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# Recent problems solved by 'Alan3354'

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 Triangles/230539: plz help me to solve this question..... Q. Three points have coordintes A(4,13), B(9,3) and C(10,8).Find the equation of (a) the line AB (b) the line through C perpendicular to the line y-4x=5. the line through C meets the line AB at point P.Calculate the coordinates of P and the ratio AP:PB 1 solutions Answer 170731 by Alan3354(30927)   on 2009-10-23 09:00:46 (Show Source): You can put this solution on YOUR website!Three points have coordintes A(4,13), B(9,3) and C(10,8). Find the equation of (a) the line AB Find the slope, m m = diffy/diffx = 10/-5 m = -2 ------ Use either point to find b, then the eqn y = mx+b to find b 13 = -2*4 + b b = 21 y = -2x + 21 (Eqn of AB) ------------- ------------- (b) the line through C perpendicular to the line y-4x=5. y = 4x+5 m = -1/4 (slope perpendicular to m=4) 8 = -1/4*10 + b b = 10.5 y = -(1/4)x + 10.5 ------------ the line through C meets the line AB at point P. Calculate the coordinates of P y = -2x+21 = -x/4 + 10.5 1.75x = 10.5 x = 6 y = -12 + 21 = 9 P(6,9) ---------- and the ratio AP:PB Since it's a straight, use the x values to get the ratio A - 4 P - 6 B - 9 AP = 2 PB = 3 AP:PB = 2:3
 Matrices-and-determiminant/230400: how can i solve this problem in matrix form? Problem: 3x-y=-2 5x+2y=151 solutions Answer 170650 by Alan3354(30927)   on 2009-10-22 21:04:02 (Show Source): You can put this solution on YOUR website!3x-y=-2 5x+2y=15 --------- |3 -1 +2| |5 +2 -15| ------- Det = |3 -1| |5 +2| = 3*2 - 5*-1 = 6+5 Det = 11 -------- x: |-1 +2| |+2 -15| = 15 - 4 = 11 11/Det = 1 x = 1 -------- -y: |3 +2| |5 -15| = -45 - 10 = -55 -55/11 = -5 -y = -5 y = 5
 Linear-equations/230459: 6y=8x+41 solutions Answer 170639 by Alan3354(30927)   on 2009-10-22 20:41:54 (Show Source): You can put this solution on YOUR website!Do you have a question?
 Linear_Algebra/230443: one number is 10 times larger as another, and their difference is 81. find the numbers.1 solutions Answer 170638 by Alan3354(30927)   on 2009-10-22 20:38:48 (Show Source): You can put this solution on YOUR website!y = 11x y-x = 81 --> y = x+81 x+81 = 11x 10x = 81 x = 8.1 y = 89.1
 Coordinate-system/230409: pleae help me solve this equation y=2x+41 solutions Answer 170622 by Alan3354(30927)   on 2009-10-22 19:40:18 (Show Source): You can put this solution on YOUR website!It's already solved.
 Pythagorean-theorem/230396: Are the numbers 8,15,and 19 a pothagorean triple? 1 solutions Answer 170607 by Alan3354(30927)   on 2009-10-22 19:19:25 (Show Source): You can put this solution on YOUR website!No
 Triangles/230371: In a plane, line e is parallel to line f, line f is parallel to line g, and line h is perpendicular to line e. which of the following must be true? A)e parallel g B)h parallel f C)g parallel h D)e parallel h1 solutions Answer 170605 by Alan3354(30927)   on 2009-10-22 19:18:41 (Show Source):
 Graphs/230297: f(x)= |x-3|1 solutions Answer 170554 by Alan3354(30927)   on 2009-10-22 17:36:49 (Show Source): You can put this solution on YOUR website!That's interesting. Do you have a question?
 Equations/230209: find the area of the region between the graph of y = x^3 and the x-axis from x= 1 to x= 41 solutions Answer 170552 by Alan3354(30927)   on 2009-10-22 17:34:37 (Show Source): You can put this solution on YOUR website!find the area of the region between the graph of y = x^3 and the x-axis from x= 1 to x= 4 ------------ The integral of x^3 = x^4/4 + C At x = 4: x^4/4 = 64 At x = 1: x^4/4 = 1/4 Area = 64 - 1/4 = 63.75 sq units
 Expressions-with-variables/230339: S= Vt + .5at^21 solutions Answer 170548 by Alan3354(30927)   on 2009-10-22 17:30:02 (Show Source): You can put this solution on YOUR website!What's your question?
