Friday
July 25, 2014

Posts by Steve


Total # Posts: 23,952

time n work
1/a + 1/b = 1/16 1/b + 1/c = 1/32 4/a + 12/b + 48/c = 1 a can do the job in 160/7 days b can do the job in 160/3 days c can do the job in 80 days. Check: a can do 7/160 jobs in 1 day, and 28/160 jobs in 4 days b can do 3/160 jobs in 1 day, and 36/160 jobs in 12 days c can do 1...

Math
incorrect. The subtraction takes place first, so f(x) = |x-1| Your function is described as take the absolute value and then subtract 1.

geometry
as with all solids, the volume changes as the cube of the linear change. So, if it dilated by a factor of 1/5, the volume changes by a factor of (1/5)^3 = 1/125.

Math
If there are x trees, the cost is 375(3/5 x) + 500(2/5 x) = 425x Not knowing how many trees were harvested, the cost is unknown, but if there were x trees worth $80M, then the tax must be 1/20 ($80M - 425x)

math
total tax is 12+5+7 = 24% So, the tax is 24% of 18.75 Add that to the 18.75 price. 18.75 * 1.24 = ?

Pre calculus
I see only a cubic, which can have only 3 roots. So, since the complex roots appear in pairs, there are either 1 real and 2 complex, or 3 real roots. Cubics have a discriminant, just like quadratics, but it's not generally known. As shown here: http://www.wolframalpha.com/...

Geometry
since all the triangles are equilateral, it must be x=60 How did you arrive at 90? I don't see any right angles in the picture!

Geometry
The large square has area 12^2 = 144 The triangle is a 30-60-90 triangle, with legs 6 and 6√3, so its area is 18√3 So, 144-18√3 = (b)

math
45000 * 0.7^5

Math
.06*30 + .04(x-30) = .04x + .6

pre cal
if y = 8/(x^2+2) Then one choice is clearly f(x) = 8/x g(x) = x^2+2 If y = 8/x^2 + 2, then we have f(x) = x+2 g(x) = 8/x^2

pre cal
if f(x) = √(9-x) then 9-x cannot be negative. So, 9-x >= 0 x <= 9

pre cal
oops - the real root is at -3.282

pre cal
I find no rational zeros, but the real zero is very near -1.3, so f(x) = (x+1.3)(2x^2+6.4x-6.12) I assume you have some graphical or numeric tools for solving general polynomials.

pre cal
Good grief. How about some math, instead of the noisy words? I'll do one. f(x) = (x^2+x-2)/(x^2-3x-4) All polynomials have domain of all reals. Rationals have a domain of all reals except where the denominator is zero. Since f(x) = (x+2)(x-1) / (x-4)(x+1) The domain is all...

Math
the identity must be true for any value of x. That is, for all values of x, whatever you choose. The identity does not say anything about the number x. If there is any value which does not satisfy the equation, then it is not an identity.

geometry
since -2/3 * 9 = -6, we want x such that -2/3 x = -10 x = 15

physics (motion)
check the units. (a) and (b) are obviously false. So, since (d) means constant velocity, (c) is the only possible choice.

Physics--check answers please
#1 ok #2 I get that the player is at (-22.5,-26.8) from the net, so his shot takes the puck to (2.5,-26.8). Making it 26.9 from the net. You can figure the angle. How did you get your solution? #3 ok

math
who said anything about coordinates? If you draw the diagram using the given values, you will have two right triangles. Their common leg will be the 20 yards from the sideline to the camera. The length of the field (plus the two end zones) will be 120 yards, divided 50:70.

math
Draw a diagram. The camera must pan to one side through an angle x, and to the other side, through an angle y, where tan(x) = 50/20 tan(y) = 70/20 Now just add up x and y.

Physics
This is a trick question. If the external load is x ohms, then the fraction of the voltage drop across the load will be x/(x+4), or 20x/(x+4) volts. You can see that if the external load is 0, then the current is 5 amps. But, that would take an infinite number of resistors in ...

trigonometry
convert radians to degrees, as usual. Then multiply by 60 and 60 on the decimal parts: 23.461° .461 * 60 = 27.66' .66 * 60 = 40" So, 23°27'40" Do the reverse to go the other way. Divide by 60 and 3600 to convert ' and " to °. Now use that...

finite
don't know the formula right off. Why don't you give the formula, and show how you evaluate it?

