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Geometry_Word_Problems/325135: A circular coin has a radius of 3/8 inch.When lying flat, how much area does the coin cover, in square inches? A.3pi/4 B.3pi/16 C.6pi/16 D.9pi/8 1 solutions Answer 232840 by Alan3354(31530)   on 2010-07-24 08:35:42 (Show Source): You can put this solution on YOUR website! A circular coin has a radius of 3/8 inch.When lying flat, how much area does the coin cover, in square inches? ------------ Area = pi*r^2 = pi(3/8)^2 = 9pi/64 sq inches

Expressions-with-variables/325143: This word problem has driven me crazy for a week. Please help me and show me how you came up with the answer. Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 m.p.h. and Train B is traveling at 50 m.p.h. Train A passes a station at 6:10 p.m. If train B passes the same station at 6:40, at what time will Train B catch up to Train A ? 1 solutions Answer 232839 by Alan3354(31530)   on 2010-07-24 08:25:48 (Show Source): You can put this solution on YOUR website! Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 m.p.h. and Train B is traveling at 50 m.p.h. Train A passes a station at 6:10 p.m. If train B passes the same station at 6:40, at what time will Train B catch up to Train A ? ----------------------- In 1/2 hour (640 - 610) train A goes 20 miles (1/2 x 40 mph) Train B gains on train A at 10 mph (50 - 40) It takes train B 2 hours to overtake train A (20/10) 6:40 + 2 hours = 8:40

Problems-with-consecutive-odd-even-integers/325148: Factor by grouping, if possible. 6x^2 - 15x + 14x - 35 -35 + -15x + 14x + 6x^2 -15x+14x=1x -35+-1x+6^2 is this right???? it dont seem right 1 solutions Answer 232837 by Alan3354(31530)   on 2010-07-24 08:19:19 (Show Source): You can put this solution on YOUR website! Factor by grouping, if possible. 6x^2 - 15x + 14x - 35 = 3x*(2x - 5) + 7*(2x - 5) = (3x+7)*(2x-5)

Polygons/325073: is it possible for the interior angles of a regular polygon to measure 145°. 1 solutions Answer 232801 by Alan3354(31530)   on 2010-07-23 20:44:56 (Show Source): You can put this solution on YOUR website! no, it isn't. The sum of the exterior angles of ALL polygons is 360º. If the interior angle is 145º, the exterior would be 35º. 360/35 is not an integer.

test/325030: Montreal’s Marathon building is 195m tall. From a point level with, and 48m away from, the base of the building, what is the angle of elevation of the top of the building, to the nearest degree? 1 solutions Answer 232800 by Alan3354(31530)   on 2010-07-23 20:42:52 (Show Source): You can put this solution on YOUR website! Montreal’s Marathon building is 195m tall. From a point level with, and 48m away from, the base of the building, what is the angle of elevation of the top of the building, to the nearest degree? ----------------- tan(angle) = 195/48 Angle =~ 76º

Evaluation_Word_Problems/324955: On 3 consecutive passes a football team gains 7 yards, loses 40 yard and gains 38 yards. What number represents the total net yardage? 1 solutions Answer 232798 by Alan3354(31530)   on 2010-07-23 20:34:42 (Show Source): You can put this solution on YOUR website! +7 -40 +38 Add them ------------ How could they lose 40 yds on a pass play? or any play?

Word_Problems_With_Coins/325085: Can you help me with this problem? A $31.50 box of nuts contains almonds mixed with pecans. Almonds cost $7.50/kg and pecans cost $9.00/kg. The number of kilograms of almonds is 3 times the number of kilograms of pecans. Find the number of kilograms of each kind of nut in the mixture. 1 solutions Answer 232797 by Alan3354(31530)   on 2010-07-23 20:33:12 (Show Source): You can put this solution on YOUR website! A $31.50 box of nuts contains almonds mixed with pecans. Almonds cost $7.50/kg and pecans cost $9.00/kg. The number of kilograms of almonds is 3 times the number of kilograms of pecans. Find the number of kilograms of each kind of nut in the mixture. ------------------- A = 3*P 7.5A + 9P = 31.5 Can you go from there?

