# Posts by Steve

Total # Posts: 55,728

1. ### Math - 3d points

Oh, yeah. But the starting point can be anywhere on a sphere centered at B's destination.
2. ### 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 ...
3. ### 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)
4. ### math

(-13/8 + 5/12)/(-13/8 - 5/12) = (-39+10)/(-39-10) = 29/49
5. ### 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)
6. ### math

surely you have a calculator, or can type that into google this must be a test post ...
7. ### Calculus-1

oops. there is also another solution at x=1 since cos(log1)/1 = cos(0)/1 = 1/1 = 1
8. ### Calculus-1

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) y-1 = x y-0.9933 = x-0.0089 y+0.9610 = x-0.2745 See the graphs at http://www.wolframalpha.com/...
9. ### Calculus-1

what's the trouble? You just need to solve 4/3 pi r^3 = (r + 1/2)^3 r = 0.817 ? (0,1)
10. ### maths

18% more pizzas, 20% less per 250*12=3000 250*1.18 * 12*0.80 = 2832
11. ### Math

(450000/90)*1.20 = 6000 How did you get 5000? Just multiply by \$1.00 per \$90?
12. ### 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 ...
13. ### math

Do you mean Legendre polynomials? P0(x) = 1 P1(x) = x P2(x) = 1/2 (3x^2-1) So, x^2 = (2P2(x)+1)/3 4x^2-3x+2 = =4*(2P2(x)+1)/3 - 3P1(x) + 2P0(x)
14. ### Calculus

Just to get you started, dP/dt=kP dP/P = k dt ln P = kt + ln c P = c*e^(kt)
15. ### 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)
16. ### Calculus

Not tan^-1(m1 - m2) but rather tan^-1 m1 - tan^-1 m2
17. ### 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)
18. ### math

so, what is the standard form? If you can't get that, you're hosed.
19. ### 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 ...

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 ...
21. ### 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=400-ax^2 Since y(200)=0, a=1/00 Thus, the height of the support at x=h is 210-y(h)
22. ### algerbra

what the heck -- post it again, and maybe this time you'll spell "algebra" correctly. Just sayin'
23. ### algerba

assuming the pole is vertical, its height is?(11^2-7^2) ...
24. ### 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.
25. ### 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.
26. ### Algebra

or how about the trivial ones x=3 y=4
27. ### Algebra

y=x+1 y=10-2x
28. ### Math

The experiment had 69 trials. The probabilities are clearly 36/69 = 12/23 and 33/69 = 11/23
29. ### 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.
30. ### math

No problem. First, collect things into a useful form. 7x^2-4x+1=2x^2-7x+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 + ...
31. ### 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

yes, he did.
33. ### Math

the slope is, as always, ?y/?x = (-5-(-10))/(-2-(-9)) = 5/7
34. ### Computer

pct = score/max_possible * 100
35. ### 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) = log|z|+arccos(a/|z|)j
36. ### 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
37. ### 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
38. ### chemistry

so, what is the index of refraction of water? Then use Snell's law
39. ### 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^2-6x+4 = 0 2(x-1)(x-2) = 0 So the lines are tangent at (1,1) and (2,4+4ln2)
40. ### College algebra

since complex roots come in conjugate pairs, f(x) = a(x-2i)(x+2i)(x-3i)(x+3i) = a(x^2+4)(x^2+9) Now use the given point to find a.
41. ### 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)
42. ### Math

your text is all messed up, so hard to say. There are lots of online graphing sites though, so use one of them.
43. ### 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: ((2-2k)-(2k))/((k)-(-k+1)) = ((6-2k)-(2-2k))/((-4-k)-(k)) (2-4k)/(2k-1) = (4)/(-4-2k) ... k = -1 (2,-2),(-1,4),(-3,8): y=-2x+2
44. ### Algebra