Calculus
I assume you mean (∛x^2)(2x+5)^3 ∛ has domain all reals all polynomials have domain all reals. f' = 2(2x+5)^2(11x+5) / 3∛x Now we see that f' is undefined for x=0 f'=0 for x = -5/2 and -5/11

Calculus
If u = 5x^2-3x+1, f(u) = csc^4(u) f'(x) = f'(u)*u' = 4 csc^3(u) (-csc(u)cot(u)) u' u' = 10x-3 Now just do the substitution.

Calculus
v = 1/3 pi r^2 h dv/dt = pi/3 (2rh dr/dt + r^2 dh/dt) Now just plug in dv/dt = 300pi dh/dt = -15 r=20 h=30 and solve for dr/dt

Calculus
v = 1/3 pi r^2 h From the shape of the cone, you know that r = h/6 so, dr/dt = 1/6 dh/dt dv/dt = pi/3 (2rh dr/dt + r^2 dh/dt) = pi/3(2(h/6)h(1/6 dh/dt) + (h/6)^2 dh/dt) = pi/18 h^2 dh/dt Now just solve for dh/dt when dv/dt = -1/4 h=4

mat/117
Not sure just what (9-5 4√6) means. But, let's ignore the 5 for now and pretend you had (9-4√6)(7- 4√8) Just expand like any polynomial: 9*7 - 4√6*7 - 9*4√8 + 4√6*4√8 63 - 28√6 - 36√8 + 16√48 Pulling out all the p...

math
Hmm. Obviously I misplaced a decimal point. I expect you can find the flaw in my reasoning.

math
look at the amounts of NaF involved: (.6/10^6)*100000 + 1.0*x = (1.75/10^6)(100000+x) x = 0.115 check: .6 ppm in 10^5L = 0.06g add 0.115 g and you have 0.175g, or 1.75ppm

physics
well, if it's incompressible, then its volume doesn't change under pressure, right? SO, since the mass also doesn't change, that must mean that the answer is (A), since density = mass/volume, both of which are constant.

HELP!!!
If h is the altitude from C to AB, we have 1/2 * ch = 3h = 7.52 So, h = 2.507 Now h/a = sin 40° a = 2.507/0.642 = 3.90

Algebra
first, you might fix your typos. Your formulas are bogus. Next, you can easily see that the values get bigger and bigger, so the 1/2 formula can't be right. Your first try is right, but should be written a(1) = 3 a(n) = 2*a(n-1) for n > 1

math
For the cost, we know that if there are n items, and each costs c, then the total cost is 330+nc For the revenue, if there are n items selling at price 25, the total revenue is 25n. So, just set things up to total revenue = total cost Not sure what your "break even" ...

algebra
-2x-2+7(x+1)=2x -2x-2+7x+7 = 2x 5x+5 = 2x 3x = -5 x = -5/3

Pre-Algebra
oops: tan 30° = 1/√3

Pre-Algebra
since the sides are in the ratio 1:√3:2 a,b) the sides are 41:41√3:82 c) as we all know (or should, because the come up repeatedly): sin 30° = 1/2 cos 30° = √3/2 tan 30° = √3 And since the co-functions are the functions of the complementary ...

math
I assume a typo, and that g(x) = -(x-1)^2 + 3 if -2 < x <= 2 just look at the data: since -2 < 1 <= 2, g(1) = -(1-1)^2 + 3 = 0+3 = 3 since -2 < 2 <= 2, g(2) = -(2-1)^2 + 3 = -1+3 = 2 since 5>2, g(5) = 3 Don't let all the symbols confuse you. Each just ...

Math
(8-4x)/(x+5) > 1-x If x+5 > 0, 8-4x > (x+5)(1-x) 8-4x > -x^2-4x+5 x^2+3 > 0 This is true for all x, but the initial condition was that x > -5. So, that is the domain: x > -5 If x+5 < 0, 8-4x < (x+5)(1-x) 8-4x < -x^2-4x+5 x^2 < √3 But, we ...

math
look at the amount of tar: 1.0*6 + .05*120 = x(126) x = 0.095, or 9.5% Or, consider that 5% of 120g = 6g So, now you have 12/126 = .095

Algebra/Steve
You're not sure about the zero? I'm not sure about the equation!

algebra
just do what you did with 13 and 6: wherever you see an x, substitute in p: f(p) = p-7 Not a numeric answer, because you haven't specified what value p has. f(bozo) = bozo-7 f(40) = 40-7 and so forth.

math
if the first term is 456, then the 17th term is 456+7*16 Tn = 456 + 7(n-1)

programming oop
sum12 = n1 + n2 diffs3 = sum12-n3 prodd4 = diffs3*n4 quotp5 = prodd4/n5 I think you can write the code to gather n1-n5 and display the values calculated above.

