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# Recent problems solved by 'HyperBrain'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719, >>Next

 Functions/214031: if f(a+b) = f(a) + f(b) for all real numbers. Show how f(2a) = 2*f(a) and show how f(0) = 0.1 solutions Answer 161676 by HyperBrain(694)   on 2009-09-15 22:50:03 (Show Source): You can put this solution on YOUR website!f(a+b) = f(a) + f(b) Replace b with a: f(a+a)=f(a)+f(a) f(2a)=2*f(a)
 Triangles/213930: find the area of the equilateral triangle with a side length of x feet.1 solutions Answer 161675 by HyperBrain(694)   on 2009-09-15 22:49:07 (Show Source): You can put this solution on YOUR website!The area of an equilateral triangle of side length x.
 Functions/213938: find the average rate of change of f(x)= 1/(x-2) between points x=4 and x=81 solutions Answer 161674 by HyperBrain(694)   on 2009-09-15 22:46:37 (Show Source): You can put this solution on YOUR website!At x=4, y=1/(4-2)=1/2 At x=8, y=1/(8-2)=1/6 --- The ave. rate of change is the slope of the line passing through (4,1/2) and (8,1/6) --- =-1/12
 Equations/214026: This question is from textbook College algebra solve the equation: square root of 3q+1 - the square root of q-1 =21 solutions Answer 161673 by HyperBrain(694)   on 2009-09-15 22:43:35 (Show Source): You can put this solution on YOUR website! Square both sides Let x=q-1 Then x=0 or x=2 If x=0, q-1=0 so q=1 If x=2, q-1=2 so q=3. So, q=1 or 3
 Equations/214025: Find a counterexample that shows the statement is false. For every number n, 2^n>n +11 solutions Answer 161670 by HyperBrain(694)   on 2009-09-15 22:37:12 (Show Source): You can put this solution on YOUR website!2^n>n +1 --- If n=1: 2^n=2^1=2 n+1=1+1=2 --- So, if n=1, 2^n=n+1. Therefore, the given statement is false.
 Geometry_Word_Problems/213949: The number of diagonals d in a polygon with n sides is given by the formula d=n^2-3n/2. If the polygon has 90 diagonals, how many sides does it have? 1 solutions Answer 161669 by HyperBrain(694)   on 2009-09-15 22:34:00 (Show Source): You can put this solution on YOUR website!Using the formula you've given, n^2-3n/2=90 So, n^2-3n=n(n-3)=180=15(12); note that 12=15-3 --- So, the polygon has 15 sides.
 Equations/214021: You are given an endpoint and the midpoint of a line segment. Find the coordinates of the other endpoint. Each midpoint is denoted by M(x, y) Q (-1,14) M (2,7)1 solutions Answer 161667 by HyperBrain(694)   on 2009-09-15 22:27:11 (Show Source): You can put this solution on YOUR website!Q (-1,14) M (2,7) --- Let A(h,k) be the unknown point. --- Using the midpoint formula, (h+(-1))/2=2 h+(-1)=4 h-1=4 h=5 --- Applying the midpoint formula for k, (k+14)/2=7 k+14=14 k=0 --- So, the other endpoint is at (5,0)
 Sequences-and-series/214017: 8 16 14 10 whats the next 3 numbers in the sequence1 solutions Answer 161663 by HyperBrain(694)   on 2009-09-15 22:14:19 (Show Source): You can put this solution on YOUR website!8 16 14 10 the first and third terms are 8 and 14. Note that 14=8+6 the second and fourth terms are 16 and 10. Note that 10=16-6 --- So, the nth term=(n-2)th term + 6 if n is odd But, if n is even, nth term =(n-2)th term -6. --- The next term is the 5th term. Since 5 is odd, 5th term=(5-2)th term + 6=3rd term+6=14+6=20
 Coordinate-system/190899: This question is from textbook saxon algebra 2 Convert the polar coordinate (5, 2pi/3) to cartesian coordinates.1 solutions Answer 160839 by HyperBrain(694)   on 2009-09-12 04:32:24 (Show Source): You can put this solution on YOUR website!Just in case you don't remember: Given the polar coordinates of a point (r, theta) then it rectangular coordinates is (r cos theta, r sin theta). --- Here: r=5 theta=2pi/3=120 degrees --- So, the rectangular coordinates of the given point is: (, )
 Human-and-algebraic-language/212912: In a writing competition, the first place winner receives ½ of the prize money. The second runner up receives ¼ of what the winner won. What was the total amount of prize money distributed if the winner receives \$6,000? 1 solutions Answer 160838 by HyperBrain(694)   on 2009-09-12 04:22:50 (Show Source): You can put this solution on YOUR website!Since the winner receives half of the total prize money, \$6000 is half of the total prize money. --- So, the total prize money is 2(\$6000)=\$12000
