Monday
July 28, 2014

Posts by steve


Total # Posts: 23,985

calculus
P = R-C

math
n+d+q = 60 d = 2q+1 10d = 5n-5 Now go for it.

algebra
you want to find when .09s = 260 + .04s So, just solve for s.

math
j+g+h = 20 j = 2g-3 h = g-1 Now just start substituting or eliminating to find the values.

business math
Looks like 18520/44568 = 42%

math
.70*x + 0(100-x) = .45*100 x = 64.28 so, 64ml of concentrate and 36ml of water

math
We assume a≠0, because then it's clear that x=0 is a common root. So, we have x²-11x+a: x = (11±√(121-4a))/2 x²-14x+2a: x = (14±√(196-8a))/2 we need some of those expressions to be equal. Some playing around shows that if a = 24: 1...

maths
if the roots of x²+px+q=0 are a and b, and x²+qx+p=0 are a and c, then ab = q ac = p a+b = -p a+c = -q b+p = c+q q/a + p = p/a + q (q-p)/a = q-p a = 1 b=q 1+q = -p 1+p+q = 0 Take a crack at part 2.

Riddle
your name

math
now: x and 18-x after 6 more whites: x and 24-x (24-x)/24 = x/8 8(24-x) = 24x 192-8x = 24x 32x = 192 x = 6

Science
well, what's 12% of 400?

general chem
looks like 8/58 to me

MGF 1106
There are 4P2 = 12 ways to fill the accounting positions There are 2P1 = 2 ways to fill the economics position There are 3P2 = 6 ways to fill the marketing positions So, there are 12*2*6 = 144 ways to fill the positions.

Math
Oops. My bad. 4y + 5(x-y) = 5x-y You can think of the party as having x cars of 5 people each, then subtract one person for each of the y cars, which only hold 4.

Math
4y+5x So much for math -- now it's time to ask for help with English.

math
it's easy to construct a 45° angle -- construct a 90° angle and bisect it. For the 5-6-7 triangle, draw the side of 7, and then a circle at each end, of radius 5 and 6. Where the circles intersect is the third vertex of the triangle.

math
250 = 2 * 5^3 175 = 7 * 5^2 so, what's the largest number which divides both 150 and 175? 5^2 = 25

Calculus
v = 2 + 3t when does v=14? now take the integral to get the distance

Physics
C'mon. In these days, you are never blind. A simple web search immediately points to http://farside.ph.utexas.edu/teaching/302l/lectures/node47.html where the whole topic is discussed, and formulas are derived. Surely you have a text for the course, where this is treated. ...

Math 221
(2/9) / (5/12) = 2/9 * 12/5 = 24/45 = 8/15

Algebra
Looks like C to me Note that in the table, y increases by a factor of 49 for each x-increase of 2.

mat/117
If you mean 6/x = 7/x + 3 then x = -1/3 If you mean 6/x = 7/(x+3) then x = 18

calc
I redid the problem using polar coordinates, where I set the (0,0,0) at the base of the paraboloid section, so that z = 4 - (x^2+y^2)/9 That means that we have only to evaluate S = 1/9 ∫[0,2π]∫[0,6] r√(81+4r^2) dr dθ and we get a nice tidy 49π ...

calc
Oops. Oh well. The observation about symmetry still holds. The surface area is just the sum of circumferences of many circles of radius y. So, dS = 2πy ds S = 2π∫[4,8] y√(1+y'^2) dx 9x = y^2+36, so y = 3√(x-4) 18 = 2yy' y' = 9/y = 9/W...

calc
9x = y^2 + 36 I assume you just mean the part above the x-axis, since the curve is symmetric about that axis. So, using discs, the volume is v = ∫[4,8] πr^2 dx where r^2 = y^2 = 9x-36 v = π∫[4,8] 9x-36 dx = π(9/2 x^2 - 36x) [4,8] = 72π Using she...

Math 221
0.05(0.3m + 35n) – 0.8(-0.09n – 22m) 0.05*0.3m + 0.05*35n + 0.8*0.09n + 0.8*22m (0.05*0.3 + 0.8*22)m + (0.05*35 + 0.8*0.09)n 17.615m + 1.822n

Math 221
just apply the distributive property as usual: 2w – 3 + 3(w – 4) – 5(w – 6) 2w - 3 + 3w - 12 - 5w + 30 15

Math 221
2a(a-5)+4(a-5) 2a*a - 2a*5 + 4a - 4*5 2a^2 - 10a + 4a - 20 2a^2 - 6a - 20

Set Theory: Sideways U with a line under it
As you said, 0 is not in the second set, So, the answer is (a): NOT a subset

algebra
look for easy roots first: 1,2,3,5,6 A little synthetic division shows that P(x) = (x-5)(x^2+3x+6) and you can do the quadratic as usual

College Algebra I
no, but I think we can assume that he wants the solution to the system of equations. Michael, you really should ask a question, and not just dump problems into the forum. Also, show where you get stuck. If you truly have no clue, then you cannot have read the material; a probl...

math
so, what did Table 11-1 say?

Algebra
you can see that -2x = 1+4y So, -6x = 3+12y Now substitute that into the 2nd equation and solve for y.

mat/117
already simplified

mat/117
multiply top and bottom by 8-√7 Then note that (8+√7)(8-√7) = 64-7 = 57

mat/117
just do normal expansion of distributed sums: √2(9-√2)+5√2 9√2 - √2√2 + 5√2 14√2 - 2

math
x^2 + 2√2 x + 6 = 0 use the good old quadratic formula: x = (-2√2 ± √(8-24))/2 = (-2√2 ± 4i)/2 = -√2 ± 2i

mechanics
just set 1/2 mv^2 = 36 and solve for v

algebra
I think that would be s slices / 6 plates = s/6 slices/plate 6/s gets ever smaller as the number of slices increases...

math
Hmmm. Seems to me that he lost 4/36 = 11.1% If he'd sold 40, and lost 4, that would be 10%

Set Theory :Complements with Ellipses
simple: A' = {40,41, ...}

geometry
6x5 gives greatest area Just think of the factors of 30, and list them in pairs for the others.

physics
The force was applied in the direction <16,-41,-13> - <11,-35,-7> F=ma gives you the magnitude of the acceleration Then just figure t to cover the given distance, and v = v0 + at to get the final velocity.

math
if the digits are a,b,c,d,e then we have a+b=c b=2a 2b=d e=a+d what is the answer? no idea. What is the question? Hint: it's already given.

Algebra
30c+40t = 270 12c+15t = 105 now, from the 2nd equation we see that 12c = 105 - 15t, so 30c = 5/2 (105-15t) plugging that into the 1st equation, we get 5/2(105-15t) + 40t = 270 5(105-15t) + 80t = 540 105-15t+16t=108 t = 3

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

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 c...

math
correct

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

Math
500(1+.08/2)^(2*15) = ?

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.

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.

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

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...

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, ...

Algebra
correct

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

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

physics
greater than 10+15

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)(...

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

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.

math
The supplementary angle is always 90° more than the complementary angle.

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

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

physics
looks like 25 mph West to me

Algebra
dang typo: y=40

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

Algebra
that's the ticket.

Algebra
evidently 46.5% per time period

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

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...

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

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...

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...

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

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?

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 equatio...

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 equ...

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

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

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.

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.

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

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 ...

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|%...

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 = 1...

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

algebra
I'd guess that depends on the size of the tank.

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

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

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

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.

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

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

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)

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.

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 ...

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.

algebra
3.14 * 1/1000 and you can massage that as you will.

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