Monday
September 1, 2014

Posts by Steve


Total # Posts: 24,526

math: set theory
the set is all integers greater than or equal to 4. Looks like (d) BTW, | means "such that" -- lose the "is"
July 4, 2014

physics word problem
conserve momentum. With everything initially at rest, momentum is zero. So, the raft moves in the opposite direction when she jumps. So, the speed s of the raft is such that 180s = 60*4 I note that you asked for speed, so I ignored the direction of the velocity. I expect you ...
July 4, 2014

math
correct
July 4, 2014

math
2x^2+5x-5 2(x^2 + 5/2 x) - 5 2(x^2 + 5/2 x + (5/4)^2) - 5 - 2(5/4)^2 2(x - 5/4)^2 - 65/8
July 4, 2014

Math
500(1+.08/2)^(2*15) = ?
July 4, 2014

math
well, the primes less than 20 are 2,3,5,7,11,13,17,19 So, pick all the pairs that add up to less than 20.
July 4, 2014

Finite Math
If there are x undergrads, y grads, and z faculty, we have x+y+z <= 20 100x + 150y + 200z <= 3200 x >= y+z maximize 18x+25y+30z Now just apply your favorite optimization tool.
July 4, 2014

Math
x(1+.08/4)^(4*4) = 8000 Now just solve for x
July 4, 2014

algebra
since there are two double roots, the graph is tangent to the x-axis at 0 and -1. It crosses only at x=2. So, since it is a 5th degree polynomial, with leading coefficient negative, it rises at the left end and falls on the right end. So, q > 0 for x < -1 q > 0 for -1...
July 4, 2014

Algebra
domain is all reals for all polynomials. So, C and D are out. since a parabola has a vertex, it has a maximum or a minimum, so the range cannot be all reals. So, A is out. B must be the answer. The only confusion might be whether the vertex is a max or a min. If B is correct, ...
July 4, 2014

Algebra
correct
July 4, 2014

Math
supply the missing width (?) and solve for x, where 2(? + x) = 354
July 4, 2014

maths Arthmetic
well, since 4 is half of 8, 4/3 is half of 8/3 so, what number is 22 half of? 44 you are correct
July 4, 2014

physics
greater than 10+15
July 4, 2014

physics
hmmm... If θ is the angle between p+q and p, cosθ = 4/5 If Ø is the angle between p+q and q, then the angle between p and q is θ+Ø Let's let |q| = a, so |p| = a+1 p•q = a(a+1)cos(θ+Ø) (p+q)•p = |p+q|*|p| cosθ = (4/5)(...
July 4, 2014

physics
The two forces clearly have magnitudes 6 and 10. So, use the law of cosines to get r^2 = 100+36-120(-1/2) = 196 r = 14
July 4, 2014

physics
recall that the electric force F = 9.0*10^9 (q1*q2)/r^2 So, plug in your values, remembering how many electrons are in a Coulomb, and you have only 1 electron at each pole. r must be in meters, of course, not km.
July 4, 2014

math
The supplementary angle is always 90° more than the complementary angle.
July 4, 2014

Algebra
(B) the slope is not a constant. Every value is possible for the slope at some point on the curve. you are correct.
July 3, 2014

Algebra
y = a(x-3)^2 + 1 10 = a(0-3)^2+1, so a = 1 Looks like (C) to me
July 3, 2014

physics
looks like 25 mph West to me
July 3, 2014

Algebra
dang typo: y=40
July 3, 2014

Algebra
write down the data. If there are x footballs and y baseballs, then we have p = 6x + 5.5y 35 <= x <= 45 40 <= y <= 55 x+y <= 80 we want to maximize p. Using your favorite linear optimization calculator, you find that x=40 y=50 profit = 460
July 3, 2014

Algebra
that's the ticket.
July 3, 2014

Algebra
evidently 46.5% per time period
July 3, 2014

Algebra
There's no algebraic way to do it. A numeric method or a graphical analysis will be required. See http://www.wolframalpha.com/input/?i=solve+3x^2%2B4lnx%2B4%3D0
July 3, 2014

Chemistry
When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...
July 3, 2014

arithmetic
After the first 1/8 died, only 7/8 were left 3/5 of those died, meaning 3/5 * 7/8 of the original number died 1/8 = 5/40 3/5 * 7/8 = 21/40 So, 26/40 = 13/20 of the fish died
July 3, 2014

Chemistry
When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...
July 3, 2014

math
nope. Just because two numbers multiply together to make 1, you still know nothing about the numbers. If nothing else, try your idea. If x=1, 2x+1=3, and 1*3≠1 However, if two numbers multiply to be zero, then one or the other must be zero. So, let's set things equal...
July 3, 2014