Problems-with-consecutive-odd-even-integers/325076: can some one look over my problem and see if i am doing this right Factor out the largest common factor. t^5 - 8t^4 -8t^4+t^5 t^4(-8+t)=0 t4 is the gcf t4=0 (-8+t) -8+t=0 add 8 to each side -8+8+t=0+8 -8+8=0+8 t=0+8 0+8=8 T=8 1 solutions Answer 232795 by Alan3354(31530)   on 2010-07-23 20:06:17 (Show Source): You can put this solution on YOUR website! Factor out the largest common factor. t^5 - 8t^4 -8t^4+t^5 Usually the order is descending exponents. It's not wrong, but there's no reason to change the order. ----------------- t^4(-8+t)=0 t4 is the gcf *** you wrote an equation??? why? You factored correctly. Neither of the 2 factors is consistently the greatest. The problem should have said, "factor", without reference to the gcf. ---------- The rest is NA. No equation was given, no solutions asked for. t4=0 (-8+t) -8+t=0 add 8 to each side -8+8+t=0+8 -8+8=0+8 t=0+8 0+8=8 T=8

test/325029: Peggy’s Cove Lighthouse, in Nova Scotia, is possibly the most photographed lighthouse in the world. From the observation deck, the angle of depression of a boat is 6º. How far is the boat from the lighthouse, to the nearest metre? 1 solutions Answer 232790 by Alan3354(31530)   on 2010-07-23 19:49:25 (Show Source): You can put this solution on YOUR website! Insufficient data. ----------------- The distance from the base of the lighthouse is: h/tan(6º) ---------- The distance from the observer is: h/sin(6º) -------------- The difference is small, less than 0.6% of the height of the lighthouse.

expressions/325080: simplify the expression. write the answer with positive exponents. Assume that all variables represent positive real numbers (-27x^9)^1/3 1 solutions Answer 232789 by Alan3354(31530)   on 2010-07-23 19:44:59 (Show Source): You can put this solution on YOUR website! (-27x^9)^1/3 =

Permutations/325078: If 1.5 chickens lay 1.5 eggs in 1.5 days, how many eggs do 9 chickens lay in 15 days? 1 solutions Answer 232788 by Alan3354(31530)   on 2010-07-23 19:36:55 (Show Source): You can put this solution on YOUR website! If 1.5 chickens lay 1.5 eggs in 1.5 days, --> 1.5 eggs/2.25 chicken-days = 2/3 eggs per chicken per day. -------------- how many eggs do 9 chickens lay in 15 days? (2/3)*9*15= 90 eggs -------------------- The usual question, given the egg-laying rate of the chickens, is "...how much does a pound of butter weigh?"

Miscellaneous_Word_Problems/325071: Solve the problem. Draw 11 through (-2,4) and (3,-1). What is the slope of any line perpendicular to 11? Draw 12 through (1,3) so that it is perpendicular to 11. *NOTE* THIS QUESTION DOES NOT HAVE AN EVEVEN IN IT. IT IS A ONE WITH A SMALLER ONE TO THE LOWER RIGHT SIDE. 1 solutions Answer 232787 by Alan3354(31530)   on 2010-07-23 19:33:24 (Show Source): You can put this solution on YOUR website! Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ Another approach using determinants: |x y 1| |2 1 1| = 0 |3 5 1| -------- x(1-5) - y(2-3) + 1(10-3) = 0 -4x + y + 7 = 0 y = 4x - 7 --------- For further assistance, or to check your work, email me via the thank you note or at Moral Loophole@aol.com ---------------------- A line and a point example. Write in standard form the eqation of a line that satisfies the given conditions. Perpendicular to 9x+3y=36, through (1,2) ----------------- Find the slope of the line. Do that by putting the equation in slope-intercept form, y = mx + b. That means solve for y. 9x+3y = 36 3y= - 9x + 36 y = -3x + 12 The slope, m = -3 ------------------ The slope of lines parallel is the same. The slope of lines perpendicular is the negative inverse, m = +1/3 ---------------- Use y = mx + b and the point (1,2) to find b. 2 = (1/3)*1 + b b = 5/3 The equation is y = (1/3)x + 5/3 (slope-intercept form) x - 3y = -5 (standard form) ------------------------ For further assistance, or to check your work, email me via the thank you note, or at Moral Loophole@aol.com