 Geometry_proofs/212913: if b is the mid point of ac and c is the mid point of bd, where a,b,c,d lie on a straight line, say why ab=cd?1 solutions Answer 160837 by HyperBrain(694)   on 2009-09-12 04:21:02 (Show Source): You can put this solution on YOUR website!Since, b is the midpoint of ac then a, b, and c are collinear (the points lie on the same line) Since, c is the midpoint of bd then b, c, and d are collinear as well. So, a, b, c, and d are collinear. --- Since b is the midpoint of ac, then ab=bc Since c is the midpoint of bd, bc=cd. --- Now, since ab=bc and bc=cd, then ab=cd
 Trigonometry-basics/197454: Solve for x in the equation (1 +sinx/cosx)+(cosx/1+sinx)=4 for 0≤ x ≤ 2π rad.1 solutions Answer 160628 by HyperBrain(694)   on 2009-09-11 03:04:14 (Show Source): You can put this solution on YOUR website! Multiply both sides by cos x (1+ sin x) Divide both sides by 1 + sin x There are only two solutions: x=pi/6 or 11pi/6
 Trigonometry-basics/199242: Given the Triangle ABC with b=8,c=10, A=74 degrees what is the length of a?1 solutions Answer 160627 by HyperBrain(694)   on 2009-09-11 02:56:13 (Show Source): You can put this solution on YOUR website!We use cosine law to solve this problem. --- = = =120 --- So,
 Trigonometry-basics/204685: Can you help me solve this trigonometric identities question: 1)Prove each of the following identities. a)cos^2 x +2sin^2 x -1=sin^2 x1 solutions Answer 160626 by HyperBrain(694)   on 2009-09-11 02:53:45 (Show Source): You can put this solution on YOUR website! But, . So = =
 Trigonometry-basics/207286: If the latitude of Chicago is about 42 degrees and the radius of the earth is about 4000 miles, how far is Chicago from the equator? ( use pi= 3.1416) 1 solutions Answer 160625 by HyperBrain(694)   on 2009-09-11 02:48:39 (Show Source): You can put this solution on YOUR website!Let x=distance of Chicago from the equator. --- x=r sin A=(4000 mi)(sin 42)=2677 mi
 Trigonometry-basics/207519: Complete the following Identity cos 2x =1 solutions Answer 160624 by HyperBrain(694)   on 2009-09-11 02:46:57 (Show Source):
 Travel_Word_Problems/212372: Joe drove 210km at 70km/h and then another 210 km at 105km/h. It took Bill the same length of time to drive the entire 420km at constant speed. What was Bill's speed?1 solutions Answer 160623 by HyperBrain(694)   on 2009-09-11 02:41:33 (Show Source): You can put this solution on YOUR website!time=distance/speed. --- So, the total time it took for Joe to drive is: hr --- speed=distance/time =-= So, Bill's speed is: km/hr
 Travel_Word_Problems/212373: A motorist driving at 100km/h can go from Wilton to Stockton in 2 hours less time than can a train which averages 75 km/h. How far apart are the two towns?1 solutions Answer 160622 by HyperBrain(694)   on 2009-09-11 02:38:53 (Show Source): You can put this solution on YOUR website!distance=speed*time so time=distance/speed --- Let x=distance between the two towns km
 Equations/212707: Calculate the density of a block of wood which weighs 750kg and has the dimensions 25cm X 0.10m X 50.0m1 solutions Answer 160621 by HyperBrain(694)   on 2009-09-11 02:35:03 (Show Source): You can put this solution on YOUR website!25cm X 0.10m X 50.0m --- So, the volume is 25*0.10*50.0=125 cubic meters --- So, the density is 750 kg/125 cubic meters =6 kg/cubic meter
 Polygons/212711: a regular polygon has an interiaor angle of 170 degrees. how many sides does it have? is it 3? 1 solutions Answer 160620 by HyperBrain(694)   on 2009-09-11 02:33:20 (Show Source): You can put this solution on YOUR website!If the interior angle is 170 degrees, the exterior angle is 10 degrees. --- The exterior angle of a regular polygon with n sides has a measure of 360/n degrees. --- So, since the exterior angle of this polygon has measure 10 degrees, then it has 360/10=36 sides.
