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Posts by steve

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Calculus
dy/(y-2) = x^4 dx ln(y-2) = x^5/5 + ln(c) y-2 = c e^(x^5/5) y(0)=0, so c=-2. y = 2-2e^(1/5 x^5) I suspect you did ln(y-2) = x^5/5 + c y-2 = e^(x^5/5) + c That still does not give your answer. Too bad you didn't show your work ...

Calculus
correct. I'd probably have written it y = 1/16 (x^2 + 11)^2

Algebra
It moved 60° in 10 minute. 11:00 t0 11:40 is 40 minutes. 4 times as long, 4 times as many degrees: 240°

chemistry
10/3 the volume, 3/10 the concentration.

chemistry
0.1L * 0.1M = 0.01 moles Now just convert that to grams.

Algebra
Assuming f is quadratic, start with y = (x-2)(x-4) y(3) = -1 So, multiply it by 2 and you have y = 2(x-2)(x-4) = 2(x-3)^2 - 2

Algebra
many functions meet those criteria, but one of them is given roots: y = (x - (1+?2))(x-(1-?2)) = x^2-2x-1 That has a y-intercept of -1. So, multiply it by 4. It has the same roots, but now y(0) = -4.

MATHEMATICS
correct.

Algebra 2
the y-intercept has noting to do with the asymptotes. Unless the asymptote is the y-axis, in which case there is no y-intercept.

Mathematics
4 painters paint 1 room in 12/3 = 4 hours 1 painter paints 1 room in 4/4 = 1 hour Now you can answer the questions.

Math
too bad you couldn't be bothered to show your work. start: $x CD: 18, leaving x-18 dress: half that, leaving x/2 - 9 lunch:11, leaving x/2 - 20 book: 1/3 of that, leaving (2/3)(x/2-20) = x/3 - 40/3 gas: 12, leaving x/3 - 76/3 CD: 1/4 of that, leaving (3/4)(x/3 - 76/3) = x/...

Calculus AP Exam review explanation pls
#1 a = ?[0,3] (3x-x^2) dx = 9/2 #2 Using either discs or shells, v = ?[0,4] ?(2-x)^2 dy = ?[0,4] ?(2-?y)^2 dy = 8?/3 or v = ?[0,2] 2?(2-x)y dx = ?[0,2] 2?(2-x)x^2 dx = 8?/3 #3 I can't make out the function, but the total distance traveled is the arc length of the path ...

Math
the diet looks linear to me. 1/80 lb/day. A cup of coffee cooling is non-linear. The amount of temperature drop depends on the difference in temperature between the coffee and the room. The cooler the coffee gets, the more slowly it cools. Or radioactive decay is non-linear. ...

maths binomial expansion
1/0! x^(1/3) (y/2)^0 + (1/3)/1! x^(-2/3) (y/2)^1 + (1/3)(-2/3)/2! x^(-5/3)(y/2)^2 + (1/3)(-2/3)(-5/3)/3! x^(-8/3)(y/2)^3 + (1/3)(-2/3)(-5/3)(-8/3)/4! x^(-11/3)(y/2)^4 = x1/3 + 1/6 x-2/3 y - 1/36 x-5/3 y2 + 5/648 x-8/3 y3 - 5/1944 x-11/3 y4

physics 11
the horizontal speed is constant. So, how long does it take to fall 36 meters? h(t) = 36 - 4.9t^2 As to the distance of the boat, it depends on the goal: hit or no hit?

maths
v = 4/3 ?r^3 r = ?(3v/(4?)) a = 4?r^2 = 4? * (3v/(4?))^(2/3) = ?(36?v^2) so, for your sphere, a = ?(36?*9000^2) = 900?(4?) ? 2092

Math
6490 * (71/59) = ?