Algebra
Think of a number between 1 and 10: n Add 1; n+1 double the result; 2(n+1) = 2n+2 add 3; 2n+2+3 = 2n+5 subtract 4; 2n+1 add 5; 2n+6 halve the result; (2n+6)/2 = n+3 add 6; subtract 7; add 8; subtract 9; n+1 subtract the number you first thought of: 1 Don't see any inductio...

geometry
Using only reflections in vertical lines, then horizontal lines, you can get B by reflecting through x = -1/2: (-2,-1) -> (-1,-1) through y = -7/2: (-1,-1) -> (-1,-6) No idea what your operations were. Just move your coordinates an equal distance on the other side of the...

calculus - unclear
Man, there's a lot of missing information here. That leads me to conclude that the hammer spins in a counterclockwise direction, then flies in a straight, horizontal line from the circle to the screen. Apparently the screen is a circle of radius 50. Now, your solution of (...

math
If the current's speed is x, then 10+x is the downstream speed of the boat 10-x is the upstream speed. the downstream time is 90 minutes (3/2 hours) less than the upstream time. Hence, the given equation. 36/(10+x) = 36/(10-x) - 3/2 36(10-x) = 36(10+x) - 3/2 (10-x)(10+x) n...

math
since time = distance/speed, 36/(10+x) = 36/(10-x) - 3/2 x = 2 check: 36/12 = 3 36/8 = 4.5 ok

math
if his rowing speed is x and the stream's speed is y, then we have 4/(x+y) = 3/(x-y) 48/(x+y) + 48/(x-y) = 14 x=7 and y=1 check: x-y=6 x+y=8 It is clear these values fit the conditions.

Math
assuming you mean integers, 501 - 1499 will both round to 1000 any number can be rounded to the nearest thousand. You will have to be a bit more specific.

math
as written, I'd say $189.95 Now, if you mean that each phone costs $189.95, then 100 of them cost $18995.00

math
6 is the same as 5 8/8 So, 5 8/8 - 3 5/8 = 2 3/8

mathematics
can you see how little context you have provided?

algebra
c'mon. You know that 99 = 9*11 So, what might the two consecutive odd integers be? ...

algebra
Note that the terms come in repeating groups of 5. 38 = 7*5 + 3 So, S38 = 7(4+8+2+6+2) +4+8+2 = 168

math
4/7 * 3/8 = 12/56 or 3/14 Good luck finding that measuring cup!

Math 11 - Rational Expressions
the only restrictions are because you cannot divide by zero. So, check the denominator of any rational expression. Wherever it is zero, those values must be omitted from the domain. Otherwise, all real numbers are allowed. So, for #3 above, since 2x^2+5x+2 = (2x+1)(x+2) the va...

math
so, just fix the typo and solve -16t^2-32t+320 = 48 t = 3.24

alegbra
(3x-1)(x+2)

Math
Add up all the numbers: 632 There are 12 numbers, so the mean is 52.666 Now, you want to remove one value so that the remaining 11 have a mean of 56.09. Well, 11*56.09 = 617 So, if you remove one of the 15's, the remaining 11 numbers add up to 617, giving the desired mean.

Pre-Calculus
You show that it is true for n=1. Then you show that if it is true for n=k, then it must also be true for n=k+1. That means that the assertion is true for all values of n, starting with n=1, and thus for n=2,3,4,... For instance, a common proof is that the sum of the first n o...

Math
to lower the mean, remove the highest scores. To raise the mean, remove the lowest scores.

finite Math
17000 * 1.04^5

physics
same seat assuming that the windows are closed...

math
63 divided by (10-3) + 2 x 4 = 63/7 + 8 = 9+8 = 17 However, (63/7 + 2)x4 = (9+2)x4 = 11x4 = 44 Normally multiplication is done before addition

math
8*600 = 4800 radios produced. That leaves 2800 more to be done in 4 days. I think probably you can take it from there.

