# Posts by steve

Total # Posts: 51,737

Math
just as with the others, the sum is a1/(1-r) just plug in your numbers.

Math A Calculus
this is calculus. Surely you can work with fractions... (a) a+b = (2/3)+(-1/4) = 8/12-3/12 = 5/12 (b) what do you think? recall that the length of ai+bj+ck = ?(a^2+b^2+c^2)

Math
so, what are the even multiples of 13? 26 52 78 so, what do you think?

Math
convert each displacement to rectangular form, and then just add them up. Then if the final position is (x,y), the displacement is ?(x^2+y^2)

Math
no diagrams here.

maths
well, 100% is all of the students. what is 100-54? no idea what the "strength" of a class is. Size? If so, then 23 = (1-.54)x

geometry
so, using the formulas, what do you get?

Math (Sorta dumb question)

Math
a1=243 r = 2/3 an = 243(2/3)^(n-1) a5 = 48 s = a/(1-r) = 5/(5/4) = 4

Math
hard to say, with no figure to compare ...

Math
recall that sin(90-?) = cos? cos(90-?) = sin? now see what you have.

Algebra 1b
(d) not (a) if n is negative

Math
huh? You surely must see from Scott's lines of text that 792 = 12C5

Math
oops tan(?) = y/x

Math
well, let's try to take this step by step. Let's call the two lower vertices L and R. Suppose we have L = (h,-k) Then the line LC has slope mLC = k/(1-h) and its equation (using point A) is y = k/(1-h) (x-1) Since LRC is equilateral, its angles are all ?/3. So, the ...

Math
well, let's try to take this step by step. Let's call the two lower vertices L and R. Suppose we have L = (h,-k) Then the line LC has slope mLC = k/(1-h) and its equation (using point A) is y = k/(1-h) (x-1) Since LRC is equilateral, its angles are all ?/3. So, the ...

Math
well, let's try to take this step by step. Let's call the two lower vertices L and R. Suppose we have ?/3 L = (h,-k) Then the line LC has slope mLC = k/(1-h) y+k = k/(1-h) (x-h) Since LRC is equilateral, its angles are all ?/3. So, the slope of LR is mLR = tan(arctan(...

Calculus
clearly, the series converges, since |sin(4n/?)+3|/4^n < |1+3|/4^n which converges to 16/3 But I can't come up with the actual limit value.

Math: Trigonometry
not quite -- 4/?7 is csc? did you draw the triangle?

Math
just set up equations to fit the facts. For example, #1 m/k = 5/6 m = k-12 so, (k-12)/k = 5/6 #2 7/15 = f/75 d = 75-f what do you get for the others?

Math
(c) because multiplying or dividing by a negative value changes the direction of the inequality 6 > 3 6(-4) = -24 < -12 = 3(-4)

Math
You know that Pn = 5+7n so, replace n with 4, and you get P4 = 5+7*4 = 33

Math
actual increase: 9.68-9.57 = 0.11 % increase: 0.11/9.57 = 0.01149 = 1.15%

algebra
15. yes 16. f(6) = 11*6+15 = 81 g(81) = -11*81^3 - 15*81^2 + 12*81 - 13 = -5,943,307 17. f(9) = 15*9^3 + 13*9^2 - 15*9 + 15 = 11,868 g(11868) = 15*11868 + 11 = 178,031 see? nothing to it! Although all the big numbers are annoying. The arithmetic just gets in the way of the ...

algebra
g(7) = -15*7^2 + 14*7 - 10 = -647 g(g(7)) = g(-647) = -15(-647)^2 + 14(-647) - 10 = -6,288,203 Not hard - just be careful with the arithmetic.

help me maths anyone
Draw a diagram. If we let T be the top of the mast O be the base of the mast P,Q be attachment points of two wires (PQ forms one side of the base of the triangle on the ground) M be the midpoint of PQ OV = 1 PV = 2 so, OP = ?3 triangle MOP is a 30-60-90 right triangle, so OP...

@Dang
Reiny is correct.

sir steve damon reiny steve help maths
Draw a diagram. Using similar triangles, if x = the distance from the lamp post s = length of shadow s/1.5 = (x+s)/6 s = x/3 so, ds/dt = 1/3 dx/dt ... Extra credit: how fast is the tip of the shadow moving?

Algebra 2
plus, since they are inverses, (b) is also correct.

Algebra 2
your answer is correct if you meant y = 2x y = log2x

Algebra
Who says it has to be simplified at all? However, since 97 is prime, 97x is a perfect square if x is 97. Or, if x is 97 times any perfect square.

I agree... I think.

Math~Algebra
just plug in the numbers to the formula. Clearly you get (C).

algebra help
if the proper branch is taken, then (5,2) would be on the inverse. As it stands, the function has no inverse function, since it fails the horizontal-line test.

