Thursday
August 28, 2014

# Posts by STEVE

Total # Posts: 24,466

calculus 2
dy/dx = y'/x' = (-3sint)/(2cost) = -3/2 tan t d^2y/dx^2 = (x'y"-x"y')/x'^3 = ((2cost)(-3cost) - (-2sint)(-3sint))/(8cos^3 t) = -3/4 sec^3 t Check: y = 3/2 √(4-x^2) y' = -3/2 x/√(4-x^2) y" = -6/(4-x^2)3/2 I'll leave it to ...
July 26, 2014

calculus 2
I think she means y = ∛x
July 26, 2014

Math
Correct. So, 5/11 - 7/11 = -2/11
July 26, 2014

Math
you're working with 11ths. So, what's 5-7?
July 26, 2014

math
s = ∫[0,6π] √((dx/dt)^2 + (dy/dt)^2) dt = ∫[0,6π] √((1-2cost)^2 + (2sint)^2) dt = ∫[0,6π] √(1-4cost+4cos^2t + 4sin^2t) dt = ∫[0,6π] √(5-4cost) dt
July 26, 2014

trigonometry
15rev/12sec = 5/4 rev/sec = 5π/2 rad/s That's the speed of the smaller pulley Assuming they are both attached to the same belt, the larger pulley's rotational speed is 6/20 the speed of the smaller one.
July 26, 2014

Math - trig
no, no. It's just a quadratic equation, in cosx, rather than just x using the quadratic formula, we have cosx = (1±√3)/4 or, -0.183, 0.683 So, just find the angles with those values as cosine.
July 26, 2014

math
the price, for n >= 150, is p(n) = 200-n Revenue is price*quantity, so r(n) = n(200-n) = 200n-n^2 That's just a parabola. The vertex is the point of maximum revenue. That's just algebra I, so no sweat. . . . right?
July 26, 2014

math
Looks like (a) to me. Just use the quadratic formula.
July 26, 2014

trig
draw a right triangle with the tops of the poles as the ends of the hypotenuse, and the bottom side perpendicular to the poles. You have a 5-12-13 triangle. It is useful to learn some of the basic triangles with integer sides -- they pop up frequently. 3-4-5 5-12-13 8-15-17 7-...
July 26, 2014

College Algebra
All you need is f(-1)*g(-1) = 4 f(x) = 2 g(x) = 2 will work, but they are rather trivial. I'm sure you can come up with two functions that work.
July 25, 2014

Algebra
Clearly E cannot exceed 5, since even with borrowing, A cannot exceed 10. That would mean something like FL50 -B55 ------- MO95
July 25, 2014

Algebra
1/3 of the mice are female, so 1/6 of the mice are white female 1/6 of the mice are brown female 3/5 are brown, so 3/5-1/6 = 13/30 are white male 1-(1/3+13/30) = 7/30 are brown male So, brownmale/whitemale = 7/13
July 25, 2014

MATH WORD PROBLEMS
to be centered, the extra space must be divided into two equal parts.
July 25, 2014

College Algebra
q(x) = 73(x+1)^2+2 h(x) = x^2 g(x) = (x-1)(x-2)(x-3) Since x^0=1 for any x, we have s(x) = 2*a^(kx) for some a and k. 2*1/2 = 1, so s(x) = 2*4^(-x/2) r(x) will involve something/(x-3) x-2 is zero at x=2, so r(x) = (x-2)/(x-3) will work
July 25, 2014

College Algebra
reflected: -|x| stretch vertically: -4|x| shifted: -4|x+3| see http://www.wolframalpha.com/input/?i=plot+y%3D|x|%2C+y%3D-4|x%2B3| You want t where 1(1+.075/4)^(4t) = 7200 The rule of 72 indicates it should double about every 10 years. Since 7200 is about 2^13, I expect it will...
July 25, 2014

