Posts by Steve
Total # Posts: 55,728

Math  3d points
Oh, yeah. But the starting point can be anywhere on a sphere centered at B's destination. 
Math  3d points
If A is going from (1000,0,0) to (0,100,1000) it will never reach (0,0,1000). Anyway, when you decide how far A has to go, divide that distance by 72 to get the time needed. Since you don't say how far B has to travel, it's tough to say how fast it needs to go ... 
math
6(a+5d)=9(a+8d) 6a+30d=9a+72d 3a = 42d a = 14d So, there are lots of answers. For example, if d=1, a=14 and the sequence is 14,13,12,11,10,9,8,7,6, ... 6(9)=9(6) 
math
(13/8 + 5/12)/(13/8  5/12) = (39+10)/(3910) = 29/49 
Maths
If xy=0 then either x or y is zero. The other can be anything. So, the solutions are (0,4) and (8,0) 
math
surely you have a calculator, or can type that into google this must be a test post ... 
Calculus1
oops. there is also another solution at x=1 since cos(log1)/1 = cos(0)/1 = 1/1 = 1 
Calculus1
f'(x) = e^x f'(0) = 1 g'(x) = cos(lnx)/x cos(lnx)/x=1 cos(lnx)=x x = 0.0089,0.2745 So, you want lines with slope=1 passing through (0,1),(0.0089,0.9933),(0.2745,0.9610) y1 = x y0.9933 = x0.0089 y+0.9610 = x0.2745 See the graphs at http://www.wolframalpha.com/... 
Calculus1
what's the trouble? You just need to solve 4/3 pi r^3 = (r + 1/2)^3 r = 0.817 ? (0,1) 
maths
18% more pizzas, 20% less per 250*12=3000 250*1.18 * 12*0.80 = 2832 
Math
(450000/90)*1.20 = 6000 How did you get 5000? Just multiply by $1.00 per $90? 
math
Let s and d be how many standard and deluxe packages Let c and d be the amounts of cashews and peanuts Now figure how many grams of each nut will be needed for the packages 120s + 120d <= 15000 200s + 40d <= 20000 s >= d You did not ask, but I assume you want to ... 
math
Do you mean Legendre polynomials? P0(x) = 1 P1(x) = x P2(x) = 1/2 (3x^21) So, x^2 = (2P2(x)+1)/3 4x^23x+2 = =4*(2P2(x)+1)/3  3P1(x) + 2P0(x) 
Calculus
Just to get you started, dP/dt=kP dP/P = k dt ln P = kt + ln c P = c*e^(kt) 
Calculus
dy/dt = 4y dy/y = 4 dt lny = 4t+ln(c) y = c*e^(4t) y(2)=450, so c*e^2 = 450 c = 450/e^2 ? 60.9 y = 60.9 e^(4t) so, now find y(8) 
Calculus
Not tan^1(m1  m2) but rather tan^1 m1  tan^1 m2 
Calculus
well, 3=?9, so 3^x = ?(9^x) = ?(9^x) So, as x gets large, 5^x is zero compared to 9^x, so it can be ignored, just as with polynomials, lower powers can be ignored. So, pick (D) 
math
so, what is the standard form? If you can't get that, you're hosed. 
Math
it might help to write everything in terms of powers of sqrt(2) 64=2^6=sqrt(2)^12 32768=2^15=sqrt(2)^30 So, if u=sqrt(2), we have 5u^(3x) * u^(12(2x+2)) = u^30x 5u^(3x) * u^(24x+24) = u^30x You sure that 5 belongs there, or is this just problem 5? Without the 5, x=8 since we ... 
Advanced Algebra
Max has just won some money on a game show! He has the option to take a lump sum payment of $500,000 now or get paid an annuity of $4,900 at the beginning of each month for the next 10 years. Assuming the growth rate of the economy is 2.9% compounding annually over the next ... 
math
With no diagram, I am left to guess that the height of the center parabola is 200. So I guess that we have the following points on the curve; (200,0), (0,200),(200,0) So, clearly y=400ax^2 Since y(200)=0, a=1/00 Thus, the height of the support at x=h is 210y(h) 
algerbra
what the heck  post it again, and maybe this time you'll spell "algebra" correctly. Just sayin' 
algerba
assuming the pole is vertical, its height is?(11^27^2) ... 
algerba
A guy rope is attached to the top of a tent pole. The guy rope is pegged into the ground 7 feet from the tent. If the guy rope is 11 feet long, how long is the tent pole? Round to one decimal place as needed. 
