# Posts by steve

Total # Posts: 56,433

1. trés simples -- |v| = ?(10^2+3^2) = ?109
2. No ideas? 8/2 (2a+11d) = 12 16/2 (2a+15d) = 56 Solve for a and d, and then get S3 = 3/2 (2a+2d)
3. distance = speed * time, so d = xy+wz You can see this by watching the units. xmin * ymeters/min = xy meters
4. Your reflector is just a parabola revolved about its axis. Recall that the parabola x^2 = 4py has latus rectum = 2p focus at (0,p) vertex at (0,0) So, your parabola has p=8, making its equation x^2 = 32y Now you want 2x where y=11 That will be 2?(32*11) = 8?22
5. I think the best way to start would be tan 4x = 2*tan 2x/(1-tan^2 2x) = 2(2tanx/(1-tan^2x)) / (1-(2tanx/(1-tan^2x))^2) Now place top and bottom over a common denominator of (1-tan^2x)^2 and you should see things going where you want them.
6. you will wind up with 6 numbers, so 14 must be the average of the 3rd and 4th numbers. Right now, you have 9,12,13,15,17 So you can add any number that is at least 15, which will make (13+15)/2=14 the median.
7. 1 1/3 = 4/3 1 is 3/4 * 4/3 So, you can paint 3/4 * 2/5 = 3/10 of a room
8. right, if you mean perpendicular bisector. otherwise, ... how many lines can go through the midpoint?
9. (d) is correct that is, after all, what perpendicular means...
10. the domain is clearly all real numbers: (-?,?) Now, the minimum value of what's inside the || is of course zero, so the range is [-2,?)
11. Review your basic trig functions and you can easily see that the distance is 60cot30° - 60cot45°
12. 4(2^2) - 2 (3*5 + 1) 4(4)-2(16) 16-32 -16
13. not (a) since the ends are not included not (b) since there is an inside and an outside and it's pi not "pie"
14. consider slicing down the side of the cylinder and unrolling the curved part. That is just a rectangle with the same height as the cylinder (h), and a width equal to the circumference (2?r). So the area is just the inside plus the outside, which are the same, if the cylinder ...
15. Let h = height of building x = distance of observer from the building Then, assuming that the antenna is not set back from the edge of the building, we have 1: h/x = tan45° 2: (h+12)/x = tan60° From (1), h=x, so in (2), (h+12)/h = ?3 Now just find h.
16. Putting all that into math, we have (l+3)(b+2) = l*b+52 (l-2)(b-3) = l*b-43 Now just solve for l and b.
17. since 5y = -11, y = -11/5 Now use that to find x. 2x-3(-11/5) = 17 2x + 33/5 = 85/5 2x = 52/5 x = 26/5
18. y = 2x-5 2x+4y = 100
19. dy/dx = e^(2x+3y) dy/dx = e^(2x)*e^(3y) e^(-3y) dy = e^(2x) dx -1/3 e^(-3y) = 1/2 e^(2x) + c e^(-3y) = -3/2 e^(2x) + c y(0) = 1, so e^(-3) = -3/2 + c c = 3/2 + 1/e^3 e^(-3y) = -3/2 e^(2x) + 3/2 + 1/e^3 or, if you insist, y = -1/3 ln(-3/2 e^(2x) + 3/2 + 1/e^3) Note that the ...
20. well, (0,0) lies on both lines, so it's a likely candidate, no?
21. well, didn't you use your distance formula? ?(-4-(-2))^2+(-9-(-7))^2) = ?((-2)^2+(-2)^2) = ?(4+4) = ?8 = 2?2
22. Let the middle integer have the value x. Then we are told that (x-4) + x = 3(x+2)-20 Find x, and the 5th integer is x+4
23. 6m-4m = -2/3 - 3/7 2m = -(14+6)/21 m = -10/21
24. d = 2x+1-x=x+1 S10 = 10/2 (2*x+9(x+1)) = 5(11x+9) = 55x+45 (2x+1)-x = (5x-1)-(2x+1) Now find x
25. 11+2m
26. If there are x lbs of mulch, then the rest (172-x) is gravel. So, 2 1/4 * x + 1 1/3 (172-x) = 172 Now just find x
27. well, -2/8 * 3/3 = -6/24
28. (18500-0.10)/0.10 * 100
29. review your section on the point-slope form of a line and you will easily see that since your given line has slope -1/2 the new line is y-8 = -1/2 (x+2)
30. It involves much more than that. I suggest you try google, where you can find full explanations.
31. Hmmm. Seems to me that the infinitive phrase to visit California acts as a noun. It has its own direct object.
32. 4x^4-17x^2-15 = (4x^2+3)(x^2-5) so, it should be easy now ...