Math
well, 45g = 0.045 kg. So, you will have 0.365 kg +.045 kg ------------- 0.410 kg
July 3, 2014

Algebra
cmon, guy. I posted an update to the first one, using substitution, and also showed elimination. What don't you get? Have you looked at them?
July 3, 2014

Algebra
another way is called elimination. You have 5x - 9y = 7 7y - 3x = -5 Rearrange terms a bit to get 5x - 9y = 7 -3x + 7y = -5 To get rid of the x values, find the LCM of 5 and 3: 15. Now multiply things a bit to get 15x - 27y = 21 -15x + 35y = -25 Now you can add the two ...
July 3, 2014

algebra
sure. the first equation 5x - 9y = 7 tells us that x = (9y+7)/5 Just plug that into the 2nd equation, and you get 7y-3(9y+7)/5 = -5 fractions are a nuisance, so multiply through by 5: 35y - 3(9y+7) = -25 35y - 27y - 21 = -25 8y = -4 y = -1/2 Now plug that value into either ...
July 3, 2014

algebra
7y-3(9y+7)/5 = -5 y = -1/2 so, x = 1/2
July 3, 2014

Algebra
v + (4+2v) = 16 v = 4 so, 4 oz vinegar and 12 oz oil.
July 3, 2014

Math
that would be (0.365 + 45.000) kg That's some loaded pizza. I suspect a typo. Just fix that and add the two numbers.
July 3, 2014

geometry - incomplete
That depends. Is DE the arc length, or the chord length? Then, you have also left out the radius or the subtended angle.
July 3, 2014

Inequalities & Absolute value
oops - a typo. should be x > -13/2 so, the solution to the first one is -13/2 < x <= 1/2
July 2, 2014

Inequalities & Absolute value
OK. To solve absolute-value problems, you really have to do them twice. Recall the definition of |z|: |z| = -z if z < 0 |z| = z if z >= 0 So, you have |2x+4|<5 That means that If 2x+4 < 0, (or, x < -2)you have -(2x+4) < 5 -2x-8 < 5 -2x < 13 x > 13/2 ...
July 2, 2014

Inequalities & Absolute value
I get -4/3 < x < 1/2, so only (ii) works. In this case, it's easy enough just to substitute in each of the values to see which works in both cases. Always keep in mind the V shape of absolute value graphs. See http://www.wolframalpha.com/input/?i=plot+y+%3D+|2x%2B4|%...
July 2, 2014

Math
Since you are adding 20 to each number, just add 20*21 to the total. Or, thinking of the values as an arithmetic progression, recall that the sum of n terms is Sn = n/2 (T1+Tn) With a=40,d=1, S21 = 21/2 (40+60) = 1050 With a=60,d=1, S21 = 21/2 (60+80) = 1470 Note that 1470 = ...
July 2, 2014

algebra
figure the common denominator. Then, using that, add/subtract the values: 1/3 + 3/7 21 = 3*7, so you really have (1*7)/(3*7) + (3*3)/(3*7) = (7+9)/21 = 16/21
July 2, 2014

algebra
I'd guess that depends on the size of the tank.
July 2, 2014

math
The smallest such number is 3*5*7 = 105 Since 64 <= 105 < 128 or 2^6 <= 105 < 2^7 That will require 7 digits: 1101001
July 2, 2014

algebra
complex zeros come in conjugate pairs. Just as in the first problem above. So, what do you think?
July 2, 2014

algebra
(x-7i)(x+7i) = x^2+49
July 2, 2014

algebra
(12-2x)(10-2x) = 80 Solve that for x, or just note that 80 = 10x8, so both dimensions are reduced by 2", making a 1" margin all around.
July 2, 2014

math
A1/A2 = (s1/s2)^2 = (2/√2)^2 = (√2)^2 = 2 (B)
July 2, 2014

math
in each suit of 13 cards, there are 5 even cards. That means, there are 8 others. So, P(~even) = 8/13
July 2, 2014