Math
I generally don't think of circles as having ends, so maybe the fence is rectangular or square. However, since you talk about using pi=22/7, I'll assume you want a circular fence, and the diameter is 10 ft. So, C = 10pi = 31.4 ft $440/31.4ft = $14.01/ft

algebra
first place is to check your text for some kind of distance formula. Next, get out some graph paper and plot the two points, then draw a line between them. Call them A and B, respectively. Now draw a horizontal line from A and a vertical line from B. Where the two lines inters...

physics
if the velocity changes from 25m/s to 0 in 5 seconds, that's an acceleration of -5m/s^2. So, the distance covered till the full stop is 25*5 + 25t + 1/2 (-5)t^2 with t=5, that's 25*5 + 25*5 - 125/2 = 187.5 m

Math
when (1/2)^(t/60) = .05 t/60 = log.05/log.5 t = 259.3 days

chemistry
HCl + NaOH -> NaCl + H2O each mole of NaOH reacts with one mole of HCl. so, how many moles of NaOH in 40g? How many grams of HCl in that many moles?

Math
25x^2 - 30x = -9 25x^2 - 30x + 9 = 0 (5x-3)(5x-3) = 0 ...

Algebra
mathematically, |b| ≠ 2 or b^2 ≠ 4

physics
on the ground, the weight is mg = 100*9.8 = 980N Now, g=9.8 because F = GMm/r^2 = mg, so g = GM/r^2 If we say that r=6371km, then at 1000km altitude, we will have 9.8 * (6371/7371)^2 = 7.32, so the 100kg mass will weigh only 732N

Algebra direction how to do it
As you know, y = 4x-4 is just a line. All the points on the line satisfy the equation. > means "greater than". So, if (2,4) is on the line, (2,5),(2,6),... are above the line, where y > 4x-4. So, the solution to an inequality is a whole region of the plane, not...

Algebra
1 - x^2/x = 1-x (1-x^2)/x = 1/x - x (2b-2)/(2b^2-8) = (b-1)/(b^2-4) = (b-1) / (b-2)(b+2) Not sure just what you're after

math
since a = bh/2, we have a = 14x/2 = 7x so, 7x <= 112 x <= 16

College Alegbra
(a) d(j(x)) = .75(j(x)) = .75(x-5) (b) j(d(x)) = d(x)-5 = .75x - 5 (c) go for it

algerbra
the difference between three-fifths and five is equal to the product of x and the sum of y and seven. Seems kinda dumb. Why all the nonsense with 3/5 - 5?

math
55+25-15 = ?

geometry
time to draw a diagram and review your basic trig functions: DE/10 = tan 25° It also helps to recall the alternate interior angles between parallel lines are equal.

algebra
well, you need a 1, so that would be 3/3 Now you need 30 more, using three 3's. Looks like 3^3 + 3 + 3/3

Math
a.bc a > 0 b = a+1 c = a+b 1.23, 2.35, 3.47, 4.59 Unless there are further conditions, just pick one.

math
Well, the roots are -1/2 and 1, so I hope some of the choices were near those values.

math
each of 5 people plays 4 others. That's 5*4 But, that counts each person twice, so you really have 5*4/2 = 10 games

math
all correct good work

algebra
If you mean 2y/3 + 2y - 6/15 then that is just 2y/3 + 6y/3 - 6/15 = 8y/3 - 2/5 = (40y-6)/15 If that's not it, then use some parentheses and show your own work.

Math
well, you have ax^2 = -h ax^2 = h In either case, a and h must have the same sign, since x^2 is always positive. Unless x=0, in which case, h=0. x = ±√|h/a| Naturally, if a=0, there is no solution unless h is also zero.

math
looks like you need to review your basic triangles: sin 60°/cos^2 45° - cot 30° + 15cos 90° √3/2 / 1/2 - √3 + 15*0 √3 - √3 0

Math
You have calculated the number of feet in 26 miles. Now divide that by (32/12), the number of feet in one stride. Or, you can multiply 137280 by 12 to get the number of inches in 26 miles, and then divide that by 32, the number of inches in one stride. Same difference.

Trigonometry
secx - √2 = 0 secx = √2 x = π/4 If this gave you trouble, it looks like you need to review your basic trig functions and common triangles.

algebra
x+y = 15000 .08x + .07y = 1100 Now just solve for x at 8% and y at 7%

Physics
(30,0) + (9.64,-11.50) = (39.64,-11.50) √(39.64^2 + 11.50^2) = 41.27 tanθ = -11.50/39.64

Math
750000 * 0.8^3 at the start of the 4th year. 750000 * 0.8^4 at the end of the 4th year you will have to decide when "during" the year you want its value.

Math
sinθ = 10/15

Math
(1*1 + 5*2 + 3*5 + 1*10 + 1*100) ------------------------------------ (1+5+3+1+1)

finite math
(# left field) / (# hits) = 6/59

math
Clearly, attendance on M-W is 33,34,35 So, attendance on Th-Sat is 36,37,38 with average=37

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