Monday
July 28, 2014

Posts by Steve


Total # Posts: 23,991

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

physics
15.7 + 17.5

math
1/2 * 1/2 * 1/6

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

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°)

math
that's because you mixed up dollars and cents. It asked for only dollars.

math
3:40 to 6:20 is just 2 hours and 40 minutes. That should get you going.

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.

math
There are only 3 colors. Any group of more than 3 cards will have to have a duplicate color.

Statistics
0.066-0.033 < p < 0.066+0.033

english
That "ing" is a big clue for a gerund.

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

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)

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 i...

algebra
take a look at http://www.jiskha.com/display.cgi?id=1406381756

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.

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

math
2(w+1.2w) = 88 4.4w = 88 w = 20 so, area = 20(1.2*20) = 480

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 y...

calculus 2
I think she means y = ∛x

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

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

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

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.

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.

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?

math
Looks like (a) to me. Just use the quadratic formula.

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-...

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.

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

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

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

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

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...

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...

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.

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

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

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)

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(...

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

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

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'...

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

Alegbra
y=0

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

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

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.

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

math
looks like 9 gallons to me.

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

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)

math
all distances are multiplied by a factor of 3.

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

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

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

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

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

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

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

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...

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!

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.

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/...

advance algebra
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

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

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...

calculus
Sounds like they wanted f'(c) rather than c.

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

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.

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

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

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

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.

Math
ACBD

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

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

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

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

Alegbra
2•5^2•7

advance algebra - oops
Oops mixed up price and quantity p(x) = x(500-x)-35(500-x) = (x-35)(500-x) assuming no extra dolls are made...

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

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...

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?

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

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.

Math
17(4+2*17) = ?

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.

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

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 =...

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

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...

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

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.

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

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

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

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

math
16 degrees warmer than it is now.

Math
1/5 - 1/15 = 1/x 2/15 = 1/x x = 15/2

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