33. Hmmm. The orthognal curves to a circle are its radii. So, since your circle is x^2+(y+f)^2 = r^2 you want all the lines through (0,f) That would be y=kx+f
34. your line has slope of -3 So, now you have a point and a slope, so use the point-slope form of the new line: y+1 = -3(x+5)
35. Recall that for ax^2+bx+c the vertex lies at (-b/2a, (4ac-b^2)/4a) Now just plug in your coefficients
36. sorry. If PF1+PF2=6 it must be an ellipse. Ahem... 9x^2 + 9y^2 + 36y + 36 = 4y^2 + 36y + 81 9x^2 - 5y^2 = 45 should be 9x^2 + 5y^2 = 45
37. add 'em up and divide: (89+90+95+72+83+100+94)/7 = ?
38. 20 total. How many primes? 2,3,5,7,11,13,17,19 = 8 so P(prime)=8/20 work the others the same way.
39. 42
40. as always in this type of question, maximum area is achieved when the fence is divided equally among lengths and widths. So, with only one length, that means it is 120/2 = 60. The other 60 is divided into two widths, of 30 each. The dimensions are this 60x30 for a maximum area...
41. GCD(18,30) = 6 So, using 18/6 = 3 soccer balls and 30/6 = 5 footballs for each bag, you can make 6 bags
42. the area of the border is the total area minus the area of the wall. So, if the width of the wall is w, then since there is border on each side, we need (w+4)(w+4+4)-w(w+4) = 240 8(w+4) = 240 w=26 The wall is 26x30
43. If the center is at (h,k) and the radius is r, then you can solve (4-h)^2+(4-k)^2 = r^2 (4-h)^2+(2-k)^2 = r^2 (8-h)^2+(2-k)^2 = r^2 or, subtracting judiciously, (4-k)^2 = (2-k)^2 (8-h)^2 = (2-h)^2 That gives (h,k) = (5,3)
44. There are 23 years between 1980 and 2003 That includes only 5 leap years.
45. 360° per hour 6° per minute so, 12:00 to 13:20 is 1 hour and 20 minutes ...
46. Profit = Revenue - Cost So, you want to find x such that (68x-0.3x^2)-(50x+40) = 200 or, in a more standard form, 0.3x^2-18x+240 = 0 or x^2-60x+800 = 0 (x-40)(x-20) = 0 ...
47. well, a cubic foot is 12^3 = 1728 cubic inches. So, 1qt * 60in^3/qt * 1ft^3/1728in^3 * 60lb/ft^3 = 3600/1728 = 2.08 lb
48. There are on average k/n windows/house So, n+1 houses have k + k/n windows where'd you get the 4?
49. clearly it would be salary + commission, or 260 + .02*1975
50. well, the circumference is C = 2?r = 120? so, the revolutions in 500cm can be found using 500cm * 1rev/120?cm = 500/120? rev = (A) Who wants to ride only 5 meters? sheesh!
51. Recall that Sn = n/2 (2a+(n-1)d) So, for the first one S10 = 5(2a+9*4) = -20 2a+36 = -4 a = -20 Do the others the same way
52. I assume you meant 2,-9,-20, ...,-141 since d = -9-2 = -11, 2+(n-1)(-11) = -141 -11(n-1) = -143 n-1 = 13 n=14
53. his final location is 4 east, 3 south so the distance is 5km
54. looks good to me.
55. 7 in favor 10 total, so 3 against so, the odds in favor are 7:3
56. -1/3 = -0.333 -2/5 = -0.400 so, what do you think? If you're not sure, plot them both on the number line, and see where they lie.
57. The outer rectangle could be as small as 31.5 by 19.5, so the lower bound on the perimeter would be 2(31.5+19.5) = 102 cm
58. well, he spent 5 times as much as he had left, right?
59. 16+j=53 now what?
60. If you haven't gotten as far as the figure on this page, you're not trying. Label each side of the triangle as r and Reiny's tip should become clear. https://www.google.com/search?client=firefox-b-1&biw=1384&bih=802&tbm=isch&sa=1&ei=VqVoW8-hC8vAsAW64JHIDA&q=...
61. maybe you mean df/dx or dy/dx or ?f/?x using implicit/or partial differentiation? if so, clean it up a bit so we know what you mean. There's no way the original problem was presented in such a vague way. We don't mind helping with the answers, but don't expect us ...
