# Posts by steve

Total # Posts: 52,076

**Physics**

well, KE = 1/2 mv^2

**Math**

each octave up doubles the frequency

**computer science**

sum=0 max=0 min=9999 for i=1,12 read amount month[i] = amount if amount < min then min = amount if amount > max then max = amount sum += amount end for avg = sum/12

**MAth**

looks good to me.

**MAth**

I'd say the one which is not showing two sets of data.

**physics**

just add up the KE before and after the collision.

**Mathematics**

As long as we're dividing by zero, what about 0/0? Why is it undefined? Suppose there is a value x such that 0/0 = x Then, multiplying by zero, we get 0 = 0*x But that is true for any value of x. So there is no particular value we can say is equal to 0/0.

**Please help with MATH**

why not post your solution to the first part, and we can see why this change is important?

**geometry**

32 * 26? in * 1ft/12in = 217.817 ft

**math**

correct. a person can determine the miles walked. After that, the calories follow.

**Math**

.03 * 27700

**math**

there are only 2 colors. 3 socks must have two of the same color...

**math**

correct

**Math - Calculus**

Actually, the shape does not matter for this question because it asked about the rate of flow through the channel. I suspect there were other parts where we'd have to work with the volume or depth in the bay, but not here.

**Math - Calculus**

just find the derivative dd/dt the shape of the bay does not matter for this question.

**math**

just divide and you get x+4 + 9/(x-2) So, as x gets huge, the 9/(x-2) vanishes, and the graph approaches the line y = x+4

**Math(Calculus)**

well, x^2-4 has a minimum at x=0, so e^(x^2-4) will as well. since x^2-4 has an absolute max at x=±2, so does e^(x^2-4) But, as long as this is calculus, dh/dx = 2x e^(x^2-4) dh/dx=0 at x=0 (minimum)

**Algebra**

Since F=ma, a = 8x/m. So, we have a(x) = -8/m x v(x) = -4/m x^2 + c1 s(x) = -4/3 x^3 + c1*x + c2 v(0) = 0 and s(0) = 10, so s(x) = -4/3 x^3 + 10 For the damping, just work with v(x) = -4/m x^2 + 8v and follow through to get s(x)

**Calculus**

Since the y-axis is also the axis of symmetry for the curves, we can just take one side and revolve it. This will be easiest using shells of thickness dx: v = ?[0,2] 2?rh dx where r=x and h=(8-x^2)-x^2=8-2x^2 v = ?[0,2] 2?x(8-2x^2) dx = 16?

**Math**

x = 3+4cos? y = 2+4sin? since cos^2? + sin^2? = 1, (x-3)^2 + (y-2)^2 = 4^2

**grades**

no way to tell all we know is that 15 students got above 74% and 15 got below 74%

**math**

x grows by 2 the slope is 2, so y grows by 4. so, y=2+4=6 or, more formally, (y-2)/(3-1) = 2

**Math**

each term is calculated using the previous term, not the next one!

**Calculus - Fundamental thm of Calc**

that would be ((1/4)(x^2)^2?1)^15 * 2x = 2x(x^4/4 - 1)^15

**Calculus - Related Rates**

Let the distance on the road be x. Then the distance z to the house is z^2 = x^2+25 z dz/dt = x dx/dt z(1) = ?26 ?26 dz/dt = 1 * 65 ...

**Calculus Help**

google hole in sphere. You will find many excellent discussions.

**Math**

well, you have a base perimeter of 30. So, the base of each triangular lateral face is 30/4 = 7.5 Now you can see what the side edges of the pyramid are, and there are four of them. let 'er rip...

**math**

reimburses? Did the doctor pay the patient something?

**maths**

L = km/h^2 So, Lh^2/m = k is constant You want L such that L*50^2 = 40*h^2/175 If you will supply the original height, then you can solve for L.

**math**

I don't see any graph ...

**algebra**

#1 The line of symmetry of y=x^2 is the y-axis (x=0). Similarly, for a translated parabola y=a(x-h)^2 + k the axis of symmetry is the line x=h. So, for y = -2x^2+3 the axis is x=0 #2 same for |x|. So, for y = 1/3 |x| - 2 the axis is x=0 #3 Huh? This stumps you? P(4,-4)-->(-...

**math**

I suspect there was meant to be a question in there somewhere, but I couldn't see it ...

**Math**

not mixed numbers. As a fraction, 87.3/8.73 = 10*8.73/8.73 = 10/1 = 10 In case you wanted individual fractions, 87.3 = 873/10 8.73 = 873/100

**Math**

I think Natavia is right. If P = 1/26 that is the theoretical probability. No mention is made of actually performing the experiment.

**Math**

recall that alternate interior angles between parallel lines are congruent. Draw a line through one vertex parallel to the opposite base. the rest is easy.

