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# Recent problems solved by 'galactus'

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 Functions/341165: Kim starts to walk 3 mi to school at 7:30 A.M. with a temperature of 0°F. Her brother Bryan starts at 7:50 A.M. on his bicycle, traveling 10 mph faster than Kim. If they get to school at the same time, then how fast is each one traveling? How do I solve this word problem because I am at a lost. I am totally pulling my hair out with this one. Please help me somebody!!!!1 solutions Answer 244401 by galactus(183)   on 2010-09-10 03:55:26 (Show Source): You can put this solution on YOUR website!I don't see what the temperature has to do with it other than it was a cold walk to school. Since d=rt, Kim travels 3=rt. Bryan starts 1/3 hour later and travels 10 mph faster, but he travels the same distance: 3=(r+10)(t-1/3) There are two equations with two unknowns. Can you finish now?.
 Surface-area/341303: Find the surface area of a torus (doughnut) obtained by rotating the circle (x-b)^2+y^2 = a^2 about the y-axis.1 solutions Answer 244400 by galactus(183)   on 2010-09-10 03:43:52 (Show Source): You can put this solution on YOUR website!The center of the circle is b units from the origin. The circle has radius a. The circle has circumference It travels a distance around the y-axis. By the Second Theorem of Pappus: the surface area is
 Travel_Word_Problems/340525: two cyclist,20 miles apart,start at the same instant and ride towards each other along a straight road at a speed of 10 miles per hour. at the same instant a fly on the forehead ofone of the riders starts to fly at 15 mile per hour toward the other rider, alights on his forehead, and the immediately flies back to the first rider. the fly travels back and forth over the continously decreasing distance between the two riders until the two riders meet. how far has the fly flown when all its journeys are added together.1 solutions Answer 244040 by galactus(183)   on 2010-09-08 18:48:53 (Show Source): You can put this solution on YOUR website!The fly take off toward the opposite cyclist, but at the same time the cyclist is coming toward the fly. This means we have 15t+10t=20. 25t=20 t=4/5 hrs or 48 minutes the fly has flown and the cyclist has pedaled. In this time the fly flew 12 km and each cyclist traveled 8 km. 15(4/5)=12. Since the cylists are pedaling 10 kph toward each other, in 1 hour they will meet. But as the fly heads back to the other cyclist, the cyclist is heading toward him at 10 km/hr. There is 4 km left to cover as the fly heads back to the cyclist it started out on. In 12 minutes the fly covers 15(1/5)=3 km Thus, the fly covers 12+3=15 km altogether.
 Quadratic_Equations/340480: HOW DO I CREATE AN EQUATION to graph a parabola for a dish thats 300 feet in diameter and has a maximum depth of 38 feet?1 solutions Answer 243995 by galactus(183)   on 2010-09-08 16:33:08 (Show Source): You can put this solution on YOUR website!Let the vertex of the parabola be at the origin and its axis along the x axis. An equation would be Where p is the distance from the center of the dish to the focus. Since the point (38,150) lies on the parabola, we have Equation can be represented by
 Quadratic-relations-and-conic-sections/338132: Find parametric equations for the rectangular equation: (x+2)^2 = 4(y-1)1 solutions Answer 243113 by galactus(183)   on 2010-09-05 18:24:40 (Show Source): You can put this solution on YOUR website!Solving this for y yields This parabola has axis parallel to the y axis and has vertex at (-2,1) p=1 and the focus is at (-2,2) and the directrix at (-2,0). The directrix is the x-axis. Parametrically, it can be represented by See, if we solve x for t, we get Sub into y and get:
 test/339142: Two bicycle racers cross the starting line on a circular track at 12:15 PM. One cylist can complete a lap in 12 minutes. The other completes a lap every 16 minutes. Assuming that their speeds remain constant, what is the next time they cross the starting line together?1 solutions Answer 243096 by galactus(183)   on 2010-09-05 17:09:29 (Show Source): You can put this solution on YOUR website!The LCM of 12 and 16 is 48. They will cross again in 48 minutes after 12:15 at 1:03 pm
 Probability-and-statistics/338808: : There is 7 friends (A1,A2,A3....A7).If A1 have to have shake with all with out repeat. How many hand shakes possible?(I dont know the exact question but like this only) 1 solutions Answer 243095 by galactus(183)   on 2010-09-05 17:07:47 (Show Source): You can put this solution on YOUR website!A1 can shake hands with 6 people, A2-A7 A2 can shake hands with 5 people, A3-A7 and so on If there are n people, there are (n-1)! ways for them to shake hands. In this case, 6!=720 ways.
