Monday

September 1, 2014

September 1, 2014

Total # Posts: 24,522

**math(precalculus)**

You don't need any c. It can be absorbed into a and b. Actually, you have solved the problem. Pick any value for c, and plug it in. As long as a=c and b=-4c, R(x) will work. So, make things easy. Let c=1. As I worked it out, R(x) = ???/(x+1)(x-2) Since y=0 is the asymptote...
*July 31, 2014*

**Math**

heads: r+c = 35 feet: 4r+2c = 94 Now just solve for r and c, in any of several ways.
*July 31, 2014*

**Science/Physics**

weight (force) = mg Look up g if you don't know it. Now, divide that by the relative gravity of the moon. For example, if the moon has 1/2 the gravity of earth, you will need double the mass for the same weight.
*July 31, 2014*

**Physics**

The resultant velocity is v = (106,106) + (0,20) = (106,126) |v| = 164.7 The angle x obeys tan(x) = 126/106 The time taken is 500,000/164.7 seconds
*July 31, 2014*

**Math**

surely you can see that A=3 B=pi/20 C=0 D=7 I mean, just read it off. Now employ your skills to convert your cos(x) to sin(pi/2-x) A and D stay the same.
*July 30, 2014*

**Math**

since y is a max when t=0, we want a cosine function, since cos(0) = 1. y = 7+3cos(pi/20 t) because the period is 40 seconds, and the level varies between 7+3 and 7-3 feet.. C=0 because cosine is a max at t=0, so there is no offset. Naturally, you can now write the sine ...
*July 30, 2014*

**Alegbra1**

depends. How much of all that is under the radical sign? Once you specify that, just remember that the domain of √u is u>=0.
*July 30, 2014*

**Math**

20% + 15% = 35% given away. That leaves 65%, so .65x = 520 Now just solve for x.
*July 30, 2014*

**math - huh?**

I see several problems. who the heck is Mary? Is Mary really male?
*July 30, 2014*

**math**

f+l = 80 2/3 f = l-10 so, 2/3(80-l) = l - 10 160-2l = 3l-30 190 = 5l l = 38 check: initially there were 38 local and 42 foreign after removing 10 local and 14 foreign, there were 28 of each.
*July 30, 2014*

**PreCalculus**

just make the usual substitution. y = rsinθ x = rcosθ so, that means r^2sin^2θ/25 - r^2cos^2θ/9 = 1 r^2(9sin^2θ-25cos^2θ) = 225 r^2 = 225/(9sin^2θ-25cos^2θ) see the expected vertical hyperbola at http://www.wolframalpha.com/input/?i=plot...
*July 30, 2014*

**statistics**

Since there are 10 choices, I'd just use the nth digit of 3 numbers chosen from the random number table. which n depends on how many digits in each entry; just make sure all use the same n. Or maybe add up the digits and take the last digit of the sum.
*July 30, 2014*

**Maths**

1+2+4=7, so if we divide the sum into 7 equal parts of size x, 7x = 126 x = 18 So, the shares are 18,36,72
*July 30, 2014*

**Math**

find the distance between the two points, as usual. Now, since the area of a square is a = d^2/2, just figure that.
*July 30, 2014*

**math**

clearly, if the angle is x, tan(x) = 7.15/10.1
*July 30, 2014*

**Math - grrr.**

all that anti-derivative stuff is too much for me that early. Thanks for the fix. I'm sure Tim caught the error and fixed it though. . . . Right, buddy?
*July 29, 2014*

**Math**

since y" = 6x y' = 6x+a y = 3x^2+ax+b we know the slope is y'(1) = -3, so 6(1) + a = -3 a = -9 so, y = 3x^2-9x+b since 5-3x=2 at x=1, y(1) = 2, and we have 3-9+b = 2 b = 8 and y = 3x^2-9x+8 See the graphs at http://www.wolframalpha.com/input/?i=plot+y%3D3x^2-9x%...
*July 29, 2014*

**PreCalculus**

sin(x)sec(x) - 2sin(x) = 0 sin(x)(sec(x)-2) = 0 sin(x) = 0 sec(x) = 2 Those are pretty standard angles, so listing the solutions should be easy.
*July 29, 2014*

**geometry**

The diagonals cross in the center, so the acute angle is the vertex of an isosceles triangle with height=24 base=14 so the acute angle x obeys tan(x/2) = 7/24
*July 29, 2014*

**Geometry**

If the dimensions are x,y,z then we have 2xy+2xz+2yz = 22 4x+4y+4z = 24 xy+xz+yz = 11 x+y+z = 6 How about 1,2,3 diagonal is √14
*July 29, 2014*

**algebra**

I'd do it by taking the log of the values, and using a normal linear best-fit on the log values. Where log(15500/v) = log4, that's the number of years you want.
*July 29, 2014*

**math**

4 = 2^2 4/(2^x) = (2^2)/(2^x) = 2^(2-x) Now, just solve the equation. Hint: 2^(x-2) = 2^x / 4
*July 29, 2014*

**Trigonometry**

The individual displacements are 150 @ 220° = (-96.4,-114.9) 130 @ 130° = (99.6,-83.6) So, the final location is at (3.2,-198.5) Just find the distance from there to the origin.
*July 29, 2014*

**math**

On the other hand, if you meant 27√3, that makes b=7/2
*July 29, 2014*

**Finite Math**

clearly it's 500-x
*July 29, 2014*

**Math**

just start by listing the facts: width=w length=w+6 height=2 area is the 4 sides + bottom = 2(width*height)+2(length*height)+(length*width) = 2(2w)+2(2(w+6))+w(w+6) = 4w + 4w+24 + w^2+6w = w^2 + 14w + 24 So, now we know that w^2+14w+24 = 280 w^2+14w-256 = 0 Solve that for w, ...
*July 28, 2014*