 Trigonometry-basics/207935: This question is from textbook College Math 1 Given a point (5,-5) on the terminal side of angle0, find the value of sin.1 solutions Answer 160393 by HyperBrain(694)   on 2009-09-09 22:46:55 (Show Source): You can put this solution on YOUR website!Let x=angle --- Since the terminal side contains the point (5,-5), the terminal side has slope -5/5=-1 and so tan x=-1 x=135 or 315 degrees Since (5,-5) is at quad. II, then x=135 degrees. --- So, sin x=sin 135=sin 45=
 Trigonometry-basics/211786: the angle of elevation from the end of the shadow to the top of the building is 63 degrees and the distance is 220 feet.find the length of the shadow to the nearest foot a)100 feet b)196 feet c)432 feet d)112 feet1 solutions Answer 160392 by HyperBrain(694)   on 2009-09-09 22:43:14 (Show Source): You can put this solution on YOUR website!Let x=length of the shadow --- Then cos 63=x/220 x=220 cos 63=220(0.454)=100 ft
 Mixture_Word_Problems/212320: HOW MANY LITERS OF A 10% ALCOHOL SOLUTION MUST BE MIXED WITH 40 L OF A 50% SOLUTION TO GET A 40% SOLUTION?1 solutions Answer 160391 by HyperBrain(694)   on 2009-09-09 22:40:07 (Show Source): You can put this solution on YOUR website!Let x=the amount of 10% alcohol solution required --- x L + 40 L = (x+40) L of mixture --- If we have x L of 10% alcohol solution, we have 0.10x L pure alcohol If we have 40 L of 50% alcohol solution, we have 0.5(40)=20 L pure alcohol --- So, we have the equation: 0.40(x+40)=0.10x+20 40(x+40)=10x+2000 4(x+40)=x+200 4x+160=x+200 3x=40 x=40/3 L
 Trigonometry-basics/212322: This question is from textbook Advanced Mathematics Draw the angle in quadrant II whose terminal side is on 1/2x + y = 0.1 solutions Answer 160389 by HyperBrain(694)   on 2009-09-09 22:35:50 (Show Source): You can put this solution on YOUR website!The line is: x/2 + y=0 2x+y=0 y=-2x --- This line is passing through the origin and quadrants II and IV. Since the angle has a terminal side at quad. II, If a is the angle, then tan a=-2 --- Getting the arc tan, tan a=-2 a=arctan -2=116.565 degrees
 Angles/212358: The measure of one angle is 47 degrees less that its supplement. What is the measure of each angle?1 solutions Answer 160388 by HyperBrain(694)   on 2009-09-09 22:31:45 (Show Source): You can put this solution on YOUR website!Let x=angle Then 180-x=supplement of the angle --- We have the equation: x=(180-x)-47 x=133-x 2x=133 x=66.5 degrees
 Expressions-with-variables/212325: This question is from textbook A rectangle and a square have the same width, but the rectangle is 5m longer than the square. Their total area 133m2. Find the dimensions of each figure. Choices for the square's width are 6,7,8.1 solutions Answer 160387 by HyperBrain(694)   on 2009-09-09 22:30:23 (Show Source): You can put this solution on YOUR website!Let x=side length of the square=width of the rectangle Then x+5=length of the rectangle --- The area of the square is x(x) The area of the rectangle is x(x+5) --- We have the equation: x(x)+x(x+5)=133 x(x+x+5)=133 x(2x+5)=133 --- But, 133=7(19) its only factors Coincidentally, if x=7, 2x+5=2(7)+5=14+5=19 --- So x=7 m
 Geometry_Word_Problems/212342: the measure of an angle is 5 less than 4 times the measure of its supplement. find the measures of both angles?1 solutions Answer 160384 by HyperBrain(694)   on 2009-09-09 22:26:15 (Show Source): You can put this solution on YOUR website!Let x=angle Then 180-x=supplement of the angle --- We have the equation: x=4(180-x)-5 x=720-4x-5 x=715-4x 5x=715 x=143 degrees
 Angles/212347: This question is from textbook the measure of the angle's supplement is 44 less than the measure of the angle. find the measure of the angle's supplement.1 solutions Answer 160383 by HyperBrain(694)   on 2009-09-09 22:24:44 (Show Source): You can put this solution on YOUR website!Let x=angle Then 180-x=supplement of the angle --- We have the equation: 180-x=x-44 2x=224 x=112 degrees
 Geometry_Word_Problems/212354: the complement of an angle is one-third the size of the supplement of the same angle. Find the measure of the angle?1 solutions Answer 160381 by HyperBrain(694)   on 2009-09-09 22:23:25 (Show Source): You can put this solution on YOUR website!Let x=angle 90-x=complement of the angle 180-x=supplement of the angle --- So, we have the equation: 90-x=1/3(180-x) multiply both sides by 3, to remove the fraction 3(90-x)=180-x 270-3x=180-x 2x=90 x=45 degrees
 Trigonometry-basics/212348: This question is from textbook Advanced Mathematics Find all angles t such that 3t is coterminal with 180 degrees and t is between 0 degrees and 360 degrees.1 solutions Answer 160379 by HyperBrain(694)   on 2009-09-09 22:20:41 (Show Source): You can put this solution on YOUR website!I shall use modular arithmetic to solve this one. An angle x is coterminal with 180 degrees if and only if when if is divided by 360, the remainder is 180. So, 3t=180 (mod 360) t=60 (mod 360) --- This is the general modular solution. Algebraically, t=360k+60 for all integer values of k
 Trigonometry-basics/211795: in triangle ABC,a=7.8, b=4.2, c=3.9. find B to the nearest tenth. a)15.1 degrees b)148.7 degrees c)78.9 degrees d)16.2 degrees1 solutions Answer 160178 by HyperBrain(694)   on 2009-09-09 03:08:09 (Show Source): You can put this solution on YOUR website!We use cosine law to solve this problem: --- Solving for cos B, B=arc cos 0.9601=16.2 degrees