 Miscellaneous_Word_Problems/338976: Ben runs around a circular track in 50 seconds, and roy, in 40 seconds. Five five secons after ben starts, roy starts from the same place in the same direction. When will they be together?1 solutions Answer 243094 by galactus(183)   on 2010-09-05 17:03:57 (Show Source): You can put this solution on YOUR website!They will be together when their distances are the same. Let d=the circumference or length of the track. By using d=rt, Ben's rate is d/50 and Roy's is d/40 Thus, their distances are (d/50)t and (d/40)*(t-5), respectively, Divide out the d's and we have: seconds.
 Probability-and-statistics/339055: Consider a standard deck of 52 cards having 13 clubs, 13 diamonds, 13 hearts, and 13 spades. If five cards of the same suit are considered a flush hand, how many such hands exist in the deck?1 solutions Answer 243043 by galactus(183)   on 2010-09-05 10:26:11 (Show Source): You can put this solution on YOUR website!You need to choose 1 suit from the 4 suits: C(4,1) and 5 cards from the same suit: C(13,5) C(13,5)*C(4,1)=5148 This includes straight flushes as well. There are 40 straight flushes (including the 4 royal flushes), so if you want to exclude those the answer is 5108.
 test/339039: Hello im am really struggling with this question,can you please help me,im desperate and this is my last option. The question says :DETERMINE THE VALUE(S) OF K FOR WHICH -2X^3 - 3X^2 +12X +20=K HAS 3 REAL ROOTS .thank you.plz help plz1 solutions Answer 243036 by galactus(183)   on 2010-09-05 09:34:45 (Show Source): You can put this solution on YOUR website!It would be tedious to guess and check so we will use the discriminant. The discriminant for a cubic is considerably longer than that for a quadratic. It is: In order for there to be three real roots, the discriminant must be > 0. Letting , and making the subs it whittles down to It has three real roots if k is less than 27.
 Quadratic_Equations/339033: If k >0 and 25x^2 + bx + 16 = (5x - k)^2 , for all values of x, what is the value of k – b? (a) -44 (b) -36 (c) 14 (d) 36 (e) 44 1 solutions Answer 243032 by galactus(183)   on 2010-09-05 09:22:07 (Show Source): You can put this solution on YOUR website!Since the constant in the given quadratic is 16, then k must equal 4. If k = 4, then we have (5x-4)^2=25x^2-40x+16 and b=-40 Thus, k-b=4-(-40)=44
 Trigonometry-basics/339038: find csc 300 degrees. If you can show me why we arrived at a negative number?1 solutions Answer 243031 by galactus(183)   on 2010-09-05 09:16:18 (Show Source): You can put this solution on YOUR website!It's negative because it lies in the fourth quadrant. csc(300)=csc(5Pi/3)= -2/sqrt(3)
 Numbers_Word_Problems/339034: If 713^10 is multiplied out completely, what is the units digit of the resulting number? (a) 0 (b) 1 (c) 3 (d) 7 (e) 91 solutions Answer 243027 by galactus(183)   on 2010-09-05 08:05:12 (Show Source): You can put this solution on YOUR website!When looking for a units digit of a large number, use mod 10 Since a number divisible by 10 ends in 0, the units digit will be the remainder when divided by 10. Note that 713=23*31 So, we have Powers of 31 always end in 1 and 23^2 ends in 9 23^2==9(mod 10) and 31==1(mod 10) 9*1=9 The last digit is 9. The idea with mod arithmetic like this is to break it up into smaller powers to work with.
 test/338540: what does c stand for in e=mc21 solutions Answer 242646 by galactus(183)   on 2010-09-03 04:55:03 (Show Source): You can put this solution on YOUR website!The speed of light.