expressions/325079: (-16)^1/4 how do I evaluate this expression 1 solutions Answer 232786 by Alan3354(31530)   on 2010-07-23 19:31:26 (Show Source): You can put this solution on YOUR website! (-16)^1/4 how do I evaluate this expression = = = and ------------------------------------- A better method: -16 = 16cis(180 + n*360) (16cis(180+n*360))^(1/4) = 2cis(45+n*90) = 2cos(45) + 2i*sin(45) = sqrt(2) + i*sqrt(2) = 2cos(135) + 2i*sin(135) = -sqrt(2) + i*sqrt(2) = 2cos(225) + 2i*sin(225) = -sqrt(2) - i*sqrt(2) = 2cos(315) + 2i*sin(315) = +sqrt(2) - i*sqrt(2) 4th root, 4 answers above.

Miscellaneous_Word_Problems/325083: One number is 3 times as large as another number.Their sum is 64.What are the two numbers? 1 solutions Answer 232785 by Alan3354(31530)   on 2010-07-23 19:27:19 (Show Source): You can put this solution on YOUR website! n + 3n = 64

Numbers_Word_Problems/324911: how many 3 person groups can be formed in a club with 8 people? daria can wash and detail 3 cars in 2 hours. Larry can wash and detail the same 3 cars in 1.5 hours. About how long will it take to wash and detail the 3 cars if they worked together? 1 solutions Answer 232776 by Alan3354(31530)   on 2010-07-23 17:52:08 (Show Source): You can put this solution on YOUR website! how many 3 person groups can be formed in a club with 8 people? The 1st chosen is 1 of 8, then 1 of 7, then 1 of 6 --> 8*7*6 But, since ABC is the same as CAB and CBA, you have to divide by 3*2*1 8*7*6/(3*2*1) = 56 -------------------- daria can wash and detail 3 cars in 2 hours. Larry can wash and detail the same 3 cars in 1.5 hours. About how long will it take to wash and detail the 3 cars if they worked together? The tasks are the same. Daria does 1/2 of the task per hour. Larry does 1/1.5 per hour. Together, they to 1/2 + 1/1.5 = 7/6 per hour --> 6/7 hours per task ------------------------- If it's a timed test, use the shortcut product/sum 2*1.5/(2+1.5) = 3/3.5 = 6/7 hours

Volume/324903: What is the volume of a cone that has an inscribed sphere removed? Use a variety of sized cones. Generalize a pattern (if any) for volume remaining to the total cone volume. 1 solutions Answer 232772 by Alan3354(31530)   on 2010-07-23 17:44:18 (Show Source): You can put this solution on YOUR website! I'll do this tomorrow. email me at moral loophole@aol.com with any questions.