Math
distance = speed * time (a) (9km)/(36km/hr) = (9/36)hr (b) 20 min = 1/3 hr, so (2km)/(1/3 hr) = 6km/hr average speed is total distance divided by total time (c) (9+2)km/(1/4 + 1/3)hr = 11/(7/12) = 132/7 km/hr I leave it to you to simplify the final values. 
Algebra
or how about the trivial ones x=3 y=4 
Algebra
y=x+1 y=102x 
Math
The experiment had 69 trials. The probabilities are clearly 36/69 = 12/23 and 33/69 = 11/23 
algebra
If b is betty's age, then Don is b+21 In 5 years their ages will be b+6 and b+27 So, b+27 = 2(b+6) Solve for b, then you can get Don's age. 
math
No problem. First, collect things into a useful form. 7x^24x+1=2x^27x+3 5x^2+3x=2 5(x^2+3/5 x) = 2 Now, divide 3/5 by 2 and square it. Make sure to add the same amount to both sides. 5(x^2 + 3/5 x + (3/10)^2) = 2 + 5(3/10)^2 5(x + 3/10)^2 = 245/100 (x + 3/10)^2 = 45/100 x + ... 
math
man, they gave you the function. Just plug in the numbers to find your answers. (a) s(3) = 16*3^2 + 75*3 + 407 (b) solve s(t) = 450 
math
yes, he did. 
Math
the slope is, as always, ?y/?x = (5(10))/(2(9)) = 5/7 
Computer
pct = score/max_possible * 100 
maths
?((2+j)^2+1)=2?(1+j) = 1.197+0.910j so you want log(3.197+1.910j) Now recall that if z=a+bj then log(z) = logz+arccos(a/z)j 
math
?(6)/(?(3) ?(4)) = (?6 i)/(?3 i * ?4 i) = (?6 i)/(2?3 i^2) = (?3*?2 i)/(2?3) = ?2 i/2 = 0  1/?2 i 
math
The radius of the red cone is 3.876 If the radius of the blue cone is the same, then its surface is 155.420 If, however, the cones are similar, then since h is twice as big, the surface area will be 4 times as big: 460 
chemistry
so, what is the index of refraction of water? Then use Snell's law 
Calculus
you got the calculus right  what bothers you about the algebra? You have the slope of the parallel line: m=6 So, that means you need 2x + 4/x = 6 2x^26x+4 = 0 2(x1)(x2) = 0 So the lines are tangent at (1,1) and (2,4+4ln2) 
College algebra
since complex roots come in conjugate pairs, f(x) = a(x2i)(x+2i)(x3i)(x+3i) = a(x^2+4)(x^2+9) Now use the given point to find a. 
Math
(ii) just divide (i) by 1.85 (b) since 360° = 24 hrs, each time zone occupies 15° X is 60° east of Y (time is later) 
Math
your text is all messed up, so hard to say. There are lots of online graphing sites though, so use one of them. 
math
they are collinear when the differences are all in the same ratio. That is, when the slope from P1 to P2 is the same as the slope from P2 to P3: ((22k)(2k))/((k)(k+1)) = ((62k)(22k))/((4k)(k)) (24k)/(2k1) = (4)/(42k) ... k = 1 (2,2),(1,4),(3,8): y=2x+2 
Algebra
?(f??g) = f(g) = 4g^2+3 = 4(4x2)^2+3 ?(g?f) = g(f) = 4f2 = 4(4x^2+3)2 now just simplify sometimes it helps not to include all those (x)'s ?(f??g)(x) = f(g(x)) = f(4x2) = 4(4x2)^2+3 you can replace g first or evaluate f(g) and then plug in g 
benghazi
all of it if it's a gas. If a liquid, then you need to look up the density of CCl4 (convert to g/L) find how many grams is .5 mol volume = mass/density divide that by 10.0L 
math
the maximum and minimum dimensions are 18.5*12.5 and 17.5*11.5 find the difference from the true perimeter P=2(12+18) and divide it by P 
math
ok. Draw your diagram and say what it is you want to know. If you want the distance from Y to Z, then use the law of sines. sin30/15 = sinZ/12 Now you have angles y and Z so you can find X. The law of cosines then tells you that x^2 = 15^2+12^22*15*12 cosX 
math
the crosssection of the pipe is a rectangular ring with area A = (12*15)(10*12) = 60 cm^2 so, if the pipe has length x meters, its volume is (60/100)^2*x = 36x/100 m^3 since mass = density * volume, we have 7000*36x/100 = 63 x = 63/2520 = 1/40 m 
Calculus
just add the components: (6,10)+<3,2> = (3,8) 
math 11
what three variables? All you have to do is see where the line intersects the parabola. Calling the first one h and d instead of y and x doesn't introduce any new variables. They are just names to describe the curve. 9x10y=14 y = (9x+14)/10 So, to see where they ... 