 Functions/336293: How do I find the range of this function : g(x) = 5+ √4-x1 solutions Answer 241099 by galactus(183)   on 2010-08-29 17:12:45 (Show Source): You can put this solution on YOUR website! The domain is what you plug in for x and the range is what you get when you do. Remember, we can not have negatives inside the radical. That would give us a complex result. So, if we plug in anything from negative infinity to 4, we get a real result. negative infinity to 4 is the domain. Written as (-inf,4] The range is then 5 to infinity. It can be written as [5,inf.) Try plugging in x=5. This is out of the domain and we get a complex result. See now?.
 Sequences-and-series/336304: a G.P has a first term of a, a common ratio of r and its 6th term is 768. another G.P has a first term of a, a common ratio of 6r and its 3rd term is 3456. evaluate a and r.1 solutions Answer 241097 by galactus(183)   on 2010-08-29 17:04:31 (Show Source): You can put this solution on YOUR website!The nth term of a geometric sequence is given by For the first condition, the 6th term is 768: For the second condition, the third term is 3456: So, we have two equations with two unknowns to solve, a and r: Solve the first one for and sub into the second one: Therefore,
 Radicals/336197: I can't solve this problem z^2-49/7-z for removing factors of 1.1 solutions Answer 241076 by galactus(183)   on 2010-08-29 14:06:32 (Show Source): You can put this solution on YOUR website! Factor the numerator: Multiply by -1: Cancel the 7-z:
 Sequences-and-series/336210: An auditorium has 20 rows of seats.These are 20 seats in the first row,21 in the second row and 22 in the third row and so on.how many seats are there in all rows? 1 solutions Answer 241074 by galactus(183)   on 2010-08-29 14:03:03 (Show Source): You can put this solution on YOUR website!Did you try just adding them up?. 20+21+22+23+24+....+39 There is a shortcut, though, using the sum of arithmetic sequences.
 test/336199: How do I solve: Thank you. 1 solutions Answer 241071 by galactus(183)   on 2010-08-29 13:57:48 (Show Source): You can put this solution on YOUR website! Subtract 5 from both sides: Square both sides to shed the radical: Expand to form the quadratic: Set to 0 by bringing everything to one side: Factor out s: Now, it is easy to see that the two solutions are s=0 and s=11. But, one of these may be extraneous. Check to see if they work: For s=0: ........clearly untrue. Check s=11: ......clearly true. s=11 is the solution we want.
 Equations/335843: Will someone please show me how to Find the derivative of: ln sin^(-1)x^(3), where sin is an inverse function of sin x. I would really appreciate a solution with steps. Thanks, -Nick.1 solutions Answer 240863 by galactus(183)   on 2010-08-28 08:16:32 (Show Source): You can put this solution on YOUR website!Is that ?. This is why it is important to use proper grouping symbols. Perhaps you mean ? Anyway, using the former: If so, we use the chain rule and product rule. The derivative of the inside times the derivative of the outside. Derivative of inside using product rule: Because the derivative of ln(x)=1/x, the derivative of the outside is: Multiply them:
 real-numbers/335848: How many real-number solutions does 0 = x^2 - 7x + 1 have? (A) None (B) One (C) Two (D) All real numbers (E) It is impossible to determine. 1 solutions Answer 240861 by galactus(183)   on 2010-08-28 08:09:05 (Show Source): You can put this solution on YOUR website!Check the discriminant, If it is a positive number, then there are 2 real solutions. a positive number. Thus, it has two real solutions. They are and
 Permutations/333570: in how many ways can five dashes and eight dots be arranged?1 solutions Answer 239012 by galactus(183)   on 2010-08-21 11:33:26 (Show Source): You can put this solution on YOUR website!There are 13 items altogether. But because there are 8 dots and 5 dashes, we divide 13! by 8!*5! The total arrangements is
 Permutations/333324: There are 7 peole assigned in a queue. 5 men and 2 women. what is the probability that the 2 woman sit next to one another?1 solutions Answer 238873 by galactus(183)   on 2010-08-20 09:23:35 (Show Source): You can put this solution on YOUR website!There are 7 people altogether, so they can be arranged in 7!=5040 ways. Now, to find how many arrangments have the women next to each other, tie the women together and pretend they are one person. Now, we have 6 'people' that can be arranged in 6!=720 ways. But the two women can be arranged in 2 ways. So, the total arrangements with the women next to each other is 2*720=1440 Thus, the probability is 1440/5040=2/7
 Circles/333357: There is a circle with a 16 inch chord. The midpoint of the chord is 6 inches from the center of the circle. What is the length of the radius of the circle?1 solutions Answer 238872 by galactus(183)   on 2010-08-20 08:33:33 (Show Source): You can put this solution on YOUR website!Make a drawing. Then, you can see that we have a right triangle with the hypoteneuse being the radius.
