Friday
July 25, 2014

Posts by Steve


Total # Posts: 23,952

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.

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.

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.

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

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

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

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

104B
500*2.5*r = 40 r = 0.032

math
19/3x - 20

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.

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.

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

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

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 ca...

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.

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.

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 multi...

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

math
surely you can count days on a calendar...

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 s...

algebra
20m

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.

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

Math
that would be 420/12 = ?

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.

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.

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.

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.

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)

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...

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.

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

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.

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

Pages: <<Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | Next>>

Search
Members