Calculus
x = t + cos t y = t^3  75 t dy/dx = (dy/dt)/(dx/dt) = (3t^275)/(1sint) As Damon said, finding where dy/dx=0 is the same as finding where dy/dt=0, since the denominator is only zero when t=pi/2. 
Calculus
y = x^2+3 dy/dt = 2x dx/dt = 2*1*4 = 8 
Calculus
A = bh/2 using the product rule, we have dA/dt = 1/2 (db/dt * h + b * dh/dt) dA/dt = 1/2 ((1)(38)+(36)(6)) = 1/2 (38+216) = 89 cm^2/min You seem to have mangled your derivative equation. 
Calculus
no, dy/dx = x/y x^2+y^2=18^2 so, when x=9, y=9?3 2x dx/dt + 2y dy/dt = 0 Now plug in your values and you have 2*9 dx/dt + 2*9?3*(3) = 0 dx/dt = 54?3/18 = 3?3 ft/s 
Maths
y = mx + n/?x Sorry, y cannot be both 11 and 20 when x=9 So, fix that, and then plug in your values to solve for m and n, then figure y(12) 
PreCalculus
(a) tan? = 225/325 (b) Assuming it was attached to vertical support from the end of the ramp, it would be 1/2 * 325 cos? or, 1/2 ?(325^2225^2) 
Algebra
oneway trip delay: (99.33*10^6km)/(3*10^5km/s) = 33.11*10 = 333.1 seconds Now just convert that to minutes & seconds. 
Math
0.9 * (36.2/10.5) = 3.1 in 
math
y6 >= 12 y >= 18 
Trigonometry
how is this trig? Anyway, just plug in your numbers. Assuming a model of A = Ao e^(kt), where t is in days, we have 37e^(0.3*9) = ? 
Differential equations
extra credit: why did Arora and I come up with different integrating factors? Can they both be correct? 
Differential equations
first you need to get y' by itself. y' + x(x^2+1) y = 3(x^2+1) Now the integrating factor is e^(1/2 (x^2+1)^2) try that. 
Differential equations
I always like to subsume the e^C into a new C so the function is Ce^(kt)+T A(0) = 100 so, C + T = 100 A(10) = 70 so, Ce^10k+T = 70 also, use the 3rd point, and then you can solve for the constants. 
math
left, right, or what? 
math
10HK * 1US/7.78HK = 1.28US 
Calculus
the speed is ?((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2) ... 
2 problemsmath
Oh, then it is clearly y=(x+3)/2 
2 problemsmath
#1 I think you have a typo. For x=4,6,10 y=x/2 For x=6,8 y=x/2 + 1/2 #2 crosses the yaxis at y = 6 y=mx+6 left 2 units and rises 3 m = 3/2 so, y = 3/2 x + 6 
Math
terms are separated by + and  signs, so ... 
Maths
If you draw the diagram, and label the points A and B for the ships and P for the port, you will see that you have a right triangle with OB=8 OA=10 so, AB=6 Ships sail on headings, not bearings. You did correctly use "bearing" when you gave the direction of B from A... 
Math
if you'd show your work, we could tell whether you were confused or not. After 3 years, Roman would have 500*1.04^3 = 562.43 so, he earned $62.43 No way to tell how you got your answer. Way too high 
Math
(210*1.40)/210 = 1.40 = 140% 210*1.4 = ? any number increased by 40% is 140% of the original 
math
e^kt = 2 t = ln2/k now plug in 6% 
Algebra
sorry ... b^2 = (20)^2 = (20)(20) = 400 not 400 400 is 20^2 = b^2 because exponents are done first. 