Sinusoidal! - Missing Data!!
Clearly, the radius of the wheel is 9.98, or, due to the careful engineering of the triangle, call it 10 meters. So, the height, starting at the bottom, will be h = 11-10cos(kt) So, we just need to find k. The vertex angle of the triangle satisfies sin θ/2 = 9.23/14.35 so...
July 25, 2014

math
one hitch is that there are only 3 ballads. Anyway, peter, fix that and redo Reiny's calculations to find that x=5. As for my hint, since there must be 12 songs in all, the missing x pieces must total 5.
July 24, 2014

math
since there are 3 ballads, and 1/4 of the total are ballads, there must be 12 songs in all. That help?
July 24, 2014

math
Since the sides are equal, and the hexagon has twice as many sides as the triangle, ...
July 24, 2014

Math 221
fix the typo. Surely you can find the slope of the line. The parallel line has the same slope -- call it m. Then, recall the point-slope form of a line with slope m that passes through the point (h,k): y-k = m(x-h)
July 24, 2014

College Algebra
it doesn't matter what value g(2) is, because f(x)=7 whatever x is. On a bit more realistic note, you can dream up lots of scenarios. Looking at exponential stuff, for instance, suppose f(0) = 7. So, we could say f(x) = 2x^2+9x+7 Then, all we need is some g(x) such that g(...
July 24, 2014

College Algebra
f(x) = 7 g(x) = whatever you want. Maybe a bit more specific constraints?
July 24, 2014

bean
875 = 25 * 35 So, you need to draw a rectangle which contains 35 squares. That should help.
July 24, 2014

calculus
for intercepts, set x=0 and evaluate y for the y-intercept Set y=0 and solve for x to get the x-intercepts. Note that g(x) = x(x-3)^2 p(x) = x^3(x-4) Max/min occurs when 1st derivative = 0. No problems there, right? But is it a max or a min? If the curve is concave up, it'...
July 24, 2014

Algebra2
since T4 = T2 * r^2, 6r^2 = 54 So r=3 (or, r = -3)
July 24, 2014

math
if she had s savings, then after spending 1/3 of it, she had 2/3 s left. So, 2/3 s = 780
July 24, 2014

math
as with all fractions, clear things out by multiplying by the denominator So, multiply by a and you have a^2 = 1 done
July 24, 2014

math
Is the smaller circle inside the larger one? If so, do they share a center? Do they touch? If the two centers are more than 7 apart, then the distance between them can be anything.
July 24, 2014

math
Huh. I thought that f was the total ounces, f>b. So, the cost is cb+d(f-b)
July 24, 2014

math
looks like 9 gallons to me.
July 24, 2014

physics
just add the two momenta. The total will remain unchanged. 1.5*10^3 * 20 - 9.5*10^2 * 26 = -5.3*10^3 kg-m/s
July 24, 2014

physics
since the speed decreases at 10 m/s every second, v = 30 - 10t after t seconds. Looks like it takes 3 seconds to stop. The distance traveled in t seconds is thus s = 30t - 5t^2 You can use that to figure out (b) and (c)
July 24, 2014

math
all distances are multiplied by a factor of 3.
July 24, 2014

Maths.literacy
first step: discover the distance to be covered. Next, divide that by 185 to get the number of hours required.
July 24, 2014

Maths
If there are n tests already taken, we need 84n + 100 = 86(n+1) 84n + 100 = 86n + 86 2n = 14 n = 7
July 23, 2014

math
we have s/b = 3/5 s/a = 9/17 total unshaded area is a+b-s, and we want s/(a+b-s) we know that b = 5/3 s a = 17/9 s so, we have s/(a+b-s) = s/(5/3 s + 17/9 s - s) = s/(23/9 s) = 9/23
July 23, 2014

Maths
what do we know? (d+k+l)/3 = 42 d = 6+(k+l)/2 k = l+6 So, start substituting: d+l+6+l = 126 2d = 12+l+6+l or, d+2l = 120 2d-2l = 18 Add these to get 3d = 138 d = 46
July 23, 2014

M
if there are b bigs and s smalls, we have b+s = 16 1200b + 1500s = 21000 since s = 16-b, we have 1200b + 1500(16-b) = 21000 or, 12b + 15(16-b) = 210 12b + 240-15b = 210 3b = 30 b = 10
July 23, 2014