 Numbers_Word_Problems/230299: The sum of the digits of a 3 digit number is 12 and the product of the digits is 48. The digits are in order from greatest to least. What is the number?1 solutions Answer 170523 by Alan3354(30927)   on 2009-10-22 15:48:43 (Show Source): You can put this solution on YOUR website!246
 Volume/230183: If the cicumference of the earth is 25,000,then what is the radius?1 solutions Answer 170481 by Alan3354(30927)   on 2009-10-22 11:33:03 (Show Source): You can put this solution on YOUR website!C = 2*pi*r r = 25000/2pi r =~ 3979 (miles, you didn't give units)
 Inequalities/230178: are the numbers: 0, -20, -13, -3 solutions of the inequality.... y-9>2y-41 solutions Answer 170480 by Alan3354(30927)   on 2009-10-22 11:21:05 (Show Source): You can put this solution on YOUR website!are the numbers: 0, -20, -13, -3 solutions of the inequality.... y-9>2y-4 ----------- y-9>2y-4 y>2y+5 -y>5 y<-5 ------- -20 and -13 are solutions. The other 2 are not.
 Triangles/230016: 3x+y+2x+40+2y=180 how would i solve this1 solutions Answer 170478 by Alan3354(30927)   on 2009-10-22 11:18:38 (Show Source): You can put this solution on YOUR website!Solve it for what?
 Triangles/230179: If the perimeter of a triangle is 49 inches, what is the length of each side?1 solutions Answer 170477 by Alan3354(30927)   on 2009-10-22 11:17:23 (Show Source): You can put this solution on YOUR website!They could be 1, 24 and 24 or 2, 23 and 24 or 5, 10 and 12 or 5.6, 22.4 and 21 or any of an infinite number of combinations that add up to 49.
 Complex_Numbers/230171: (4-7i)(4+7i) please solve and show work thank you1 solutions Answer 170476 by Alan3354(30927)   on 2009-10-22 10:48:52 (Show Source): You can put this solution on YOUR website!(4-7i)(4+7i) ------------ = 4*(4+7i) - 7i*(4+7i) = 16 + 28i - 28i - 49i^2 = 16 - 49i^2 i^2 = -1 = 16 + 49 = 65 ------------ These are similar to (a-b)*(a+b) = a^2 - b^2 EXCEPT the sign is plus. (a - bi)*(a + bi) = a^2 + b^2 ------ Also, nothing is solved for, there's no variable in 65. It's only simplified.
 Complex_Numbers/230169: (6-sqrt(-9)-(-3-sqrt(-25) sqrt is for the square root sign. How do you solve this equation please explain and show work1 solutions Answer 170475 by Alan3354(30927)   on 2009-10-22 10:45:27 (Show Source): You can put this solution on YOUR website!6-sqrt(-9)-(-3-sqrt(-25)) I added and deleted some parentheses to make them match. ---------- This can't be "solved" since it's not an equation. Equations have equal signs: equal, equate, equation are all related. This can be simplified. ------- 6-sqrt(-9)-(-3-sqrt(-25)) = 6 - 3i - (-3 - 5i) = 6 - 31 + 3 + 5i = 9 + 2i
 Complex_Numbers/230168: i^37 plese explain how to get the answer thank you1 solutions Answer 170474 by Alan3354(30927)   on 2009-10-22 10:41:45 (Show Source): You can put this solution on YOUR website! i^37 plese explain how to get the answer thank you ------ Since i^4 = 1, any power of i is the remainder of the exponent/4 ------------- 37/4 = 9 REM 1 i^37 = i^1 = i
 Percentage-and-ratio-word-problems/230164: If a peddler marks up his \$12 ball caps 80% and then puts them on sale for 20% off, what will you have to pay for a cap if tax is added at 7%?1 solutions Answer 170473 by Alan3354(30927)   on 2009-10-22 10:30:48 (Show Source): You can put this solution on YOUR website!If a peddler marks up his \$12 ball caps 80% and then puts them on sale for 20% off, what will you have to pay for a cap if tax is added at 7%? --------------- Does he sell them for \$12? Or buy them for \$12? Assuming you mean he buys them for \$12: He adds 80% --> \$12*1.8 = \$21.60 20% off of that --> \$21.60*0.8 = \$17.28 Add 7% for tax --> \$17.28*1.07 = \$18.49
 Numbers_Word_Problems/229990: If next year (2010) is written as a product of two positive integers, who's difference is as small as possible, then what is the difference?1 solutions Answer 170420 by Alan3354(30927)   on 2009-10-21 22:13:54 (Show Source): You can put this solution on YOUR website! If next year (2010) is written as a product of two positive integers, who's (sic) difference is as small as possible, then what is the difference? ---------- The numbers that multiply to 2010 (or any number) with a difference of zero(0) is the square root of the number. The sqrt(2010) = ~ 44.8 so look for numbers close to that. 2010 = 2*3*5*67 67 is prime so it has to be one of the numbers 2010 = 30*67 Difference = 37
 Complex_Numbers/229997: (3-2i)(2+4i) please show work1 solutions Answer 170419 by Alan3354(30927)   on 2009-10-21 22:08:46 (Show Source): You can put this solution on YOUR website!(3-2i)(2+4i) = 3(2+4i) - 2i(2+4i) = 6+12i - 4i - 8i*i (i*i = -1), so -8i*i = +8 = 6+12i - 4i + 8 = 14 + 8i
 Numbers_Word_Problems/230005: The second number is 6 more than twice the 1st number? 1st number X 2nd number ? Thank you!1 solutions Answer 170418 by Alan3354(30927)   on 2009-10-21 22:04:46 (Show Source): You can put this solution on YOUR website!2x + 6
 Probability-and-statistics/230013: 32. Find the minimum and maximum possible areas for a rectangle measuring 4.15 cm by 7.34 cm. Round to the nearest hundredth. (Hint: Remember to include appropriate units in your final answers.) (3 points) 1 solutions Answer 170416 by Alan3354(30927)   on 2009-10-21 22:03:42 (Show Source): You can put this solution on YOUR website!Area = 4.15*7.34 sq cm Area = 30.461 sq cm --> 30.46 sq cm That's what it is, there's no max or min.