**Math**

4 * 1/4 = 1

**Math**

6 * 2/3 = 4

**Math**

4/12 = 2/6 = 1/3

**Intermediate Maths**

(a) 12(1/2)^(t/5700) = 10 t = 1499.3 years (b) 12(1/2)^(1599.3/5700) = 9.879 grams

**calculus please help!!**

The region is a semi-circle of radius 6, so the area ranges from 0 to 18? The integral is the area moving from the left side to some point x in [-6,6].

**Pre calculus**

set this up as a geometric series and then just apply the sum formula. a = 2 r = 0.9 allow for round trips up and down

**Probability**

to start out, there are 13 diamonds in 52 cards. As you draw the cards, the probabilities change, due to the makeup of the remaining cards. The result is 13/52 * 12/51 * 11/50 * 10/49 = (13*12*11*10)/(52*51*50*49) = 13P4/52P4

**Calculus**

A,C,D are true. The Intermediate Value theorem says that there is a zero in (-2,1) and (1,4) Rolle's Theorem (or MVT) says that f'(x)=0 somewhere in (-2,4) Mean Value Theorem says D is true

**Math 1**

I must say, these problems of yours are some cumbersome. I'm not sure they are teaching much about factoring, since most of them only have a single monomial common factor. Like this one: 48x^3 - 128x^2 -56x -16 8(6x^3-16x^2-7x-2)

**Math 1**

392n^4 + 168n^3 + 168n^2 +72n 8n(49n^3+21n^2 + 21n+9) grouping gives 8n(7n^2(7n+3)+3(7n+3)) 8n(7n+3)(7n^2+3)

**Math 1**

5x(16x^3-12x^2-12x-9) 5x(2x-3)(8x^2+6x+3) the discriminant of the quadratic is negative, so it has no real factors.

**Math1**

The x^2 is easy: 195x^5 + 168x^4 - 28x^3 - 24x^2 x^2(195x^3+168x^2-28x-24) Now things get tough. If there are any rational roots of the form p/q, then we know that p divides 24 q divides 195 Some time and effort should convince you that there are no other rational roots, so no...

**Maths ( Higher Level) Simultaneous Equations.**

the method is just to write the words as math: mother is x years old, her son is y years old and the sum of theirs ages together is 58 x+y = 58 Five years ago, the mother was five times as old as the son (x-5) = 5(y-5) Now it's easy! x+y=58 x-5y = -20 subtract and you get ...

**algebra 2, check my answer plzzzzzz**

x = 5y^3 x/5 = y^3 y = (x/5)^(1/3) Or, if you insist on rational denominators, y = (25x)^(1/3)/5 your notation would seem to indicate 3?(25x)/5 rather than cubrt(25x)/5 = ∛(25x)/5

**Check my math question please? Very urgent!**

correct

**Math**

5/8

**Math**

well 45/3 = 15 = one-third of the bag. So, ...

**Math**

well, each foot of rope has 3 pieces, right ? 1 foot = 3/3 So, how many in 8 feet?

**Math**

42

**Math**

If b is breaths, then 10^9 b * 1min/16b * 1day/1440min * 1yr/365day = 118.9 years This makes sense, since 1 billion seconds is about 30 years.

**Functions (Math)**

Draw the angle. It should be clear that y = -5 x = 2 r = ?29 Now just recall that sin? = y/r cos? = x/r tan? = y/x now let 'er rip

**MATHS**

Note that ?STP is similar to ?RTS and angle SRT = angle TPQ (alternate interior angles)

**Calculus**

dy/dt = k/y y dy = k dt 1/2 y^2 = kt + c y^2 = 2kt + c y = ?(2kt+c) E does not work, as you can easily see: y = ?(2kt)+4 dy/dt = 2k/(2?(2kt)) = k/?(2kt) but that is not k/y = k/(?(2kt)+4)

**calculus**

just plug and chug. The surface can be thought of as a stack of thin rings. A = ?2?r ds where r=y and ds=?(1+y'^2) dx so, y' = (9x^4-4)/(12x^2) A = 2??[1/2,1] (x^3/4+1/(3x))*((9x^4+4)/(12x^2)) dx = 1981?/3072

**Calculus (trig derivatives)**

Draw a diagram. It is clear that when the distance of the beam from the point P on shore nearest the lighthouse is x, tan? = x/2 sec^2? d?/dt = 1/2 dx/dt when x=4, we have (1+(4/2)^2)(2?/20) = 1/2 dx/dt dx/dt = ? mi/s

**MATHS**

Since the bisector meets BC at a 45° angle, CB=PB = 15 so AP=25-15=10

**Mathematics**

on each trip, walk = 1/3 bus = 2 3/4 - 1/3 = 2 5/12

**math**

the hexagon has an apothem a=9. so, its sides are s=6?3 Now, you know how to find the area of a hexagon of side s. The area A of the pyramid is just A=6(sa/2) The volume is 1/3 (area of hexagon)*42

**Math**

Let Ø = angle to bottom of picture ? = angle subtended by the picture x = distance from wall to observer tanØ = 4/x tan(?+Ø) = 9/x so (tan?+tanØ)/(1-tan?tanØ) = 9/x (tan?+(4/x))/(1-(4/x)tan?) = 9/x see what you can do with that. or, if y=...