 Sequences-and-series/332819: infinity E 6(.02)^i i=11 solutions Answer 238458 by galactus(183)   on 2010-08-18 14:04:09 (Show Source): You can put this solution on YOUR website!It would appear you mean: Use the formula for a geometric series and then multiply by 6 So, we get as the sum of the infinite series.
 Rate-of-work-word-problems/332755: Five machines can produce 12 gallons of Glorious Goo in 10 days. How many days would it take 4 machines to produce 48 gallons? 1 solutions Answer 238453 by galactus(183)   on 2010-08-18 13:13:08 (Show Source): You can put this solution on YOUR website!Since 5 machines produces 12 gallon in 10 days, this means they produce 12/10=1.2 gallons per day. Thus, each machine produces 1.2/5=.24 gallons per day. Therefore, 4 machines produce 4(.24)=.96 gallons per day. So, it takes the 4 machines 48/.96=50 days to produce 48 gallons.
 test/332548: A turboprop plane flying with the wind flew 1,400 mi in 5 h. Flying against the wind, the plane required 7 h to travel the same distance. Find the rate of the wind and the rate of the plane in calm air.1 solutions Answer 238331 by galactus(183)   on 2010-08-17 16:36:53 (Show Source): You can put this solution on YOUR website!With the wind, we add the two rates. Against the wind, we subtract them. Let rp=rate of plane and rw = the rate of thr wind. With the wind: Since d=rt, we have 1400=5(rp+rw) Against the wind: we have 1400=7(rp-rw) These reduce to rp+rw=280 rp-rw=200 Now, from the first equation we have rp=280-rw Sub into the second equation: 280-rw-rw=200 280-2rw=200 rw=40=rate of wind. That means the rate of the plane, rp, is 240.
 Equations/332007: if sum of the roots of the equation kx2+2x-3k=o is equal to their product then value of k is thank you in advance1 solutions Answer 238000 by galactus(183)   on 2010-08-15 17:43:07 (Show Source): You can put this solution on YOUR website!The sum of the solutions of a quadratic are given by -b/a The product of the solutions of a quadratic are given by c/a Therefore, This means The quadratic is Check:
 Quadratic-relations-and-conic-sections/331973: Write an equation for the hyperbola with vertices (-10, 1) and (6,1) and foci (-12, 1) and (8,1).1 solutions Answer 237968 by galactus(183)   on 2010-08-15 15:56:07 (Show Source): You can put this solution on YOUR website!The vertices are at (-10,1) and (6,1). Note, there is a distance of 16 units between them. This means the center of the hyperbola is 8 units from either one. Namely, at (-2,1). There is a distance of 10 units from the center to a focus. This is c. There is a distance of 8 units from the center to a vertex. This is a. b is the vertical distance up the conjugate axis forming the auxiliary rectangle. Since , we have So, and The equation is:
 Probability-and-statistics/331931: find the number of ways to seat n married couples around a table in the following cases 1/ men and women are alternate 2/ every woman is next to her husband 1 solutions Answer 237953 by galactus(183)   on 2010-08-15 12:33:15 (Show Source): You can put this solution on YOUR website!Seat the n women around the table in (n-1)! ways. The n men are then seated in the n spaces between the women in n! ways. Thus, there are ways to seat the men and women alternating. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Tie each married couple together and pretend they are one person. We can seat them in (n-1)! ways. Now, since each couple can be switched around in 2 ways, there are 2^n ways to arrange all of them So, there are ways to arrange the couples with the women sitting with their husbands.
 Quadratic-relations-and-conic-sections/331970: Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the end points of the minor axis are at (5,0) and (-3,0)1 solutions Answer 237951 by galactus(183)   on 2010-08-15 12:12:20 (Show Source): You can put this solution on YOUR website!The distance between the vertices of the minor axis is 5-(-3)=8 8/2=4, 4^2=16 The distance between the vertices of the major axis is 6-(-6)=12 12/2=6, 6^2=36 The center is at (1,0)