 Miscellaneous_Word_Problems/230014: A lot is in the shape of a right triangle. The shorter leg measures 60 meters. The hypotenuse is 20 meters longer than the length of the longer leg. How long is the longer leg?1 solutions Answer 170415 by Alan3354(30927)   on 2009-10-21 22:01:40 (Show Source): You can put this solution on YOUR website!A lot is in the shape of a right triangle. The shorter leg measures 60 meters. The hypotenuse is 20 meters longer than the length of the longer leg. How long is the longer leg? --------- a^2 + b^2 = c^2 60^2 + b^2 = (b+20)^2 3600 + b^2 = b^2 + 40b + 400 3600 = 40b + 400 40b = 3200 b = 80 meters
 Travel_Word_Problems/230004: An airplane flying at 500 miles an hour leaves Minneapolis. One-half hour later, a second airplane leaves Minneapolis flying in the same direction at rate of 600 miles per hour. How long will it take the second airplane to overtake the first? 1 solutions Answer 170413 by Alan3354(30927)   on 2009-10-21 21:55:07 (Show Source): You can put this solution on YOUR website!An airplane flying at 500 miles an hour leaves Minneapolis. One-half hour later, a second airplane leaves Minneapolis flying in the same direction at rate of 600 miles per hour. How long will it take the second airplane to overtake the first? ----------- There's a hard way to do these, but take the easy way: ------ In 1/2 hour, the 1st plane is 250 miles away (500*0.5) The 2nd plane gains in it at 100 mph (600-500) 250/100 = 2.5 hours.
 Linear-equations/230010: Find Slope (3,1) (-2,6) Thank you! I get 6-1 =5 -2+3 =-5 m=5/-51 solutions Answer 170411 by Alan3354(30927)   on 2009-10-21 21:52:58 (Show Source): You can put this solution on YOUR website!Find Slope (3,1) (-2,6) Thank you! I get 6-1 =5 -2+3 =-5 ?? m=5/-5 You're correct, that's = -1
 logarithm/229981: how do you write 2[logx+logy] as a single logarithm?1 solutions Answer 170406 by Alan3354(30927)   on 2009-10-21 21:44:20 (Show Source): You can put this solution on YOUR website!how do you write 2[logx+logy] as a single logarithm? =========== = 2log(xy) =
 Rational-functions/229858: is this equation linear ? 6y - x = 71 solutions Answer 170341 by Alan3354(30927)   on 2009-10-21 18:56:08 (Show Source): You can put this solution on YOUR website!yes it is. there are no exponents higher than one.
 Graphs/229879: PLEASE HELP ME GRAPH THE EQUATION Y= 5 - X1 solutions Answer 170340 by Alan3354(30927)   on 2009-10-21 18:54:49 (Show Source): You can put this solution on YOUR website!Y= 5 - X ---------- Find 2 points and draw a straight line thru them. Pick values for x and find y. x = 0, y = 5 --> (0,5) x = 5, y = 0 --? (5,0)
 real-numbers/229888: # 679 #308 #214 Thank you1 solutions Answer 170338 by Alan3354(30927)   on 2009-10-21 18:52:08 (Show Source): You can put this solution on YOUR website!Do you have a question? What do those 3 numbers mean?
 test/229852: Find the pair of parallel lines. (1) 12y + 6x=2 (2) 6x-12y=2 (3) -4y=-2x+2 which pair is it? (1) and (3) (1) and (2) (2) and (3) There are no parallel lines.1 solutions Answer 170334 by Alan3354(30927)   on 2009-10-21 18:43:17 (Show Source): You can put this solution on YOUR website!Find the pair of parallel lines. (1) 12y + 6x=2 m = -1/2 (2) 6x-12y=2 m = +1/2 (3) -4y=-2x+2 m = +1/2 which pair is it? (1) and (3) (1) and (2) (2) and (3) 2 and 3 have the same slope, m = +1/2, so they're parallel.