Struggling on math please help :(
just keep adding/subtracting 360° 47+360 = 407+360 = 767° 47-360 = -313 - 360 = -673°

Rpcc
horizontal velocity is constant. vertically after t seconds, v = -9.8t

maths trigonometry,
Always start by finding the reference angle in QI. Then you can work with angles in the standard position (with one corner at (0,0) and lying on the x-axis). tan ?/4 = 1 tan? is positive in QI and QIII so, the solutions are ? = ?/4 and ?+?/4=5?/4 cos ?/3 = 1/2 cos? is negative...

maths trigonometry
(2cos? + 1)(tan? - 1)=0 see your other post, where you have taken the next step.

calculus
as it stands, I think there's something wrong. you want dt/dx = 0 but since ?n is always >= 0, that means that ?(x^2+a^2) + ?(b^2+d^2) = 0 since even powers are always non-negative, that means that x,a,b,d are all zero. and 0 is not in the interval (0,d)

calc
1/f = 1/p + 1/q 0 = -1/p^2 dp/dq - 1/q^2 dp/dq = -p^2/q^2

Maths
same question: how many 1cm cubes does it take to fill a 6cm cube?

math
Since the 30th minute is at the end of the 1st quarter, there is a 3/4 probability that he missed the goal.

math
350.5 is one possible value

Calculus
read the question carefully. v(0) = 3 you want v to be three times its initial value. 3*3 = 9

math
first, 80% interest is too weird to be real. second, I can't quite figure out just what you're asking. Take a look at what you wrote...

Calculus
well, the line has slope 3. So, where does the curve have that slope? y' = 2e^x = 3 x = ln(3/2)

maths
I'd say separation of variables, since you can write it as dy/y^2 = -(t+t^3) dt ------------------------------------------- next is just direct integration, since you already have dy/dt as a function of t. ------------------------------------------- The last is of the form...

calculus-snell's law
try this discussion: http://dev.physicslab.org/Document.aspx?doctype=3&filename=GeometricOptics_LeastTime.xml

math
D because you did not show the data ...

math
actually, since there is only one variable, there is no direct variation. If you meant -4+7x+4 = y then y = 7x is a direct variation.

Maths
using a weekly rate for simple interest, you want p*rt = 1500 50000*(.06/52)t = 1500 t = 26 makes sense, since you will earn 6% of 50000 = 3000 in a year.

calculus
ok, Sam/Maggie, see whether you can set up the needed integrals, and show what you tried.

calculus I
at x=h, the tangent line to the parabola is y - (3-h^2/10) = (-h/5)(x-h) y = -h/5 x + 3+h^2/10 So, find where the line intersects the circle, and find h so that there is only one solution. It might be useful to pick a value of x close to what you expect, and then use an ...

geometry
tan 36° = 0.7265 x^2+y^2 = 25^2 y = 0.7265x x^2 (1 + 0.7265^2) = 25^2 x = 20.2258 p = 2(x+y) = 2(20.2258 + 14.6949) = 69.8414

linear approximation
You want to pick a value of cos(x) where x is near 2?/13, and you know what it is. you know cos(?/6) = ?3/2. 2?/13 = ?/6 - ?/156, which is pretty close to ?/6. cos(2?/13) ? cos(?/6)+(-sin(?/6))(?/156) = ?3/2 - (1/2)(?/156) = 0.8560 the true value is 0.8855 That seems kind of ...

calculus
using shells of thickness dx, and taking advantage of symmetry, v = 2?[0,1] 2?rh dx where r=1-x and h=y=?(1-x) v = 2?[0,1] 2?(1-x)?(1-x) dx = 4??[0,1] (1-x)^(5/4) dx = 16?/9 using discs (washers) of thickness dy, we have v = 2?[0,1] ?(R^2-r^2) dy where R=1 and r=1-x v = 2?[0,1...

Math related rates
if the water depth is h, the radius of the surface is 2/3 h. So, the volume of water is v = 1/3 ?r^2 h = 1/3 ? (2/3 h)^2 h = 4/27 ?h^3 dv/dt = 4/9 ?h^2 dh/dt plugging in the numbers, 3/2 = 4/9 ?*2^2 dh/dt dh/dt = 27/(32?) Too bad you didn't bother to show your work...

Algebra 1 - Help!?
think about it. If a line has a nonzero slope, it extends forever, both left-right and down-up. So, the domain and range are both All Real Numbers. To sketch the graphs, just pick two values for x, figure the corresponding values for y, plot the two points, and draw the line ...

maths
(?*14.642 km)/(50/60 hr) = 55.2 km/hr

math
Your mistake happened early. You said 5x+3y=2 eq.2 X=-3y/5 but really x = (2-3y)/5

Precalculus
it's an exponential function.

math
I'm not talking about angles, but sides. Remember the Pythagorean Theorem? a^2 + b^2 = c^2

math
LM = ?(5^2+3^2) = ?34 LN = ?(4^2+1^2) = ?17 MN = ?(1^1+4^2) = ?17 So, it is isosceles. But since ?17^2 + ?17^2 = ?34^2 17+17 = 34 it is a right triangle.

math
Somehow you messed up the final answer. It is just 15w^3 + 25w^2x - 5wx^2 There are no wx terms anywhere.

math
pyramids have a base and one top vertex prisms have two parallel bases. so, ...

