Saturday
April 19, 2014

Posts by STEVE


Total # Posts: 21,780

Math
pi*(15/2)^2

Please help!
f(x-12) shifts the graph right by 12 units. (Now all the x-coordinates are 12 less than they were...) g(x) = f(x-12) = ((x-12)+10)^2 = (x-2)^2

Calculus
y = e^x (c1 + c2*x) y' = e^x (c1 + c2 + c2*x) Now plug in the initial conditions to get e^2 (c1 + 2c2) = 0 e^2 (c1 + c2 + 2c2) = 1 Now just solve for c1 and c2

Maths
excluding the twins means only 27 people are available. So, C(27,4) is the number of teams possible.

Calculus
y = c1 e^-6x + c2 e^x Plug in your boundary conditions, and you get c1 + c2 = 0 c1/e^12 + c2/e^2 = 1 Now just solve for c1 and c2

AP Calculus
∫[a,b] x^2 dx = 1/3 x^3 [a,b] = 1/3 (b^3 - a^3) Consider only integer values. Then that will give you a^2 + (a+1)^2 + ... + (b-1)^2 + b^2 Now, we know that n ∑ k^2 = n(n+1)(2n+1)/6 k=1 So, we want sum from a-b = sum from 1-b - sum from 1-a, or b(b+1)(2b+1)/6 - a(a+...

AP Calculus
each cross-section has base 2x and altitude x√3 So, we want to add up all those triangles v = ∫[a,3] 1/2 * 2x * x√3 dy = √3 ∫[a,3] x^2 dy But, y = |x| + a y-a |x| (y-a)^2 = x^2 v = √3 ∫[a,3] (y-a)^2 dy and now it's cake, right?

Trigonometry
2sinx cosx = cosx cosx(2sinx-1) = 0 so, where do you have cosx = 0 sinx = 1/2 ??

Calculus Help
actually, I see I did forget to include a factor of 1/(x^2+x+1) in the first term. Dang! Luckily, it's not my job to fix it!

Calculus Help
log y = log (e^-x - xcos^2(x)) - log(x^2+x+1) 1/y y' = (-e^-x - (cos^2 x - 2xcosx*sinx))/(e^x - xcos^2 x) - (2x+1)/(x^2+x+1) y' = (-e^x - cos^2 x + xsin2x) - (2x+1)/(x^2+x+1)^2 If you want to put it all over the common denominator, it gets fairly messy on top.

mat 116
(2x)^3 + (2^x)^3 that's a sum of cubes, so (2x + 2^x)((2x)^2 - (2x)(2^x) + (2^x)^2) (2x + 2^x)(4x^2 + 2x*2^x + 2^2x) I'm not sure that's any simpler. Maybe you just wanted 8x^3 + 2^3x ?

Calc
no big deal f = ln (ln ln x) f' = 1/(ln ln x) * (1/x * 1/ln x) = 1/(x(lnx)(ln lnx))

Physical Science 9
when an electric current is passed through water 2 gasses are formed is this a chemical or physical change

math
No genius required. Just use your favorite numerical method to find the root: x^.223 - x^.123 - 1 = 0 x = 92.6740 Newton-Raphson is a likely one for this, since the curve is nice and smooth

Physical Science 9
How would you separate a mixture of iron fillings , salt, sand, and wood chips

Physical Science 9
when exposed to the same amount of heat for the same amount of time, a 3 g sample of copper will experience a greater temperature change then a 12 g sample of copper due to its smaller what?

Physical Science 9
a substance made of two or more elements chemically combined in a set ratio or proportion is called what

Physical Science 9
the contents of a can of air freshener are gaseous when sprayed but remain a liquid in the can due to what?

calculus
for shells, we need to integrate on y, since the area is rotated about a horizontal line, and the shells have thickness dy v = ∫[1,2] 2πrh dy where r = y-1 and h = x = ln y v = 2π∫[1,2] (y-1)lny dy Just use integration by parts to evaluate it.

Science
a substance made of two or more elements chemically combined in a set ratio or proportion is called what

Science
when molecules of water vapor in the air come into contact with a cold can of soda they lose energy slow down and form a liquid due to a decrease in what?

basic college math
in questions like these it is usually to find where the two deals are equal in cost. Or, equivalently, for how many miles is deal A cheaper than deal B. The cost the same when 25 +.4m = 30 + .25m Now just solve for m

Science
do pure substances have different chemical and physical properties?

Science
Particles have enough energy to break free from each other and can move around freely; particles spread out in different directions solid liquid gas molecule my answer is molecule

maths
as we all know, x=2

math
time to review the quadratic formula, or follow Damian's excellent advice about online solvers.

Algebra
S = {a,b} 89+45 = 134 So, the extra 14 students must play both games

MATH 104
how about 24/244 ?

algebra
since 2003 is half-way between 2002 and 2004, its cost will be half-way between the costs for those years. by the way, the number half-way from a to b is a + (b-a)/2 = (a+b)/2, the average of a and b.

math
max at x = -13/(2* -.5) = 13 Now just evaluate N(13)

cal
f(3/√2 , 2√2) = 24

math
cone: ok pyramid: v = 1/3 Bh = 1/3 * 81 * 4 = 108 B is the area of the base, not the side length

Introduction to Computers
You have probably used 3 of these devices, and no information was lost. The other is your computer's internal memory, which loses all data when the computer is shut down.