Algebra
#1 ok #2 nope. the polynomial is 2(x5)^2 always check the discriminant. For this one, it is zero, indicating one repeated root. 
math
switch variables and solve for y: x = 2^y/(1+2^y) x + x*2^y = 2^y x = 2^y(1x) 2^y = x/(1x) J1 = y = log2 x/(1x) 
Algerbra 1 B
Factor out all the perfect squares in the roots: ?363  3?27 = ?(121*3)  3?(9*3) = ?121*?3  3*?9*?3 = 11?3  3*3?3 = 11?39?3 = 2?3 
Algebra 1
You just have to write in algebra what all those words are saying. First, count the items: candy bags = x trail mix = x+7 Now, add up the cost of the items, and make it equal to the total cost: .80x + .65(x+7) = 21.95 Now just solve for x 
math
so, solve for r... V = 4?/3 r^3 r^3 = 3V/(4?) ... 
math
"such" a cone? what kind of cone? 
Maths
hmmm. many possible solutions if y=0, x=pi/4 if y=pi/4, x=pi/6 not sure where this is going. 
Physics HELP Plz
assuming the end of the ramp is at the same height as the tops of the buses, you just need to solve for ? using the range: v^2/g sin2? >= 40.5 
Physics HELP Plz
recall that the range R = v^2/g sin2? so, plug in your values to get the range, then divide that by v cos? for the flight time. 
math
what's the trouble? Just plug in your numbers! p(1000000) = 40?(0.0001*10^6+1) = 40?101 ? 29.95 If p=12.95, 40?(0.0001x+1) = 12.95 ?(.0001x+1) = 27.05 .0001x+1 = 731.7025 x = 7,307,025 
math
just plug in your numbers, as in the book problem. What do you get? 
Calculus Answer Check
looks good to me. or, you could say y = 5kx+c using a different c. 
Physics
how long does it take to fall 23m? 4.9t^2 = 23 speed = distance/time 
Physics
figure the time to fall 206m: 4.9t^2 = 206 The vertical speed v = 9.8t so the final speed is ?(v^2+2.9^2) 
algebra
w(w+60) = 1600 now crank it out. hint: 20*80=1600 
Math
look at the volume formulas. For equal dimensions, pyramids and cones have v = 1/3 Bh while prisms and cylinders have v=Bh 
Algebra 1
compare the two values. If each has n coins, then 25n = 10n+300 
math
huh. Just plug in the numbers. I'll do the first one... 2x^2y^2 for x=3 and y=2 = 2 * 3^2 * (2)^2 = 2 * 1/3^2 * 1/(2)^2 = 2 * 1/9 * 1/4 = 1/18 These aren't as hard as they look, as long as you are careful with each step. so, what do you get for the other one? 
physics
(a) clearly the acceleration is (5.810? rad/s)/(10.65s) = 1.714 rad/s^2 (b) starting from when? t=0, or after reaching the final speed? just as with linear motion, the "distance" (total radians) is 1/2 at^2 
math
The complete job takes 6*8*5=240 manhours 240/(4*5) = 12 days for the 4 men. Or, using ratios of the number of men and hours, it will take 5 * (6/4)*(8/6) = 12 days That is, with only 4/6 as many men, it will take 6/4 as long; working only 6/8 as many hours per day, it will ... 
Math
sometimes you need to think outside the ball! 
Math
go with B D is a sphere 
physics
well, F = GMm/r^2 5.00 = GM(0.5)/(5.0*10^5)^2 Plug in G and solve for M 
Math
a nice solution is found here https://www.mathalino.com/reviewer/differentialcalculus/12conemaximumconvexareainscribedsphere 
Math
If the pen costs $p, then the ruler costs p1.30 So, just solve 5p + p1.30 = 11.60 
Math pre algebra
to the nearest tenth means one decimal place. 380.000 is not the rounded value for any precision. 376 is rounded to the nearest integer 375.9 to the nearest tenth 375.91 to the nearest 100th 375.907 to the nearest 1000th