?(f??g) = f(g) = 4g^2+3 = 4(4x-2)^2+3 ?(g?f) = g(f) = 4f-2 = 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(4x-2) = 4(4x-2)^2+3 you can replace g first or evaluate f(g) and then plug in g
45. ### 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
46. ### 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
47. ### 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+12^2-2*15*12 cosX
48. ### math

the cross-section 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
49. ### Calculus

just add the components: (-6,10)+<3,-2> = (-3,8)
50. ### 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. 9x-10y=-14 y = (9x+14)/10 So, to see where they ...
51. ### Calculus

x = t + cos t y = t^3 - 75 t dy/dx = (dy/dt)/(dx/dt) = (3t^2-75)/(1-sint) 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.
52. ### Calculus

y = x^2+3 dy/dt = 2x dx/dt = 2*1*4 = 8
53. ### 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.
54. ### 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
55. ### 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)
56. ### Pre-Calculus

(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 ?(325^2-225^2)
57. ### Algebra

one-way trip delay: (99.33*10^6km)/(3*10^5km/s) = 33.11*10 = 333.1 seconds Now just convert that to minutes & seconds.
58. ### Math

0.9 * (36.2/10.5) = 3.1 in
59. ### math

y-6 >= 12 y >= 18
60. ### 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) = ?
61. ### Differential equations

extra credit: why did Arora and I come up with different integrating factors? Can they both be correct?
62. ### 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.
63. ### 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.
64. ### math

left, right, or what?
65. ### math

10HK * 1US/7.78HK = 1.28US
66. ### Calculus

the speed is ?((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2) ...
67. ### 2 problems---math

Oh, then it is clearly y=(x+3)/2
68. ### 2 problems---math

#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 y-axis at y = 6 y=mx+6 left 2 units and rises 3 m = 3/-2 so, y = -3/2 x + 6
69. ### Math

terms are separated by + and - signs, so ...
70. ### 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...
71. ### 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
72. ### Math

(210*1.40)/210 = 1.40 = 140% 210*1.4 = ? any number increased by 40% is 140% of the original
73. ### math

e^kt = 2 t = ln2/k now plug in 6%
74. ### Algebra

sorry ... b^2 = (-20)^2 = (-20)(-20) = 400 not -400 -400 is -20^2 = -b^2 because exponents are done first.
75. ### Algebra

#1 ok #2 nope. the polynomial is 2(x-5)^2 always check the discriminant. For this one, it is zero, indicating one repeated root.
76. ### math

switch variables and solve for y: x = 2^y/(1+2^y) x + x*2^y = 2^y x = 2^y(1-x) 2^y = x/(1-x) J-1 = y = log2 x/(1-x)
77. ### 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?3-9?3 = 2?3
78. ### 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
79. ### math

so, solve for r... V = 4?/3 r^3 r^3 = 3V/(4?) ...
80. ### math

"such" a cone? what kind of cone?
81. ### Maths

hmmm. many possible solutions if y=0, x=pi/4 if y=pi/4, x=pi/6 not sure where this is going.
82. ### 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
83. ### 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.
84. ### 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
85. ### math

just plug in your numbers, as in the book problem. What do you get?

looks good to me. or, you could say y = 5kx+c using a different c.
87. ### Physics

how long does it take to fall 23m? 4.9t^2 = 23 speed = distance/time
88. ### 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)
89. ### algebra

w(w+60) = 1600 now crank it out. hint: 20*80=1600
90. ### Math

look at the volume formulas. For equal dimensions, pyramids and cones have v = 1/3 Bh while prisms and cylinders have v=Bh
91. ### Algebra 1

compare the two values. If each has n coins, then 25n = 10n+300
92. ### 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?
93. ### 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
94. ### math

The complete job takes 6*8*5=240 man-hours 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 ...
95. ### Math

sometimes you need to think outside the ball!
96. ### Math

go with B D is a sphere
97. ### physics

well, F = GMm/r^2 5.00 = GM(0.5)/(5.0*10^5)^2 Plug in G and solve for M
98. ### Math

a nice solution is found here https://www.mathalino.com/reviewer/differential-calculus/12-cone-maximum-convex-area-inscribed-sphere
99. ### Math

If the pen costs \$p, then the ruler costs p-1.30 So, just solve 5p + p-1.30 = 11.60
100. ### 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
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