62. clearly a test post
63. a+3d=11 a+7d=2*11+5 Solve for a and d, and then, of course, S20 = 10(2a+19d)
64. Recall that the equation of a hanging cable is y = a cosh(x/a) where 2a is the distance between the poles and a is the height of the lowest point of the cable. Now, that has a minimum height of y=a, which we cannot guarantee. So, let's include a scale factor of k, giving ...
65. The LCM(25,30)=5*LCM(5,6)=150 So, after 150 minutes they will both have finished sets of papers. ...
66. lots of ways, if I understand what you want. For example, 1/3 + 1/4 + 1/12 = 2/3
67. in QIV, x is positive and y is negative. So, if sin? = -2/5, you have y = -2 r = 5 x = ?21 Now, recall that sin? = y/r cos? = x/r tan? = y/x and of course, there are the reciprocals: csc, sec, cot
68. see https://www.jiskha.com/questions/1751649/300-1-2-14-8-3-8-20-17-g
69. I know the formula. Take a look at the ones I started for you, and take a stab at the other, eh?
70. again, the formula... 1000(1+.08/4)^(4t)=5000 Now just solve for t.
71. Just plug in your formula ... 5000(1+.08/4)^(4*5)
72. x^2-xy-2y^2 = (x+y)(x-2y)
73. r=0 at ?=7?/6, 11?/6 So, using symmetry, the area is a = 2?[7?/6,3?/2] 1/2 (4+8sin?)^2 d? = 8(2?-3?3) ? 8.6963
74. r=0 at ?=7?/6, 11?/6 So, using symmetry, the area is a = 2?[7?/6,3?/2] 1/2 (4+8sin?)^2 d? = 8(2?-3?3) ? 8.6963
75. looks good to me
76. yes
77. yes - the diameter of the circle
78. now subtract that from the selling price.
79. x^4-y^4 = (x^2-y^2)(x^2+y^2) -15 = -3(x^2+y^2) ... and, of course, x=±1, y=±2
80. Assuming your reaction is CaCO3 + 2HCl -> CaCl2 + H2O + CO2 then it will take two moles of HCl for each mole of CaCO3 So, how many moles of CaCO3 in 50g? double that for HCl and figure the mass.
81. log_8(15) = log15/log8 use whatever base you want for the fraction
82. 4 faces total 1 face has a 4 on it so, p(4) = 1/4 this is just like rolling a regular number cube, but with only 4 faces instead of 6.
83. the area grows as the square of the linear ratio sides 4 times as large means area 4^2 = 16 times as large 25*16=400 Too bad you didn't show your work ...
84. cylinder: 2?rh+2?r^2 sphere: 4?r^2 Now, since h=2r, 4?r^2 / 2?r*2r+2?r^2 = 4?r^2 / 6?r^2 = 2/3
85. 300*(1/2)^(14.8/3.8) = 20.17 g
86. a1+8d=a9 So, x+8(3x)=25 ...
87. yes. I assume you solved 1/3x + 1/6x + 2 + 2 = x
88. No, the average speed will be totaldistance/totaltime now, recall that distance=speed*time
89. the average will be total-attendance / #-theaters: (15*600)/(15-6)
90. Nothing hard about this ... -2x(x+3) - (x+1)(x-2) -2x^2-6x - (x^2-x-2) -2x^2-6x-x^2+x+2 -3x^2-5x+2
91. The area of the region, A=?[0,ln5] e^-x dx = 4/5 So, using the normal formulas, x? = 5/4 ? x f(x) dx = ?[0,ln5] xe-x dx y? = 5/4 ? y f(y) dy = ?[0,1] -y lny dy You can do those using integration by parts.
92. impatient much?
93. 56 5/7 = 397/5 397/5 * 2/5 = ?
94. since the difference is 3, there are (99-3)/3 + 1 = 33 terms S33 = 33/2 (3+99)
95. 1/60 + 1/x = 1/40
96. (3 * 9) / 12 = \$2.25
97. rows 5 and 16 are 11 rows apart. So, 11d = 75-31 = 44 d=4 a+4d = a+16=31, so a=15 S20 = 20/2 (2*15+19*4)
98. the independent variable is the one you can control. Most people decide how many pizzas to order, not how much they want to pay, right? Looks like you need to review the topic.
99. you can tell what the temperature is -- it is independent
100. The volume of a pyramid is 1/3 Bh Consider the many-faceted polyhedron as a collection of pyramids. Each small patch -- of area, say, B, of the surface of the sphere is the base of a pyramid of height r, giving it a volume of 1/3 Br. Adding up all the patches, you get the ...