Math
357mi/21gal = 357/21 m i/gal = 17 mi/gal dr = 1/3 p lr = 2k k = 3/2 p - dr-lr-k = 3/2 p - p/3 - 2(3/2) - 3/2 = 3/2 p = 9
July 23, 2014

math
m * 1/2 * 1/3 = 1/6 m Use one envelope and a stamp to advertise for a new office manager!
July 23, 2014

Math
surely you can solve at least some of these exercises. At least the amplitude? Review the material about sinusoidal functions, and I think some of it will become clear. Recall that A sin(Bx) has amplitude A and period 2pi/B. Also, look at the graph of cos(x). It has a max at t...
July 23, 2014

Alegbra
surely you know that division by zero is undefined. For if x = 3/0, that means that x*0 = 3 There is no number you can multiply by zero and get anything other than zero!
July 23, 2014

calculus
assuming six digits, a,b,c,d,e,f, we have a = √b b = a^2 (well, duh) c+f = 14 c+d+e+f = d^2 a+b+c+d+e+f = 37 ae = d+e+f b+c+d = af Play around with that for a while.
July 23, 2014

trigonometry
one complete rotation moves the container a distance equal to the circumference of the winch spool. one complete rotation is 2pi radians. 5pi/6 radians is thus (5pi/6)/(2pi) = 5/12 of a complete rotation. the circumference is 2pi*6 = 12pi inches, so the container is lifted (5/...
July 23, 2014

If you mean synthetic division, the web site below shows all the details involved. http://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php
July 23, 2014

maths
the job takes 3*8*10=240 typist-hours. 2 typists working x hours per day perform 2x typist-hours per day. So, 2x*12 = 240 x = 10 hours per day
July 23, 2014

Calculus
I find it a bit easier not to expand the derivative f'(x) = 2x(4x-15)/(8x-15)^2 Clearly f'=0 when x is 0 or 15/4 So, f'(15/4)=0, and 3 < 15/4 < 5 f'(0)=0 also, but 0 is not in [3,5] The graph at http://www.wolframalpha.com/input/?i=x^2%2F%288x-15%29+for+3...
July 22, 2014

calculus
Sounds like they wanted f'(c) rather than c.
July 22, 2014

math
add 1 for each successive integer. So, what is y-3 + 1+1+1+1 ?
July 22, 2014

Calculus
Think of the graph for y = x^3 It has no max/min, but just an inflection point at x=0. You function is just the same, only stretched by 2, shifted left by 5, and shifted up by 7.
July 22, 2014

math - bogus
Two problems: (1) no value given for x (2) I suspect a typo, since there is no "x" term, and two constants.
July 22, 2014

Geometry
area of 3x3x3 cube is 6*9=54 area of 2x2x2 cube is 6*4=24 If not joined, total area is 78 The maximum concealed surface area is an entire face of the 2-cube, on both solids: 2*4 = 8 So, the minimum exposed area would be 78-8 = 70
July 22, 2014

algebra
3/5x is not defined for x=0 1 - 3/5 = 2/5 1 - 3/10 = 7/10 If you meant y = 1 - (3/5) x then just plug in the values: 1 - (3/5)(0) = 1 1 - (3/5)(1) = 2/5 1 - (3/5)(2) = -1/5
July 22, 2014

Math
I'd have to say 90 degrees. If the struck ball has some backward velocity, the striking ball would have to increase its forward speed to compensate.
July 22, 2014

mathematics
If there are x bundles, x/3 are morning 2 = afternoon That leaves 2x/3 - 2, of which x/3 - 1 are regional 1 is local 1 is out of state Add them up to get x/3 + 2 + x/3 - 1 + 1 + 1 = x 2x/3 +3 = x 3 = x/3 x = 9
July 22, 2014

Math - thanks Reiny
I guess I didn't read the question too carefully, and failed to answer it fully.
July 22, 2014

Math
look at the differences between successive terms: -1 -3 -5 -7 so, the next will be 15-9=6
July 22, 2014