Algebra
x(x-3)(x+8)

Algebra Question~!
(x+10)(x-3)

Math
1C 40 people will or might attend 2A 285/3.75 = 76 jumps/min

cal
for ∂/∂z, enter http://www.wolframalpha.com/input/?i=d%2Fdz+%283x^2z-x^2y^2%2B2z^3%2B3yz-5%29

geometry
False - just two external tangents

math
apparently 2x+3x+4x = 25+70+49 9x = 144 x = 16 So, A:B:C = 32:48:64 Now figure the shortfalls.

math
(a-b):(a+b):ab = 1:4:15 (a-b)/(a+b) = 1/4 4a-4b = a+b 3a = 5b (a-b)/ab = 1/15 15a-15b = ab 15a-9a = a(3a/5) 30a = 3a^2 a = √10 b = 3/5 √10 15a+15b = 4ab 15a + 9a = 4a(3a/5) 120a = 12a^2 a = √10 a-b = 2/5 √10 a+b = 8/5 √10 ab = 6 = 30 * 2/5 √...

algebra
just google scatter plots electricity bill and click on images. Lots of examples.

physical science
seconds

science
even if you don't know #1, it's evident from the other questions that this is an exercise set involving matrices. #10: a=2 Now, what ideas do you have on the others?

Math
sorry; that's the angle between the diagonal and a side of the rectangle. so, draw a diagram, and the angle you want is Ø, where 2θ+Ø = 180

Math
tanθ = 130/170 or, for the other angle, tanθ = 170/130

kinridg
there are 1/8 left, so that's 3 half-lives

chemistry 101
How many grams of bromine are in 1.57 grams of phosphorus tribromide?

Math, Please Help!
he has n/3 + 2 he wants 3n - 2 to get the 3n, he needs to multiply by 9. That will give him 3n+18 So, then he needs to subtract 20.

Calculus
Hmmm. I get 10x-15y = 75 http://www.wolframalpha.com/input/?i=plot+x^2%2B4y^2%3D36+and+y%3D3+and+10x-15y%3D75

Calculus Help and Check
x^5(x + y) = y^2(9x − y) 5x^4(x+y) + x^5(1+y') = 2yy'(9x-y) + y^2(9-y') 5x^5+5x^4y + x^5 + x^5y' = 18xyy' - 2y^2y' + 9y^2 + y^2y' y'(x^5 - 18xy - 3y^2) = 9y^2 -6x^5 - 5x^4y y' = (9y^2-6x^5-5x^4y)/(x^5-18xy-3y^2) you were close, but mus...

algebra
ummm. No 1.1(5) = 5.5 5.5+1.7 = 7.2 c = 1.1d + 1.7 Did you even try your formula against the data?

algebra
If the formula is c=ad+b, then 5a + b = 7.20 9a + b = 11.60 Solve for a and b. Or, note that as the distance increased by 4, the cost increased by 4.40 So, the slope is 1.1 That eliminates two of the choices right away. Now just see how much extra there is in each case when mu...

Chemistry
half the concentration means twice the volume. so, add another 600.0 mL of H2O

Math
slope is y-change/x-change so, as x changes by 2 each time, y changes by -3. So, the slope is ...

I need help (Physics)
PE = mgh = 28*9.8*159 KE = 1/2 mv^2 = 1/2 * 28 * 31.3^2 Because of friction, not all of the PE changed to KE. Subtract to see how much energy was lost.

algebra
Try actually plugging in the points to see which equation fits! Or, arrange the points from left-to-right: (-4,-3) (-2,1) (0,5) (1,7) (3,13) as x changes by 2, y changes by 4 (except for the last one - typo?) It appears that none of the choces will work.

Mathematics
60 = 14*3 + 18 So, 14 will do the trick if they have 3 chickens each.

math
(x-6)(x+3) = 0 for the product to be zero, one of the factors must be zero.

math
so, add up the taxes: .18+.124+.029 = .333 Since it's a quarterly return, .333/4 * 20640 = 1718.28 Now, how about showing some ideas on the others you posted?