Calculus
at time t hours after the observation, the distance z between the ships is z^2 = (15-12t)^2 + (9t)^2 2z dz/dt = 90(5t-4) dz/dt=0 when t = 4/5 z(4/5) = 81

Calculus
(a) there is a local extreme every time sinx = cosx: x = ?/4 + k? (b) since the maxima occur when sinx=1, the envelope of these maxima is the curve y=e^-x.

Math
#1 ok #2 h(t) = 3(t-1)^2+2 is apparently a typo, but your solution is correct as written #3 ok if you ignore 3.00-0.5(2)=\$11.5 good work

Math
I read it as meaning that 2/5 of the original amount was spent on fruits, giving: 50 on chocolate 180 on fruit then subtract all that from the original 450.

Algebra
Midway between 14 and 26 is 20. |x-20| <= 6

Algebra
A is right. Although, it could just as easily be 57 <= t <= 73 On the number line plot the points 57 and 73, and shade the line between them. Then make sure the two points are either open or closed circles, depending on whether the endpoints are to be included.

Algebra 2
If you want rational coefficients, then that ?6 has to go, just like the i terms. So, you need f(x) = (x-2)(x-2i)(x+2i)(x-(4-?6))(x-(4+?6)) = (x-2)(x^2+4)((x-4)+?6)((x-4)-?6) = (x-2)(x^2+4)(x^2-8x+10)

algebra 1
for all the details of long division, you can verify your results by entering your polynomials at http://calc101.com/webMathematica/long-divide.jsp

GPA
there's a lot not being said, but if all the classes are weighted equally, they would indeed "cancel out." You don't say what an A means as far as percentages, so it's hard to say just what the effect is. If you have all those A's, including math, you...

math
1:2:3 = 7:14:21

math test help
that covers a lot of ground. Don't expect an online course here. That's what your text was for. Any general explanations we can provide will look a lot like your text, dontcha think? Or, you can google topics of interest.

math test help
but if you have a particular problem that is vexing you, we can help get to the solution. If you haven't studied the topic by now, it may be too late...

math
The sum of their ages 2 years ago was 8*20 = 160 So, if the new child's age is x, 160 + 8*2 + x = 9*20 x = 4

math
Hmmm. I'm not sure I agree. Since A&B can fill the tank so fast, and it takes about 9 times as long to fill it with the leak, the leak must be pretty fast in relation to the fill speeds. You sure that 5 minutes is right?

math
A&B together take 1/(1/5 + 1/20) = 4 minutes to fill the tank. So, if the leak takes x minutes to empty the tank, 1/4 - 1/x = 1/(30+4) x = 68/15 = 4 8/15 minutes

calculus
use product rule

calculus
these are all just powers of x. Use the power rule: d/dx x^n = n x^(n-1)

math
If his speed was x, then since time = distance/speed, 30/15 + 16/x = 10/3

Math
If the two legs are x, then x^2/2 = 25/2 x = 5 so now you can get the hypotenuse. Or, since a = s^2/2 h = s?2 h^2 = 2s^2 = 4a h = 2?a

Maths
a little synthetic division shows that (x-?2) does not divide the cubic. In fact f(?2) = 4-2?2 Check for typos and try again. Once you have done the division, you will be left with a quadratic, which you can then solve in the usual way.

Science
you have a right triangle. Shouldn't be too hard to get one of the angles, eh?

Science
another right triangle.

Science
draw the parallelogram. The two vectors have magnitude 3x and 5x, so (3x)^2 + (5x)^2 - 2(3x)(5x)cos(120°) = 35 find x from that...

mathematics
impatient much?

mathematics
average speed is totaldistance/totaltime: (100+40)/(8+2) = 14 km/hr more like a bicycle, at that speed.

Math
P(9,4) = 9*8*7*6 C(9,4) = P(9,4)/4!

physics/calculus
the product rule. Both t and y are functions of t, so d/dt (bty) = b(y dt/dt + t dy/dt) = b(y + ty')

Math
5P4 = 120 3*2*5

Math
c'mon. Just substitute values for n, from 1 to 5: a1 = 3(4*1-1) = 3(4-1) = 3(3) = 9 and so on

Math
If his average so far is x, then 9x+9 = 10(x-2) x=29 9*29+9 = 270

Algebra
if the width is w, then the length is w+7, so the diagonal is w+14: w^2 + (w+7)^2 = (w+14)^2

maths
well, the angle ? between the two boats' headings (not bearings!) can be found via the law of cosines: 12^2 = 8^2+10^2 - 2*8*10 cos?

Math
how can angle BAC be measured in cm?