**math**

after 1/8 were purchased, 7/8 were left. So, now we have 7/8 x + 10 = 52 7/8 x = 42 x = 48
*July 28, 2014*

**math**

a/p = 3/5 (2/5 a)/(p-40) = 2/5 a=60 p=100 so, she paid 60(.30)+100(.45) = $63.00
*July 28, 2014*

**math**

3278164781246
*July 28, 2014*

**math**

9/180 = 0.05 = 5%
*July 28, 2014*

**chemistry**

32 days is 4 half-lives. So, the mass is reduced to 1/2^4 = 1/16 of 40mg, or 2.5mg
*July 28, 2014*

**Math**

so far so good. Now just solve for b and plug that into your formula. Then check that (-3,-8) satisfies the equation.
*July 28, 2014*

**Math**

plot the point. Since the slope is 2/3, go right 3 and up 2 and plot another point. Draw the line connecting the two points.
*July 28, 2014*

**physics**

the difference is 4.9µC. So, move half that, or 2.45µC. Now just convert that to no. electrons.
*July 28, 2014*

**math/help**

4 1/6 = 25/6 1 1/6 = 7/6 so, (25/6)/(7/6) = 25/7 3 3/1 ??? fix that and work it as in the above one.
*July 28, 2014*

**math**

just as usual. Where is y" positive? e^-3t is always positive, so all you need is 2t-3 > 0 t > 3/2 e^3/2 = 4.48, and you can see from the graph that it is concave upward for x > 4.48 http://www.wolframalpha.com/input/?i=plot+x+%3D+e^t%2C+y+%3D+te^-t+for+1%3C%3Dt%...
*July 28, 2014*

**math**

x = e^t y = te^-t dy/dx = y'/x' = (1-t)e^-t/e^t = (1-t)e^-2t d^2/dx^2 = (x'y"-x"y')/x'^3 = ((e^t)(t-2)e^-t - (e^t)(1-t)e^-t)/e^3t = (2t-3)e^-3t or, do it directly x = e^t, so y = lnx/x y' = (1-lnx)/x^2 = (1-t)e^-2t y" = (2lnx-3)/x^3 = (2t...
*July 28, 2014*

**Science**

why do you include a third dimension? The taxi cannot travel vertically. The total displacements are 20+6=26 blocks south 15 blocks east. So, √(15^2+26^2) = √901 = 30.0
*July 28, 2014*

**physics**

15.7 + 17.5
*July 28, 2014*

**math**

1/2 * 1/2 * 1/6
*July 28, 2014*

**Algebra**

Start by expanding the parentheses: 3(x-1) -2(x^2+3x+4)-5(x+9) 3x - 3 - 2x^2 - 6x - 8 - 5x - 45 Then collect terms of like degree: -2x^2 + (3-6-5)x + (-3-8-45) -2x^2 - 8x - 56
*July 27, 2014*

**Math**

If their heights are k and r, then k/375 = sin 32° r/375 = sin 38° So, the difference is r-k = 375(sin38°-sin32°)
*July 27, 2014*

**math**

that's because you mixed up dollars and cents. It asked for only dollars.
*July 27, 2014*

**math**

3:40 to 6:20 is just 2 hours and 40 minutes. That should get you going.
*July 27, 2014*

**Math**

Assuming you mean "I" and not "O", just pick any two values for x and calculate the y: x=0: y=4 x=4: y=5 So, the points (0,4) and (4,5) are on the line. Plot them, and draw a line between the two points.
*July 27, 2014*

**math**

There are only 3 colors. Any group of more than 3 cards will have to have a duplicate color.
*July 27, 2014*

**Statistics**

0.066-0.033 < p < 0.066+0.033
*July 27, 2014*

**english**

That "ing" is a big clue for a gerund.
*July 27, 2014*

**chemistry**

when you say it was immersed, that implies there was some other liquid in the cylinder. If all you mean is that the sodium exactly filled the cylinder, then the density is obviously 405.5g/32.5ml = 405.5/32.5 g/ml
*July 27, 2014*

**Chemisrt**

What you have is just D = D0*x where x is all that exponential stuff. So, D0 = D/x Of course, R is not specified. If it's R you are looking for, then just work it out like this: exp[-Ea/R*T] = D/D0 -Ea/R*T = ln(D/D0) R = -Ea*T/ln(D/D0)
*July 27, 2014*

**maths**

if you mark off a length of 4, you can easily construct a length of 30. Double the 4 to 8, double the 8 to 16, double the 16 to 32. Halve the 4 to get 2, and subtract that from the 32. Now construct the leg BC, and the right angle at C. Then mark off a circle of radius 30 to ...
*July 27, 2014*

**algebra**

take a look at http://www.jiskha.com/display.cgi?id=1406381756
*July 27, 2014*

**math**

just plug in the values and see. For example, take (1,-2). Is 3*1 + 3*1 - 6 < -2 ? 0 < -2 ? No. Now try the others.
*July 27, 2014*

**math**

if you can recognize a quadratic and an inequality (as opposed to an equation), you should have no trouble picking the correct choice.
*July 27, 2014*

**math**

2(w+1.2w) = 88 4.4w = 88 w = 20 so, area = 20(1.2*20) = 480
*July 27, 2014*

**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*

**Alegbra**

y=0
*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*

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