Probability-and-statistics/325063: I cannot seem to figure out how this problem is worked. Any help is appreciated. I Know the answer is 1/56 but I don't have a clue at the moment how that can be. Here is the problem: In a certain lottery, 3 different numbers between 1 and 8 inclusive are drawn at random. These are the winning number. If you choose 3 different numbers at random between 1 and 8, what is the probability you will match the winning numbers? Assume that the order of the numbers is unimportant. Answer: 1/56 ---- I need help getting this answer. I have tried evrything I can think of. Thank you 1 solutions Answer 232770 by Alan3354(31530)   on 2010-07-23 17:39:00 (Show Source): You can put this solution on YOUR website! In a certain lottery, 3 different numbers between 1 and 8 inclusive are drawn at random. These are the winning number. If you choose 3 different numbers at random between 1 and 8, what is the probability you will match the winning numbers? Assume that the order of the numbers is unimportant. -------------------- It's not specified, but to get that answer: No repeats are allowed, ie, 888 is not valid. ------------- The 1st number is one of 8, then 1 of 7, then 1 of 6. = 8*7*6 But since is says order doesn't matter, 876 is the same as 678 and 786, etc That gives each possible number 6 different ways it can be selected. --> 8*7*6/6 = 8*7 = 1/56

Miscellaneous_Word_Problems/324896: When dropped, a ball rebounds to 4/25 of its original height. How high will the ball rebound after the 6th bounce if it is dropped from the height of 25ft? 1 solutions Answer 232768 by Alan3354(31530)   on 2010-07-23 17:16:53 (Show Source): You can put this solution on YOUR website! When dropped, a ball rebounds to 4/25 of its original height. How high will the ball rebound after the 6th bounce if it is dropped from the height of 25ft? ---------- h = 25*(4/25)^6 = 4^6/25^5 = 4096/9765625 = 4.194304E-4 feet = 0.0004194304 feet = 0.1278 mm It's no longer bouncing

Polynomials-and-rational-expressions/325055: why can't we substitute 3 for x in the rational expression 2/x-3? 1 solutions Answer 232766 by Alan3354(31530)   on 2010-07-23 17:10:33 (Show Source): You can put this solution on YOUR website! you get 2/0, which freaks people out. Not all people, but some of them.

Trigonometry-basics/325056: I have a problem that states: Show that sin theta = cos theta tan theta. I have put in numbers for theta, but they never come out equal. Can you help? 1 solutions Answer 232765 by Alan3354(31530)   on 2010-07-23 17:09:13 (Show Source): You can put this solution on YOUR website! Show that sin theta = cos theta tan theta. tan = sin/cos sin = cos*(sin/cos) sin = sin What numbers did you put in that didn't work?

Travel_Word_Problems/324951: The path of a ball projected in the air can be represented by the equation h=16t^2+64t where h represents height, and t represents time at what time is the ball 48 feet high? 1 solutions Answer 232754 by Alan3354(31530)   on 2010-07-23 15:57:45 (Show Source): You can put this solution on YOUR website! The path of a ball projected in the air can be represented by the equation h=16t^2+64t where h represents height, and t represents time at what time is the ball 48 feet high? ------------------------------- h=16t^2+64t Set h = 48 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=28 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.645751311064591, -4.64575131106459. Here's your graph: ------------------ no units given I don't think your equation is right. The ball never comes back down.

Evaluation_Word_Problems/324982: 5/4x+1/8x=7/8+x The solution to x is: 1 solutions Answer 232713 by Alan3354(31530)   on 2010-07-23 14:09:55 (Show Source): You can put this solution on YOUR website! 5/4x+1/8x=7/8+x Multiply by 8x 10 + 1 = 7x + 8x^2 8x^2 + 7x - 11 = 0 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=401 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.814061524656299, -1.6890615246563. Here's your graph:

Trigonometry-basics/324978: Prove Identities: cscx + cotx/tanx + sinx = cotx cscx 1 solutions Answer 232712 by Alan3354(31530)   on 2010-07-23 14:06:07 (Show Source): You can put this solution on YOUR website! Prove Identities: cscx + cotx/tanx + sinx = cotx cscx Put everything in terms of sine and cosine: 1/sin + (cos/sin)/(sin/cos) + sin = (cos/sin)*(1/sin) 1/sin + (cos^2/sin^2) + sin = cos/sin^2 (sin + cos^2 + sin^2)/sin = cos/sin^2 (sin + 1)/sin = cos/sin^2 sin + 1 = cos/sin It's not true, not an identity.