Calculus
As above, using discs of thickness dx, v = ?[0,ln3] ?(R^2-r^2) dx where R=y and r=1 v = ?[0,ln3] ?((e^(x/2)^2-1^2) dx = ?[0,ln3] ?(e^x-1) dx = ?(2-ln3) or, using shells of thickness dy, v = ?[1,?3] 2?rh dy where r=y and h=ln3-x v = ?[1,?3] 2?y(ln3-2lny) dy = ?(2-ln3)

calculus- optimization
base = 2x height = y = ?(4-x^2) a = 2x?(4-x^2) da/dx = 4(2-x^2)/?(4-x^2) da/dx=0 when x = ?2 so, max area is 2(?2)?(4-2) = 4

Math
don't know about the triangles, but the rectangles' areas are clearly in the ratio 25:240

Math
well, which is larger/smaller?

math
the other angles are 11x and 17x. So, 11x+17x+40 = 180 find x, then you can get the other angles.

Math
as always, draw a diagram. Label the lighthouse L, and the two ship positions S and N. Draw an E-W line from L to SN, intersecting at P. SP = 15.5 cos40° PL = 15.5 sin40° PN = PL cot54.9° The ship has sailed a distance of SP+PN

Math
(6x^3y)(8x^2y^4) = 48 x^5 y^5 now just plug in your values...

Math plz help
rewrite them all as just radicals, and then it is easy to compare them: 1. -?18 2. ?9 3. ?12 4. -?28 or, convert to decimals, but that's more work...

Math
3^4?2 81?2 4?(81^2/16 * 2) 4?(6561/8) somehow I doubt that's what you were after if by 4?n you mean 4th root (?n) I'm also confused. 3^?2 is trés bizarre. Try again using ^ for exponents and ? for square root, and ? for 4th root.

Math
just subtract the exponents of y. y^7/y = y^6 take it from there.

Math
do you mean (7^3)?32 or 7^(3?32) ? in either case, just type it in at wolframalpha.com

Math
I suspect you mean p = 100(0.5)^(t/20) So, plug in t=30

Math
You could go through the math of finding the side lengths of all six sides, and comparing them, but these are easy to figure out if you just plot the points. Then its easy to see that ABC is a 3-4-5 right triangle. Now take a look at DEF.

Math
You are correct. Whoever said it was 0.402 was nuts. Or there are some serious typos in the problem.

Chemistry
Would the percent yield of Ni(NH3)nCl2 be high, lower, or unchanged if you made the following procedural changes? a) You performed the synthesis reaction at 100 degrees instead of 60 degrees b) you dissolved the NiCl2*6H2O in 50 mL of distilled water instead of 10mL c) You did...

Trigonometry
A = (ab sinC)/2 so, how do you get C? sinA/a = sinB/b Now, having A and B, C is easy, since they add up to 180°

Math
if xy is constant, it's inverse. xy=k If y/x is constant, it's direct. y=kx So, take a look and see what you find.

Aditi
There are 4C2 = 6 ways to choose the two required biographies. That leaves 8 other books, with 8C2 = 28 ways to pick them. So, there are 6*28 = 168 ways to pick 4 books as required.

Trigonometry
after t hours, the distance d between the hikers is d^2 = (.24t)^2 + (.17t)^2 - 2(.24t)(.17t)cos109.167° so, find t when d = 0.0568182 I get about 10 minutes. The radios aren't much use, I guess...

Geometry
eq. 1 says 2y = 3x+23 use that in eq. 2 and you have 5x + 3x+23 = -17 for elimination, this web site gives all the details: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

Geometry
since ?x^2 = x, you want to factor out all the perfect squares. 224 = 16*14 so, ?224 = ?(4^2 * 14) = 4?14

Calculus
google is your friend. You can find what you need here: http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeProofs.aspx

maths
a + ar^4 = 34 ar * ar^2 * ar^4 = 512 a(1+r^4) = 34 a^3 r^7 = 512 Looks kind of messy, but since the only factors of 34 are 2 and 17, it appears that a=2 and r=2 I think the second condition should have used the 4th term, rather than the 5th. If so, then since 2^9=512, that ...

calculus
if w has a max at t0, dw/dt = 0 at t0. so, (f'(t0)(c+t0)-f(t0))/(c+t0)^2 = 0

Maths
p(man) = 3/4 p(woman) = 1/4 ...

