Thursday

April 28, 2016
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*

**quadratic equations**

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*

**Pre calc quadratic stuff**

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*

**physics - my bad**

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*

**math (5th grade)**

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*