Math
when the lines are the same. 2x-y = 5 Hmmm. a typo - no y term in the 2nd equation. Anyway, since there are 8x, the same line would be just 4 times the other. 8x - 4y = 20 Looks like a=10

Algebra
#1: N = {1,2,3,6,9,18} --------------- #3: subsets of {2,9} are {},{2},{9},{2,9} Now, how about showing some of your ideas on the other problems?

math
Hmmm. I think I mean 1 : 5/6 : 2/3

math
(2/5) : (1/3) : (1 - 2/5 - 1/3) 1 : 6/5 : 3/2

pragati
since angle B is a right angle, AB is the height of the trapezoid. So, the area is (16+40)/2 * √(41^2 - 40^2)

Calculus
(-4,185°) (-4,-75°) got any more?

math
best to use shells here: v = ∫[0,2] 2πrh dx where r = 3-x and h = y = x^3 v = 2π∫[0,2] (3-x)x^3 dx Simply polynomial, so just plug and chug.

pragati
a = (42+54)/2 * √(19^2 - 12^2)

math
You won't find any diagrams here, but division is just a shorthand way to subtract. 2.6/.4 tells you how many times you can subtract .4 from 2.6 without passing zero. 2.6 - .4 = 2.2 2.2 - .4 = 1.8 1.8 - .4 = 1.4 1.4 - .4 = 1.0 1.0 - .4 = 0.6 0.6 - .4 = 0.2 Now you must sto...

Calculus Help
#1: 2y y' = 2x + 0 #2: 2y y' + ay' = 2x + a + 0 just solve for y' in each case.

math
what's the smallest number that is a multiple of both 2 and 3? And for 8 and 10?

Algebra
slope is (-8-4)/(3 - -3) = -2 Now plug in the point-slope form: y-4 = -2(x+3) Now it's easy, right?

science pls help
correct. At least it appears you can match up the provided answers with the lists of choices...

science pls help
Looks like you need to brush up on one of the most basic and useful identities in mechanics: F = ma F(N) = m(kg) * a(m/s^2) 1 N = 1 kg-m/s^2 So, with that in mind, #1: F = ma = 40kg * 10m/s^2 = 400 kg-m/s^2 = 400N #2: F = ma = 60kg * 2m/s^2 = 120N Note that you can eliminate t...

Math
after n hours, 1+3+3^2+3^3 + ... + 3^n = (3^n - 1)/2 people have heard the joke. So, we want n such that (3^n - 1)/2 = 8500 3^n = 17001 n = 8.8666 hours = 8 hrs 52 min

Math
7*8*4 = 56*4 = 224 recall that using a variable, 7x * 8x * 4x = 224x^3 Now, using units, 7ft * 8ft * 4ft = 224 ft^3

Math
did you multiply the three dimensions? If so, what did you get? If not, what's the problem?

Math - Answer Check
I'd say #15 is right, since you were given 180,000 inches. 2.84 miles is close enough, IMO.

Math - Answer Check
#12. a mile is 5280 ft, not 5820 The rest look ok (including #15!)

MATH
1/5 is correct 1/4 may be correct, but only if there is exactly one white sweater in the bunch.

Pre-Calculus
r = 5sinθ r^2 = 5r sinθ x^2+y^2 = 5y x^2 + (y - 5/2)^2 = 25/4

Pre Calculus
rcosθ = 3 r = 3secθ

MATH
but 1 is not a prime. It is explicitly excluded from the list of primes.

Geometry
recall that if the legs of a right triangle are a and b, and the hypotenuse is c, then the Pythagorean Theorem states that a^2 + b^2 = c^2 So, the height of the triangle is 12 There are several commonly used right triangles which you would do well to commit to memory: 3-4-5 5-...

Geometry
5^2 + height^2 = 13^2

Which compound is made up of three elements?
Do you know how to count the elements in a chemical formula?

algebra
hint: y = -4/6 x + 2

math
Hmmm. of the 11 numbers, how many are NOT 23?

math
So, P(violet, pink, or blue) = V+P+B

math
assuming that what was meant is that the jar contains ONLY green and purple marbles . . . I think we can say that, but it's also possible that other marbles were not mentioned. Read Heinlein's Stranger in a Strange Land. One of the characters is a professional observer...

math
correct

Probability - Math
total junior or seniors / total students (.16+.24)/1.00 = .40 Those who live in the dorm: (.16*.30 + .24*.20)/1.00 = .096

Science
hint: both correct choices involve only water

math
now you're cookin' (aside from that pesky 32!)

math
ummm, 6+7+26+13 = ?

math
number 2 is ok #1. Come on! The numbers are 1,2,3,4,5,6 only FOUR is divisible by 4! P(4) = 1/6

math
If there are 6 numbers on the die, how many of them are multiples of 4? I think not 2. How many numbers are there from 16-23? Remember to count both 16 and 23. #3 ok

Calculus
well, x^2/(2logx) = x^2/log(x^2), so if you can figure out the limit of x/logx, you're ok. Since x->0 and logx->-∞, x/logx -> 0/-∞ = 0 -------------- e^-x -> 0 as x->∞, so the upper limit -> 0 e^0 = 1, so the lower limit -> 2

Math
well, the factors of 18 are 1,2,3,6,9,18 The -21 in the middle makes me think that 2,9 will be likely, so (4x+9)(x-2) gives +x nope (2x+9)(2x-2) gives +14 Hmmm. That pesky 4. So, (4x+3)(x-6) : -21x YAY!

Math
after the 1/3, she had 2/3 left 1/2 of that is another 1/3, so if she started out with x, x - x/3 - x/3 = 6 x = 18 check: she spent 6, had 12 left. she lost half of 12, or another 6, leaving her with just 6.

Math
yes

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