**Calculus**

g'(x) = ?((x^2)^3+2) * 2x now just plug in x=2

**Alg II COT**

cot ?/6 = ?3

**Alg II COT**

google radicals and examples

**Math**

true

**programming**

there are lots of sort routines you can find online. So, this will accept an arbitrary number of names: n=0 name="x" while name ? "" read name if name?"" then names[n++] = name end while snames = sort names,n while n>0 print names[n--]

**trig**

(4cosx+1)(2cosx+1) = 0 now it's a cinch...

**maths**

There are 11P4 ways to pick the pained boats.

**Maths**

well, all the 400's and all the 900's and all the 40's & 90's of the other 8 hundreds and all the other 8 numbers ending in 9 for the other 8 hundreds

**maths**

a set of n elements has 2^n-1 non-empty subsets

**Algebra**

correct

**Math**

The way you have written it is incorrect. It should be 4tanx(1-tan^2(x)) ----------------------- (1+tan^2(x))^2 = 4tanx/(1+tanx^2) * (1-tanx^2)/(1+tanx^2) = [4sinx/cosx * secx^2][(1-tanx^2)/(1+tanx^2)] = (4sinx cosx)(1-tanx^2)/secx^2 = 2sin2x (cosx^2-sinx^2) = 2sin2x cos2x = ...

**Math**

take sin of both sides and use your sum and double-angle formulas to get a polynomial in x sin(2arcsin(x/?6)+arcsin(4x)) = 1 x = ?39 - 6 see http://www.wolframalpha.com/input/?i=sin(2arcsin(x%2F%E2%88%9A6)%2Barcsin(4x))+%3D+1

**Maths**

well, 22 tens is 220 ...

**algerbra**

looks ok to me, aside from using "square of" to mean "square root of"

**Math**

use a common denominator. Then you have 12/28 + 7/28 not so hard now, eh?

**algerbra**

right on.

**geometry**

their areas are in the ratio 2:3:4

**Math**

wrong in so many ways. First, 1.00 is 100% .609 = 60.9% so, 2.608 = 260.9% But you read the question wrong. You know that 2 is 50% of 4, right? So, you divide 2/4 = 0.5 = 50% But you divided 321 by 123. Surely you could see that 2.6% is a totally unreasonable answer. Actually...

**maths**

380 They have no common factors LCM(x,y) = xy/GCD(x,y)

**maths**

I guess he is then lost. Or, try the law of cosines.

**Maths**

A. usingsymmetry, the area is just ?[0,?/4] 2cosx - secx dx = ?2 - 2tanh-1 ?/8 Using discs of thickness dx for the volume, v = 2?[0,?/4] ?(R^2-r^2) dx where R=2cosx and r=secx v = 2?[0,?/4] ?((2cosx)^2-(secx)^2) dx = ?^2 Using shells of thickness dy, we have to split the ...

**Maths**

sides have shrunk by ?4 = 2

**Math**

well, just add up the numbers!

**math**

(8/6) * 48 = 64

**math**

well, the sum of all 9 angles is 7*180 = 1260 (1260-462)/6 = ?

**math**

x+x+9 < 24 2x < 15 x < 7.5 so, x <= 7 The sides of length x must each be > 9/2, so x >= 5 5 <= x <= 7

**Maths**

well, 05 is half of 10, so ...

**Math**

If R is the radius at the equator, then let r be the radius at 45°. That is Rcos45° = R/?2 So, the ratio is R/r = ?2

**Algebra**

6(j + j+10) = 780

**maths**

(A) subtract each number from 1000. Which difference is smallest in size, + or -? (B) 46+2x+96+x+62 = 306 (C) add up all the rentals and divide by the number of days

**geometry**

it can only be angle PKE=16° That means angle PKN=32° and KPM=148° MK and PN bisect the angles of the rhombus. Now you can get all the angles you need. Note that diagonals are perpendicular.

**Math**

do you not have a formula for the payments? Just plug your numbers into the formula.

**Math**

There are 10C3 ways to pick the females, and 10C2 ways to pick the males. So, that makes 10C3 * 10C2 ways to form the committee.

**Geometry**

If the area is 10, then 1/2(5+15)h = 10 1/2(20)h = 10 10h = 10 h = 1 If the radius is 7.5 (diameter=15) then 3.14*7.5^2/2 = 3.14*56.25/2 = 176.625/2 = 88.3125

**math**

6/(6+8+6) * 30 = 9

**math**

4 esses in 13 letters, so p = 4/13 * 3/12