# Posts by Steve

Total # Posts: 51,712

math
x means multiply, so 12n If a number is placed right next to the variable name, it means to multiply. n over 12 = n/12 = n divided by 12

Geometry
well, it's half the distance from (9,5) to (-5,5) Note that both points are on the line y=5, so the distance is just 14.

Math
since F=ma, a = -8x/4 = -2x x" + 2x = 0 the general solution to this is x = c1 sin(?2 t) + c2 cos(?2 t) so, the frequency is 1/(?2 ?)

maths(variation)
you still have not given the first height.

Math
I'd say a pentagon in 6 pieces

Math
draw the chord. Draw the radius through the center of the chord. Draw a radius to the end of the chord. If the radius of the gear is r, you can see that r^2 = (r-4)^2 + 7^2 r = 65/8

Geometry

Algebra
y is increasing where y' > 0 y' = -0.08x+4 y' > 0 when x < 50 The average rate of change is (y(50)-y(0))/(50-0) = 100/50 = 2 I don't know what c is supposed to be, but if you're angling toward the Mean Value Theorem, it is where y' = 2

Calculus
1/21 is just the 2nd term in the sequence, but is not a partial sum S1 = 1/12 S2 = 1/12 + 1/21 = 11/84 ...

Calculus
well, 3n/(8n+9) -> 3/8 as n->?, so if that's what you meant to say, then you're off. But the series clearly diverges, since the terms do not tend to zero.

calculus
just separate the variables as usual dy/dt = -1/50 (y-17) dy/(y-17) = -1/50 dt ln(y-17) = -1/50 t + C y = c e^(-t/50) + 17 y(0) = 87, so c=70 y(t) = 17+70e^(-t/50)

Precalculus -- Systems of Equations
substituting for x, we have (2y+8)^2 + y^2 = r^2 5y^2+32y+64-r^2 = 0 For that to have one real solution, the discriminant must be zero: 32^2-4(5)(64-r^2) = 0 r = 8/?5

Geometry
of course there's an equation. 5/8 y + y + 1/4 y = 180 y = 96 so, x = 60 and z = 24

looks good to me. Of course, the series is ? ? 1/k! f(k) (x-2)k The (2n)! series is for cos(x) k=0

science
4m = 50*12

math
assuming a linear function, the slope is (25-10)/(5-2) = 15/3 = 5 ft/yr

then it's just like the one I showed first. divide and hen integrate.

correct. So, just do it... ?[0,5] F(t)-E(t) dt = ?[0,5] (t+7)/(t+2) - ln(t+4)/(t+2) dt ?(t+7)/(t+2) dt = ?1 + 5/(t+2) dt = t + 5ln(t+2) For ?ln(t+4)/(t+2) dt, you're in trouble. It is not doable with elementary functions. You sure there's no typo? ?ln(u)/u du = 1/2 ln^...

maths (variation)
#1 done below #2 s = kt^2 so, s/t^2 is constant. You want 648/t^2 = 1800/15^2 #3 p = kq^2/?r so, p?r/q^2 is constant p?9/25 = 16?9/64 Kinda dumb to give you the same r value...

maths (variation)
E = a + kL a+20k = 1.4 a+30k = 2.0 Now just solve for a and k, and then go for L=50

Calculus
?[-1,2] x^2 dx = 3 so far, so good For the horizontal strips, you need the width on the left side as 1-?y, since that is the distance from x = -1 to the parabola. Just as it is 2-?y on the right side. ?[0,1] (1-?y)) dy + ?[0,4] (2-?y) dy = 1/3 + 8/3 = 3

I'd say so, yes.

not so. ?[0,2] t^2+2t+1 dt = t^3/3 + t^2 + t [0,2] = (8/3 + 4 + 2)-0 = 26/3

Pre-Calculus
1.1 times as many pens are sold each year, so after t years the sales will be 2000 * 1.1^t To get the sum of all sales, do the integral ?[1,5] 2000 * 1.1^t dt You need to check on how to integrate a^t for any constant a

physics
ok

chemistry
you are told that 1 mole of gas fills 22.4 Liters so, how many moles of H2 were produced?

physics
well, 7/10 the mass of the wood is submerged, so ...

Maths
10/.092 = 108.69 so, ...

math
There are 36 possible outcomes. How many of these are even and not 2? Well, of the 36 outcomes, half are even and half are odd. But you want even?2, so throw out 1,1. That leaves just 17/36 Just to be sure, list all possible successes: 13 15 22 24 26 31 33 35 42 44 46 51 53 55...

Calculus
(12x+6)(3x^2+3x+5)^7 dx = 2(3x^2+3x+5)^7 (6x+3) dx Let u = 3x^2+3x+5 du = 6x+3 dx so, now your integrand is just 2u^7 du not so hard now, eh?

math-precalculus
the amplitude is (87-73)/2 = 7 the center line is (87+73)/2 = 80 y = 7sin(k(x-h))+80 since y(8) = 0, y = 7sin(k(x-8))+80 since the period is 24 hours, 2?/k=24, so k = ?/12 y = 7sin(?/12 (x-8))+80 so, when is y=77?

Calculus
dr/dt = 3 r = 3t + c since r(0) = 0, r = 3t a = ?r^2 da/dt = 2?r dr/dt ...

Math, Algebra, Graphing Systems of Linear Equation
I'm confused by your impatience and reposting the same problem...

Math, Algebra, Graphing Systems of Linear Equation
try playing around here, where I have plotted the first pair... http://www.wolframalpha.com/input/?i=plot+3x%2B2y%3D-6,+x-4y%3D-16 since your lines have different slopes, the have to intersect. You must have plotted them wrong. 3x+2y = -6 x-4y = -16 2y = -3x-6 -4y = -x-16 You ...

\$60 is the discount, not the price.

math
starting when? 6 degrees each minute, however.

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.

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

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

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

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=...

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