Travel_Word_Problems/325000: how long will it take to run 24 miles at a rate of 6 miles per hour? use the formula D=rt 1 solutions Answer 232709 by Alan3354(31530)   on 2010-07-23 14:00:52 (Show Source): You can put this solution on YOUR website! You have 2 numbers. Use d = rt.

Length-and-distance/324981: I have two questions now I am having so many problems out of this math it is unreal I would appreciate any help with these. Thanks #1) 7,000,000ps = ________ms #2) 6min = _________ms 1 solutions Answer 232687 by Alan3354(31530)   on 2010-07-23 13:04:41 (Show Source): You can put this solution on YOUR website! #1) 7,000,000ps = ________ms If ps is a picosecond, then 7E6 ps = 7E6 * 1E-9 milliseconds = 7E-3 ms, or -.007 ms ---------------------- #2) 6min = _________ms 6 minutes = 360 seconds = 360,000 milliseconds

Quadratic_Equations/324949: A golf ball is hit from the ground with an initial velocity of 208 feet per second. How long will it take the golf ball to hit the ground? 1 solutions Answer 232678 by Alan3354(31530)   on 2010-07-23 11:30:10 (Show Source): You can put this solution on YOUR website! Is that the vertical speed? It could be on the ground rolling, --> 0 seconds. Not enough info.

Linear_Equations_And_Systems_Word_Problems/324863: Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s3 - 13s2 + 54s - 72. a) Find V(10). b) If the new width is s - 6 centimeters, then what are the new length and height? 1 solutions Answer 232589 by Alan3354(31530)   on 2010-07-22 21:24:51 (Show Source): You can put this solution on YOUR website! Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s3 - 13s2 + 54s - 72. a) Find V(10) V(10) = 10^3 -13*100 + 54*10 - 72 = 168 --------------- b) If the new width is s - 6 centimeters, then what are the new length and height? They're the same, s-6 cm.

Polynomials-and-rational-expressions/324463: I am stuck..... Help me solve this equation 1/x-1 + 2/x = x/x-1 /= written in fraction form like 2 over x 1 solutions Answer 232587 by Alan3354(31530)   on 2010-07-22 21:19:50 (Show Source): You can put this solution on YOUR website! 1/x-1 + 2/x = x/x-1 ------------------ If you mean 1/(x-1) + (2/x) = x/(x-1) Multiply thru by x(x-1) x + 2(x-1) = x^2 x^2 - 3x + 2 = 0 (x-1)*(x-2) = 0 x = 1 x = 2 ------ x = 1 is not allowed, it makes the denominators zero.

Circles/324860: if the circumference of a circle is 64 cm, what is the lenth of an arc that measures 45 degrees? 1 solutions Answer 232586 by Alan3354(31530)   on 2010-07-22 21:12:32 (Show Source): You can put this solution on YOUR website! 45º is 1/8 of the circle. 64/8 = 8 cm

Travel_Word_Problems/324799: A boy rows his boat 8 km downstream in 1 hour and 4 minutes, and returns in 2 2/7 hours. At what rate will he row in still water? What is the rate of the current? 1 solutions Answer 232582 by Alan3354(31530)   on 2010-07-22 20:21:28 (Show Source): You can put this solution on YOUR website! A boy rows his boat 8 km downstream in 1 hour and 4 minutes, and returns in 2 2/7 hours. At what rate will he row in still water? What is the rate of the current? --------------- 8 km/64 minutes = 1/8 km/min = 15/2 km/hr 8 km/(16/7) = 7/2 km/hr --------------------- The boat's speed is the average, = (15/2 + 7/2)/2 = 5.5 km/hr ------------- The current is the difference, = 2 km/hr

Expressions-with-variables/324742: Solve V=2/5>Bh for h 1 solutions Answer 232578 by Alan3354(31530)   on 2010-07-22 20:15:03 (Show Source): You can put this solution on YOUR website! That makes no sense.