Math
There are several standard right triangles with integer sides. It will help a lot if you just learn them -- they turn up often in problems, and it's nice not to have to do the calculations every time. 3-4-5 5-12-13 8-15-17 7-24-25 and multiples of those values
July 22, 2014

Alegbra
2•5^2•7
July 22, 2014

Oops mixed up price and quantity p(x) = x(500-x)-35(500-x) = (x-35)(500-x) assuming no extra dolls are made...
July 22, 2014

profit = revenue - cost revenue = price * quantity. So, p(x) = x(500-x)-35x Now just plug in your data
July 22, 2014

SECONDARY ALGEBRA
nice try, but you're mixing things up. Why do you say 120 m^3? m^3 is volume, not are or length! And why multiply the perimeter by the length, anyway? Just take a step back and work things out. The area is length * width The 120m of fencing reaches around the field -- that...
July 22, 2014

Math
Just translate the words to algebra. Then solve. For example, #3: 3/8 of 768 = 288 5/6 are below senior, so 1/6 are seniors. 1/6 of 288 = 48 Where do you get stuck on the others?
July 21, 2014

Calc
If you mean f'(t) = -8 * 0.8^t, then f(t) = -8/ln(0.8) * 0.8^t + C since f(0) = 90, 90 = -8/ln(0.8) + C C = 90 + 8/ln(0.8) So, f(t) = -8/ln(0.8) * 0.8^t + 90 + 8/ln(0,8) = 90 + 8/ln(0.8) (1-0.8^t) = 90 - 35.85 (1-0.8^t) So, plug in t=10
July 21, 2014

ENGLISH
If you are looking for a complete sentence, What can he do? is the only option. The other phrases are all acceptable in various contexts.
July 21, 2014

Math
17(4+2*17) = ?
July 21, 2014

math
You can see some analysis here: http://www.wolframalpha.com/input/?i=sum+3%28-1%29^n%28n%29%28x^n%29 It will probably give you a start on proving the answer.
July 21, 2014

algebra
if the length is x, 2(3/4 x + x) = 100
July 20, 2014

Math
28' = 853.44 cm 18' = 548.64 cm Easy way, assuming partial pieces are tucked in as needed: (853*548)/(60*40) = 195 Now, you can do several kinds of approximation, requiring whole pieces, etc. One easy way is to round up the lawn area to multiples of 40 and 60: 853/60...
July 20, 2014

physics
just figure how much potential energy (mg ∆h) has been lost. That has been converted to kinetic energy.
July 20, 2014

physics
consider the takeoff to be at (0,0). The height of the skier is thus y = vt - 4.9t^2 maximum height is thus reached at t = v/9.8 y(v/9.8) = v*v/9.8 - 4.9(v/9.8)^2 = v^2/9.8 - v^2/(4*4.9) = v^2/9.8 (1 - 1/2) = v^2/19.6 Since the max height is directly proportional to the square...
July 20, 2014

Math
well, what is 2/3 of 18? If that stumps you, what is 1/3 of 18? Just double that.
July 20, 2014

chemistry
since density = mass/volume, we have 1112.50g/(5.00cm)^3 = 1112.50/125.00 g/cm^3 # atoms is g * moles/g * 6.02*10^23 atoms/mole So, just look up the atomic weight of copper and plug it in.
July 20, 2014

Math
enter your data here http://www.gregthatcher.com/Mathematics/GaussJordan.aspx It will show all the details of how the elimination works.
July 20, 2014

algebra 2
y=2 should immediately be discarded, since fractions with y-2 in the denominator are not defined. The steps should be 3y/y(y-2) - (y-2)/y(y-2) = 4/y(y-2) 3y-y+2 = 4 2y = 2 y = 1
July 20, 2014

algebra
w=2 satisfies the original equation, so I guess your solution is correct. However, the steps should be 2(w-1)/2(w-1) + 4w/w(w-1) = 10/w(w-1) 2w-2 + 4w = 10 6w = 12 w = 2
July 20, 2014