Math (Calc) (Differential Equation Solution)
huh? what's to start? The 1st equation is the solution to the second. All you have to do is find C such that y(x^2+y) = C goes through (0,2). 2(0+2) = C

math
well, 184/8 = 23, so ...

math
If the original price was x, then 1.4x*.95 - 1.4x*.90 = 14 x = 200 1.4*200 - 1.4*200*.8 = 224 so, the profit would be 24, or 12%.

physics
the weight of the man is unaffected by all the horizontal pushing and shoving: mg = 60kg * 9.8 m/s^2 = 588N

physics
since speed = distance/time, just plug in your numbers: ((2?*0.6)*5 m)/(2s) = 3? m/s

Math
If the westbound car has gone a distance w, then w^2 + 24^2 = (3w+4)^2

Math
(1/2)(1/4)w = 1/4 ...

Algebra 2
Let the amounts be x,y,z. Then the facts are: x+y+z = 15000 y = x+2000 .05x + .06y + .04z = 730 Now just solve for x,y,z

math

Trigonometry
no!! it is an ellipse. when t=0 you are at the right side, ready to move up and to the left: counterclockwise. http://www.wolframalpha.com/input/?i=plot+x%3D2cost%2B2,+y%3D3sint%2B3,+t%3D0+to+pi%2F2 better review how to plot points!

Trigonometry
well, x starts at a max and decreases y starts at the center point and increases. if that doesn't help, note that the ball is moving from (4,3) toward (2,6) care to try again?

Math
P(match) = 1/6 so, E = 20/6 * 5 - 20 ? -3 surprise, surprise -- the house wins. You only win 5/6 ticket per game. But it costs a whole ticket to play.

sir steve help me reiny reiny
small books! 10.98kg * 1book/54.9g = 10980/54.9 g/book = 200 g/book

maths
1 - 1/3 - (2/3)(2/3) = 2/9

Math Trigonometry
17sec^2(?)-13tan(?)sec(?)-15=0 17+17tan^2? - 13sec?tan? - 15 = 0 13 sec?tan? = 17tan^2? + 2 169 sec^2? tan^2? = 289tan^4? + 68tan^2? + 4 169tan^4? + 169tan^2? = 289tan^4? + 68tan^2? + 4 120tan^4? - 101tan^2? + 4 = 0 (24tan^2?-1)(5tan^2?-4) = 0 tan^2? = 1/24 or 4/5 ...

math
If it is now N, then in t years it will be N(1.02)^t

Math
(3/2 * 4/5)^2 = 36/25 = 1.44 so, 44% bigger

math
since AB=5, AC=12, BC=13 ABC is a right triangle. Similarly, ACD is a right triangle. So, the area should be easy to figure out, eh?

math
(a) 3 (b) 16 (c) 76

math
assuming you meant h(t) = 50+30t-5t^2 = 5(10+6t-t^2) max height is at t = -b/2a = 6/2 = 3 so, what is h(3)?

physics
pressure = force/area = N/m^2 so, plugging in your numbers, (1200*9.8)/(.06/4) = 784kPa or 115 psi If you mean each wheel is .06m^2, then divide that pressure by 4.

maths
3,4cm:17km = 1cm:5km = 1:500000

physics
r is distance (m), so assuming that x and y are also distance, a(m) = m, so a is just a constant b(s)(m) = m, so b = 1/s velocity = r' = ax' + by + bty' acceleration = r" = ax" + by' + by' + bty" = ax" + 2by' + bty" where ' ...

Math
(78/12 + 8/3) ------------------- = 55/23 (78/12 - 8/3)

geometry
try this: https://artofproblemsolving.com/wiki/index.php?title=2006_AMC_12B_Problems/Problem_23

math
(999-99)/11 = 81.81 so, there must be 81 multiples of 11 between 100 and 999 99+81*11 = 990 99+82*11 = 1001

math
http://www.wolframalpha.com/input/?i=plot+y%3Dx%2F(x%2B1)%5E2,+y%3Dx%5E5%EF%BC%8Dx

Physics
I'm having a bit of trouble with F. Force is in units of N = kg-m/s^2 Having v^2 there makes the units m^2/s^2. How do you get rid of the extra meters? Anyway, when you fix that, just remember that F = ma, so a = F/m. Just add that to the -9.8 m/s^2 of gravity, and find ...

Maths
the bug gains 1m each 2 minutes after 20*2 minutes it has climbed 20 meters During the 41st minute it climbs to 30m and is done.

maths
if there are b boys and g girls, b-1 = 2g 5(g-1) = b 5g-5 = 2g+1 3g = 6 g = 2 so, b=5 There are b+g=7 children

math
s:g = 3:2 = 9:6 g:r = 3:5 = 6:10 s:g:r = 9:6:10 9+6+10 = 25 so, we have s:g:r = 90:60:100 90+60+100 = 250

math
3b+4a+6m = 29 2b+6a+3m = 23 multiply the 2nd equation by 2, then add the two equations.

math
hits: 3*2 ? 5 7*6 ? 6 7*6 ? 4*7 2*5 = 5*2

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