Maths
doing selection without replacement, the chance is 1/5 * 1/4 * 1/3 = 1/60 or, since there are 5P3 = 60 permutations of 3 of the 5 letters, and only one of them spells BED, the chance is 1/60

Calculus
I assume you have drawn a diagram of the situation. The length z of cord when the kite has flown to a horizontal distance x is z^2 = x^2 + 135^2 so, z dz/dt = x dx/dt Find x when z=285, and you can find dz/dt.

calculus
Think of the solid as a stack of thin squares. At a distance y from the origin, the square has side 3y. So, add them all up and the volume is ?[0,3] (3y)^2 dy

Calculus
horizontal tangents occur when dy/dx = 0 vertical tangents occur when dx/dy = 0. dx/dy = -(x+2y)/(2x+y), =0 when x = -2y and you get Reiny's answer.

Chemistry
(16.22mL) * (1L/1000mL) * (0.100 moles/L) = ? moles

Math
12^(1/4) = ?12 (-50)^(5/3) = ?(-50)^5 just remember that the nth root is the 1/n power since ?x * ?x * ?x = ?x^3 = x, expressed as powers, you need x^(1/3) * x^(1/3) * x^(1/3) = x^(1/3 + 1/3 + 1/3) = x^1 = x

Math
we've done a bunch of these -- how about you take a stab at these first?

Calculus
recall that the average value of f(x) on [a,b] is (?[a,b] f(x) dx)/(b-a) now just plug and chug.

computer programming
x=0 i=0 sum=0 while x ? -1 read x if x ? -1 { v[++i] = x; sum+=x } end while print i if i==0 exit avg = sum/i print avg for j=1..i print v[j],v[j]-i you can add any labels you see fit for user interaction.

cal
A little synthetic division will get you -2 as a solution. Further information is here: http://www.wolframalpha.com/input/?i=x%5E5-3x%5E3-x%2B6

Geometry
Hmmm. I can't seem to make them out ...

Math
well, he used the distributive property of multiplication...

cal
Nope. Show your work, and we can see what went wrong. Don't forget your Algebra I now that you're taking calculus...

cal
recall that the average rate of change on [a,b] is (f(b)-f(a))/(b-a) now just plug and chug.

Math - implicit differentiation
5x^2 + 2x + xy = 2 10x + 2 + y + xy' = 0 Now just plug in your numbers and solve for y'.

Math
24 kids get evenly bitten by 1152 ants. How many bites did each one get?

math 1
so, y = -1 now you can find x.

math
1 wafer = 64/4 = 16 grams 3200/16 = ? wafers/box

math 1
so, you got x=1 Use that in the other equations and see whether you get the same value of y for each. If so, then that x and y are the solution.

Math grade 6
so, what's the volume of one block? ya gotta start somewhere, eh?

math
Jim, Bob, Walk-Fast

Intermediate Algebra
copy/paste of special symbols doesn't work too well here. On the other hand, parentheses () and +-/* operators work just fine, as does the caret ^ for exponents, as in t^2. Not sure how "​" appears to you, but it...

Math
? means the 1/2 power. As with any exponents, powers of powers multiply exponents. ?(3^5) = (3^5)^(1/2) = 3^(5/2) (?3)^5 = (3^(1/2))^5 = 3^(5/2) Now try your problems.

Pre Calculus
#1 There are two 8's, so while there are 6! permutations of the six digits, in any one of them, the two 8's can be swapped, and it's still the same arrangements. Same for the 5's. So, there are only 6!/(2!2!) = 180 distinguishable arrangements. The same caveat ...

Enough Already!
check your first post.

Math
the base has area ?(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 so the area of the base is ?(15.075(15.075-14.4)(15.075-8.25)(15.075-7.5)) = 22.936 so the volume is 22.936*2.1 = 48.1656 I suspect a typo somewhere. Or I misinterpreted the description.

Algebra
well, a = -15 and d = -8 now use the formula for the general term of an AP.

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