Algebra
just recall that a^2-b^2 = (a-b)(a+b) So, first, make sure that both terms are perfect squares. In this case, they are not. However, if you factor out a 2, you have 2(49-4w^2) 49 is 7^2 and 4w^2 = (2w)^2. So, we now have 2(7-2w)(7+2w)
July 2, 2014

math
look up you standard form for ∫√(u^2-a^2) du Now, if you let u = 2x, you have u^2 = 4x^2 du = 2 dx, so dx = du/2 Also, let a = √3 So, now your integral is 15/2 ∫√(u^2-a^2) du and just go for it.
July 2, 2014

math
a+b+c+d+e = 35 (mean=7) c = 7 (median) e = a+7 (range) a+b+7+d+a+7 = 35 2a+b+d = 21 If a=1, b+d=19 But b<=7 and e=8 1,b,7,d,8 But, if b<=7, and d<=8, no go If a=2, b+d=17 2,b,7,d,9 same problem as above If a=3, b+d=15 d<=10, so b>=5 so we can have 3,b,7,d,10 as ...
July 2, 2014

Math
all the prime factors of c are less than p, so n has 4 unique prime factors. n^2 does not have any new prime factors, so it also has 4.
July 2, 2014

algebra
3.14 * 1/1000 and you can massage that as you will.
July 2, 2014

Math
just replace each expression in parentheses, and you will see that the values are the same. An illustration of the associative property of addition.
July 2, 2014

algebra
mary's age 5 years ago is x-5 1/3 of that is (x-5)/3 3 less than that is (x-5)/3 - 3 Now, that may not be the answer, since it's difficult to parse just who's how old when, with your unusual verb tenses.
July 2, 2014

math
If there are t tourists and r rooms, t = 6r-9 t = 3(r+4) 6r-9 = 3r+12 3r = 21 r = 7 so, t=33
July 2, 2014

math
(ab)^2 = abab If abab = aabb then the middle ba = ab
July 2, 2014

math
y" + 9y = cos2x+sin2x You know that y"+9y=0 has solutions y = a cos3x + b sin3x so the solution here is y = a cos 3x + b sin 3x + (cos2x+sin2x)/5
July 2, 2014

Algebra
first step: expand the polynomial. You will see that x^3 goes away, leaving you with just 3x^2+2x = 85 Now just solve as you normally would: 3x^2 + 2x - 85 = 0 (3x+17)(x-5) = 0
July 2, 2014

104B
500*2.5*r = 40 r = 0.032
July 1, 2014

math
19/3x - 20
July 1, 2014

Math
if x at 7%, then .07x + .08(x+6000) = 7.80 Fix the interest amount and solve for x. And pay more attention to what you type.
July 1, 2014

Math
4c + 5m = 25.50 2m = c+1.75 Now just solve the two equations, using your favorite method. I get (A) assuming a missing decimal point.
July 1, 2014

Math - incomplete
some data missing here. Read what got posted and fill in what got omitted.
July 1, 2014

physics 1
if the initial velocity was v, v - 3.55*2.13 = 4.90 v = 12.46 m/s the displacement s is thus s = 12.46*2.13 - 3.55/2 * 2.13^2 s = 18.49 m
July 1, 2014

math
we want to approximate ∫[0,4] e^(3√t) sin 3t dt So, divide the interval[0,4] into 8 pieces, each of width 0.5 Now apply each Rule named above, calculating f(x) for each value from 0 to 4, and add up the areas of all the rectangles or trapezoids. There are online ...
July 1, 2014

Heron's formula
anything to do with the area of triangles. Just look around your home and see what triangles you might be interested in. Painting gables, carpeting a corner of a room, etc.
July 1, 2014

Math - bzzzt
Sorry. If PQ joins the midpoints of AB and AC, then it is parallel to BC and half its length. You cannot have PQ=2 and BC=3.
July 1, 2014

Chem
You have: .0286*.169 = 0.004833 moles of Na3PO4 .0397*.255 = 0.010124 moles of Ca(NO3)2 If the reaction is 2Na3PO4 + Ca(NO3)2 = 2NaNO3 + Ca(PO4)2 then you need 2 moles of Na for each mole of Ca. Since there is extra Ca, you will wind up with .09666 moles of Ca(PO4)2 Just ...
July 1, 2014

algebra 1
well, the triangle obviously has area = 12 So, the whole outfit has area 6x+12. So, 6x+12 = 150 6x = 138 x = 23
July 1, 2014

math
surely you can count days on a calendar...
July 1, 2014

Math
If you subtract the 2nd equation from the first, you get 4x-3y-4 = 0 4x+2y+5 = 0 ---------------- -5y-9 = 0 now add 9 to both sides: -5y = 9 now divide by -5: y = -9/5 Knowing that y = -9/5, just plug it into either of the original equations and then solve for x. The work is ...
July 1, 2014

algebra
20m
July 1, 2014

math
Just think about it. Every second it travels 1 meter. So, 5 seconds ago it was down 5 meters. now think forward in time for 120 meters above.
July 1, 2014

math
if now is time t=0, then the temperature at any time t is -2t. So, we want -2(-3) and -2(5)
July 1, 2014

