# Posts by Steve

Total # Posts: 52,313

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.

Math check my answer
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
depends on the base radius.

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

math
3*60 = 2*90

algebra
How can 3 be a 2-digit number??? t = tens digit u = units digit so, the value of the number is 10t+u t+u = 6 10u+t = 10t+u + 36 The number is 15

algerbra
11s+4c = 93 9s+2c = 71 double the 2nd equation: 11s+4c = 93 18s+4c = 142 subtract the top from the bottom: 7s = 49 s = 7 11s+4c=93, so 77+4c = 93 4c = 16 c = 4 So, they sold 7 senior and 4 child tickets

algebra
11s+4c = 93 9s+2c = 71

Math
time = distance/speed so, figure average speed as (total distance)/(total time)

Math
correct. assuming that the ball isn't spinning in reverse, in which case it's green.

Math
not really. Aside from being incomplete, you did find that you can get 10 tickets along each side of the square. So, there are 10^2 = 100 tickets

Math
He can land anywhere he wants between A and B. If you want to find the path of least time, however, you need to minimize ?(x^2+12^2)/4 + (16-x)/8 where he lands x km from point A.

Math
why worry about the area? You are interested in the perimeter. One lap around the field covers 4*50 = 200 meters. Now, how many laps in 3000 meters?

math algebra
x+y = 400 .80x + .85y = 400-68 ...

math
why are you dividing? Does it even make sense to divide one dimension by another? The round cake has volume and area ?r^2h = ?(7/2)^2(2) = 76.97 in^3 ?r^2 + 2?rh = ?(7/2)^2 + 2?(7/2)(2) = 82.47 in^2 The rectangular cake has volume and area lwh = 6*9*2 = 108 in^3 lw + 2(lh+wh...

math
x/3 + 10 = 3x/4 4x + 120 = 9x 5x = 120 x = 24 The tank is 3/4 full, so 6 more gallons are needed.

Calculus
tossing in that extra x factor makes it beyond elementary functions, as shown here: http://www.wolframalpha.com/input/?i=%E2%88%AB(x+cos%5E2(x)sin(x))%2F(a-cos(x))+dx

Calculus
well, the first thing is to get rid of all those "nx" things. Let u = nx and we have 1/n ?(cos^2(u)sin(u))/(a-cos(u)) du now let v = a-cos(u) dv = sin(u) du cos(u) = a-v 1/n ?(a-v)^2/v dv Now it's simple.

Math
4000-460

math
the formula for y (distance) is bogus m/s^3 * t^2 = m/s the units don't work out right. It could be that you meant x = 4t + t^2 y = 2t + 2t^2 If so, then (a) set x=y and solve for t (b) set the speeds equal and solve for t

math
t:g = 13:8 g:b = 2:3 = 8:12 t:g:b = 13:8:12 ...

calculus
a good place to start is this site, with several useful examples. See what you make of it. http://tutorial.math.lamar.edu/Classes/CalcII/PowerSeries.aspx

Math
well, duh: 2222 or 4444

math
If the quantities of coins are x = \$1 y = \$2 z = \$5 then we are told x = 9z y = 8z x+2y+5z = 90 now solve for y

English
1 -- abandon, forsake

algebra
find the midpoint of the given segment: (0,-3) find the slope of the segment: -5/3 so, the slope of the bisector is 3/5 Now we have a point an a slope, so the perp. bisector is y+3 = 3/5 (x-0) or, in slope-intercept form, y = 3/5 x - 3

Math
clearly, the circle is (x+6)^2 + (y-7)^2 = r^2 So, I suspect a typo. Check your coordinates again, and recall that a circle with center at (h,k) is (x-h)^2 + (y-k)^2 = r^2 Once you fix your error, just find how far away it is from (4,-2).