimize C=86A+130B subject to A+B >= 100 45A + 35B >= 3850 Now use your LP tools
March 4, 2016

trig
draw a diagram. Review your basic trig functions. You will see that the height h is h/1860 = tan29°10’ now just grind it out.
March 4, 2016

maths
each minute the tank gains 1/15 loses 1/20 So, the net gain in volume is 1/15 - 1/20 = 1/60 So, it will take 60 minutes to fill up.
March 4, 2016

math
There are 7 people in all. Review your permutations to find P(7) Actually, the question is poorly worded. If there are assigned seats, there is only one you can all sit in your assigned seats!
March 4, 2016

Math Trigonometry
If we label the points order A,B,C, then we want the bearing of A from C. Using the law of cosines, you could find the angles, and then compute the bearing. Or, you can find that the intersection of x^2+y^2 = 19^2 x^2 + (y+16)^2 = 32^2 is (14.1,12.7) and now you can figure the...
March 4, 2016

Math
as you know, the vertex of a parabola is at t = -b/2a = -25/-32 So, just evaluate H(25/32)
March 4, 2016

Algebra
the angles must add to 180, so the missing angle is 55°, since 50+75+55 = 180
March 4, 2016

Differential equation Hmmm
that siny in both factors is bad news. I'd expect one of them to have cosy. Sure there's no typo? Also the lone x is not good. There ought to be an x^2 in the dy factor. Also, the form is usually M dx + N dy = 0 not M dx - N dy = 0 This whole one is weird.
March 4, 2016

Math
1 - 4/5 = 1/5 1/2 of 1/5 = 1/10 1 - 4/5 - 1/10 = ?
March 4, 2016

one way is 312132
March 4, 2016

Trig application
man, you have the equation. As you know the parabola h = at^2 + bt + c has its vertex at t = -b/2a So, just plug and chug. As for the range, find t when h=0 and then recall that the (constant) horizontal velocity is vo cosθ
March 4, 2016

Calc
usually the integral of 1/x is expressed as ln |x| So, ln(x-1), ln(1-x) makes no difference. Actually, of course, I think it makes quite a difference, but wolfram pops up with this quite often.
March 4, 2016

Calculus
If f(x) = ∫[0,x] √(4-t^2) dt f(x) = 1/2 √(4-t^2) + 2 arcsin(x/2) clearly, the domain is [-2,2] f(-2) = -π f(2) = π Those choices don't seem to work. Better check my math.
March 4, 2016

math
see Damon's solution in the related questions below.
March 4, 2016

math
800 * 6/10 ------------------       5
March 4, 2016

Science
P = EI = 120 * 0.5 = 60W 1W = 1J/s, so 60W = 60J/s * 900s = 54000J
March 4, 2016

Geometry
Draw a diagram. Clearly, the cow can graze 3/4 of a circle of radius 20m So, the area is 3/4 * πr^2 = 300π m^2
March 4, 2016

Algebra
see your previous posts of the same problem. note that y = -3(t^2-6t) + 53 now complete the square to get the vertex form
March 4, 2016

precalc
recall that log_a(b) = 1/log_b(a) so, your expression is ln(e^5) + ln(e) + (1/2)(1/8)) = 5+1+1/16 = 97/16
March 3, 2016

Precalc
e^(ln7 + 2ln4) = e^(ln7+ln16) = e^ln112 = 112 √27/27 = 1/√27 = 27^(-1/2) = (9^3)^(-1/2) = 9^(-3/2) log_9(9^-3/2) = -3/2 remember that log_b(b^n) = n b^log_b(n) = n that is the definition of the log.
March 3, 2016

Trig application
the angular speed is clearly 2πrad/110s = π/55 rad/s * 60s/min = 60π/55 = 12π/11 rad/min the linear speed is thus 2π(65/2)m/rev * 1rev/110s = 130π/220 = 13π/22 m/s I assume you can tackle converting that to mi/hr
March 3, 2016

math
well, the factors of 24 are 1,24 2,12 3,8 4,6 so pick something and figure the perimeters.
March 3, 2016

Calculus
y = -0.2/√(6+5x) y' = 0.5/√(6+5x) y'(2.5) = 0.5/√18.5 ≈ 0.116 So, now you have a point and a slope. The line is thus y+0.0499 = 0.116(x-2.5) sub in x=0 to find the y-intercept.
March 3, 2016

calculus 1
maxima and minima are where f' = 0 f = 3x^3 - 9x + 5 f' = 27x^2-9 = 9(3x^2-1) so, when 3x^2-1 = 0, f has a max or a min.
March 3, 2016

Discrete math
(a) true: a=0 or b=0 ∃ a,b ∊ R : (a+b)^2 = a^2+b^2 (b) true (c) true (d) false
March 3, 2016

Math \ algebra
the numbers are clearly declining. I can't see your graphs, but the curve you want is probably like a slide, sloping down, but concave up.
March 3, 2016

Discrete math
well, you have p: ABCD is a square q: its diagonals are perpendicular and have the same length Now just substitute the words for your logic symbols
March 3, 2016

Algebra II
the wind speed is clearly not 50, since 2400/500 + 2400/400 = 10.8, not 11 You have solved for a round trip. The problem didn't say that, but taking 11 hours for one-way means a speed of about 218 mph, too slow. Something is screwy with this problem. Solving your equation ...
March 3, 2016

Algebra II
looks good, except that online, due to formatting handicaps, you should use parentheses to remove ambiguity: 11 = 2400/(450+x) + 2400/(450-x)
March 3, 2016

Physics
the remaining fraction after t days is f(t) = (1/2)^(t/2.6) Your equation is exactly right. After 1 day, f(1) = (1/2)^(1/2.6) = 0.766 = 76.6% After 1 week, f(7) = (1/2)^(7/2.6) = 0.155 = 15.5%
March 3, 2016

algebra word problem
If the side of length x is parallel to the wall, then x + 2y = 16 xy = 30 (16-2y)y = 30 2y^2 - 16y + 30 = 0 y^2-8y+15 = 0 (y-3)(y-5) = 0 y = 3 or 5 so, x = 10 or 6 The garden is 10x3 or 6x5
March 3, 2016

math
W = 55 + 1.5(h-60) for h >= 60in
March 3, 2016

ratio
There are 5+3=8 parts. 6400/8 = 800 So, the division is 800*5 and 800*3
March 3, 2016

math
If the number of units of iron, lead, and kryptonite are x,y,z respectively, then we have to maximize p = 55x+70y+60z subject to 3x+3y+z <= 22 4x+3y+z <= 22 x+y+4z <= 23 Now use your favorite linear programming method
March 3, 2016

Mathematics
Draw a diagram. It is clear that angle T is 120 degrees. So, using the law of sines, CP/sin120 = 6/sin40
March 3, 2016

AP pre Cal
convert to x-y components so they can be added: 45@20° = <42.29,15.39> 90@115° = <-38.04,81.57> add them up to get <4.25,96.96> = 97.05 @ 87.49°
March 3, 2016