Math
that would be 420/12 = ?
July 1, 2014

math
If they were laid out flat, they'd each be 4.8 units long. So, they must be more than that, and since 4.8 is not an acceptable answer, 4.9 is what we have to go with.
July 1, 2014

math
The midpoint of two points is (6,2). One of the points is (3,5). Since the two ends must be equidistant from the midpoint, 3 = 6-3, 9 = 6+3 5 = 2+3, -1 = 2-3 So, (9,-1) is at the other end.
July 1, 2014

Physics
it gained (18-12)=6 m/s in (4-2)=2 seconds, so that is 6/2 = 3 m/s^2 In the first 2 seconds, then, it gained 6 m/s, so it started at 6 m/s.
July 1, 2014

geometry
hmmm. you have the formula. What's the trouble? The same formula applies for ym: (y1+y2)/2 A value midway between two others is just their average: the sum/2.
June 30, 2014

10 gr math
ok. plug in the data and evaluate: the distance between (1,3) and (7,2) is √((7-1)^2 + (2-3)^2)
June 30, 2014

Chemistry
When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...
June 30, 2014

algebra
A. No - the decrease in intensity is not a constant, but depends on the previous intensity. The intensity I of x meters of cable is I = 1500 * 0.964^x C yes you can probably write that one on your own.
June 30, 2014

Math
if there are 8x tools, then there are 3x shovels and 5x rakes. So, 5x = 3x+10 x=5 so, there are 15 shovels and 25 rakes
June 30, 2014

Math
If you can find the midpoint of a line segment know that the slope of the perpendicular is -1/(slope of line segment) remember the point-slope form of a line then all of these problems are straighforward. Review those topics, give it a try, show where you get stuck, if you do.
June 30, 2014

Non
just a note: that's mu sub-k, not "muse of k" µk
June 30, 2014

Volume
Just figure the tank's volume (66.75*132*10) and divide it by 231 in^3, the volume of a gallon.
June 30, 2014

algebra
x^2+8x = x(x+8) Pick any positive value for x and you get a rectangle.
June 30, 2014

math
take a look at the graph of (1+.10/n)^(n) It shows the effective yield of 10% compounded n times per year. It approaches continuous compounding, e^.1 http://www.wolframalpha.com/input/?i=plot+y%3D%281%2B.1%2Fn%29^n+for+n+%3D+1..40%2C+y%3De^.1
June 30, 2014

algebra
solve it just as you would an equation: 42 = -6d -7 = d However, multiplying and dividing by negative values changes the direction of the inequality. So, you have 42 < -6d 7 < -d -7 > d or d < -7 Since you can always add and subtract without changing the direction...
June 30, 2014

science
I may have messed up the sign change, so double check my math.
June 30, 2014

science
the position falling from a height of h feet is y = h - 16t^2 After t seconds, y=0, so h=16t^2 So, we have (h-16t^2) - (h-16(t-1)^2) = 11h/36 0 - (16t^2 - 16(t-1)^2) = 11(16t^2)/36 32t-16 = 44/9 t^2 11t^2 - 72t - 36 = 0 t = 7.01 So, h = 16t^2 = 786.24 ft
June 30, 2014

calc
first off, I'd use partial fractions: (x^3 -3x^2 -9)/(x^3 -3x^2) = 1 + 1/x + 3/x^2 - 1/(x-3) There are no discontinuities on [4,5], so it's straightforward. The integral is just x + logx - 3/x - log(x-3) so we get (5 + log5 - 3/5 - log2)-(4 + log4 - 3/4 - log1) = 23/20...
June 30, 2014

Math
54° is 3/20 of a full circle. SO, the whole circumference 3/20 c = 9 c = 60
June 30, 2014

ALGEBRA - eh?
cannot parse the "8n 12" part
June 30, 2014

math
The solution of this equation is so complex, I have to assume you're doing numerical methods or something. Take a peek at http://www.wolframalpha.com/input/?i=sin^6x+-sin^2+4x+%3D+sin2x+sin10x for further insight.
June 30, 2014

trigonometry
well, we have h/120 = tan 10°18' h = 21.8 ft
June 30, 2014

Maths
y = 1/x y' = -1/x^2 y'(1/4) = -1/(1/16) = -16 I think you lost a minus sign. And, of course, you have displayed the usual sloppiness with parentheses.
June 30, 2014

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