algebra
you want (a+b+c)/3 (a+b)/2 = 45 (b+c)/2 = 43 (a+c)/2 = 50 Add them up and you have (a+b+b+c+a+c)/2 = 45+43+50 (2a+2b+2c)/2 = 138 (a+b+c) = 138 (a+b+c)/3 = 46
July 20, 2014

math
16 degrees warmer than it is now.
July 20, 2014

Math
1/5 - 1/15 = 1/x 2/15 = 1/x x = 15/2
July 20, 2014

Math
since speed = distance/time, 120/c = 200/j j = c+35 so, 120/c = 200/(c+35) 120(c+35) = 200c 120c + 120*35 = 200c 80c = 120*35 c = 3/2 * 35 = 52.5
July 20, 2014

Math
how much of the job does each pump do in an hour? 1/12 + 1/16 = 1/x together they take x hours.
July 20, 2014

Algebra
how many std above the mean is Z=2? That's how many oz. more than 16 is the box.
July 19, 2014

math
just plug those numbers into your amortization formula.
July 19, 2014

math
well, what is 30^2?
July 19, 2014

Maths
As usual, draw a diagram. Assuming the plank is just long enough to join the tops of the ladders, there is a 1/2 m overlap on each end, above the sloping side. So, the height is √(2.5^2 - .5^2)
July 19, 2014

algebra
If there were x adult tickets, then there were 340-x students. So, 5.00x + 3.50(340-x) = 1535.00 Now just solve for x...
July 18, 2014

Calculus
x = t^2-t dx/dt = 2t-1 y = t^3-3t dy/dt = 3t^2-3 dy/dx = (dy/dt)/(dx/dt) = (3t^2-3)/(2t-1) If the normal to the curve is vertical, the tangent is horizontal. So, dy/dx = 0. That happens when t=±1 So, the normal is vertical at (2,2) and (0,-2) See the graph at http://www...
July 18, 2014

Math Question
just convert everything to the same unit, say cm. 1 inch = 2.54 cm, so 176 cm = 176 cm 5'4" = 64" = 162.56 cm 1.8 yd = 64.8" = 164.59 cm and so on For the truck, just look up the conversion for feet-to-meters. 8'6" = 8.5 ft...
July 18, 2014

math
the hour hand moves 360° in 12 hours. That is 30° per hour. So, in 1/2 hour, it moves 15°
July 18, 2014

math
Write down the facts: 2h+3s = 4.21 3h+2s = 5.24 Now you can solve for h and s, and calculate h+s. Nope, too much work. Instead, just add the two equations, and you see that 5h+5s = 9.45 So, divide by 5 to get h+s = 1.89
July 18, 2014

maths lit, geography, life science, history, life orientation, english, tswana
quite a variety of things. The question is, what to you enjoy doing? Train yourself in that, now that you have some basic knowledge and study skills.
July 18, 2014

math
If Jones borrowed \$j at a rate r, he paid 75.00 in interest. So, we see that jr = 75 (3j)*r*2 = 3*2*jr = 6*75 = 300
July 18, 2014

math
Read up on these work problems. If Jack can do the job in 6 hours, he does 1/6 of the job in an hour. If together they can do the job in 2 hours, they can do 1/2 the job in one hour. So, you need to add up how much each guy can do in one hour, and the sum is what fraction of ...
July 18, 2014

math
1/2 = 1/6 + 1/x Just by inspection, we can see that x=3, so it takes Jerry 3 hours to do the job.
July 18, 2014

MATH
8+4+5 = 17 So, we have 17x = 48 x = 48/17 You can use Heron's formula to find the area of a triangle with sides 8,4,5. Now just multiply that area by (48/17)^2 An odd set of values, I must say.
July 18, 2014

maths
x^3+2x^2-15x = x(x+5)(x-3) 2x^2-18 = 2(x-3)(x+3) Now just cancel the (x-3) top and bottom
July 18, 2014

Maths (factor theorem)
27x^3-8y^3 is the difference of two cubes: (3x)^3 - (2y)^3 So, it factors as (3x-2y)(9x^2+6xy+4y^2)
July 18, 2014

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