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# Recent problems solved by 'venugopalramana'

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 Quadratic_Equations/93185: I need help to solve these problem I am having problems figuring it out. Identify the axis summetry, greate a suitable table of value, then sketck the graph(include the axis of summetry). The first one is y=x^2-4x and the other one is y= -x^2+3x-3 thanks a million1 solutions Answer 67814 by venugopalramana(3286)   on 2007-08-18 10:32:01 (Show Source): You can put this solution on YOUR website!I need help to solve these problem I am having problems figuring it out. Identify the axis summetry, greate a suitable table of value, then sketck the graph(include the axis of summetry). The first one is y=x^2-4x Y=(X-2)^2-4 HENCE X=2 IS THE LINE OF SYMMETRY X...........-2......0...........2.........4.........6....ETC Y=X^2-4X....12......0..........-4.........0.........12...ETC and the other one is y= -x^2+3x-3 = 1.5^2-3-[X^2-2*X*1.5+1.5^2] Y=-0.75-(X-1.5)^2 X=1.5 IS LINE OF SYMMETRY X...............-3.........-1.........0.........1.........3...ETC. Y=-X^2+3X-3.....-21........-7........-3........-1........-3...ETC
 Quadratic_Equations/93184: I need help to solve this problem I am having problems figuring it out Find the x - intercepts y=x^2-2x+4 thanks a million1 solutions Answer 67811 by venugopalramana(3286)   on 2007-08-18 09:04:30 (Show Source): You can put this solution on YOUR website!I need help to solve this problem I am having problems figuring it out Find the x - intercepts y=x^2-2x+4 thanks a million THAT IS WE HAVE TO FIND X WHEN Y=0 X^2-2X+4=0 DISCRIMINANT = (-2)^2-4*1*4=4-16=-12<0 HENCE X IS IMAGINARY. HENCE THERE ARE NO REAL X INTERCEPTS
 Signed-numbers/93182: 1)Given the binary operation * defined over the set of real numbers R by a*b=a+b+ab. What are the invertible elements of R with respect to *. 1 solutions Answer 67810 by venugopalramana(3286)   on 2007-08-18 09:00:14 (Show Source): You can put this solution on YOUR website!1)Given the binary operation * defined over the set of real numbers R by a*b=a+b+ab. What are the invertible elements of R with respect to *. LET I BE THE IDENTITY ELEMENT WRT * OPERATION.SO A*I=A=A+I+AI I(A+1)=0 I=0 HENCE IF X IS INVERSE OF A THEN A*X=I=0=A+X+AX X(A+1)= -A X=-A/(A+1) HENCE A SHOULD NOT BE -1 SO ALL ELEMENTS IN R EXCEPT A=-1 ARE INVERTIBLE
 Exponential-and-logarithmic-functions/93116: How do i evaluate the following: log3 81 log4 256 log2 (1/32) log5 1 log3 (-1) Please help thanks Lucy1 solutions Answer 67751 by venugopalramana(3286)   on 2007-08-17 12:10:41 (Show Source): You can put this solution on YOUR website!How do i evaluate the following: log3 81 WRITE THE NUMBER AS A POWER OF BASE.THAT POWER IS THE LOG OF THE NUMBER TO THE BASE. HERE NUMBER = N =81 BASE = B =3 WE KNOW THAT 3*3*3*3=3^4=81........P=4 HENCE LOG(81) TO BASE 3 = 4 [LOGARITHM] = P=4 log4 256 N=256.......B=4............4^4=256.....P=5 LOGARITHM =4 log2 (1/32) N=1/32.B=2...........[2*2*2*2*2]^(-1) =2^(-5)=1/32........P=-5 LOGARITHM =-5 log5 1 N=1........B=5...........5^0=1.........P=0 LOGARITHM =0 log3 (-1) N=-1....B=3.........WE HAVE NO POWER P WHICH MAKES 3^P=-1 SO IT DOES NOT EXIST... INFACT LOG OF 0 OR NEGATIVE NUMBER DO NOT EXIST WE CAN HAVE LOGS FOR POSITIVE NUMBERS ONLY. Please help thanks Lucy
 Trigonometry-basics/93114: This question is from textbook Algebra and Trigonometry Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=-2, that passes through the point P(1,4).1 solutions Answer 67748 by venugopalramana(3286)   on 2007-08-17 12:02:57 (Show Source): You can put this solution on YOUR website!Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=-2, that passes through the point P(1,4). Y=B(A^X)+C Y INTERCEPT =2...THAT IS AT X=0...Y=2 2=B*(A^0)+C = B+C..................1 PASSES THROUGH (1,4).........Y=4 AT X=1 4=BA+C...................2 HORIZONTAL ASYMPTOTE IS Y=-2......THAT IS AS X TENDS TO + OR - INFINITY,Y TENDS TO -2...HERE WE TAKE X TENDING TO -INFINITY AS OTHERWISE , A^X WILL BE INFINITE.HENCE -2=B*0+C............3 C=-2 FROM EQN.1,WE GET B-2=2 B=4 NOW FROM EQN.2 4=4A-2 A=6/4=1.5 HENCE EQN. IS Y=4*(1.5)^X -2
 Linear-equations/93107: Write an equation for the linear function f satisfying the given conditions. f(3) = 4 and f(0) = 9 I know that these would be looked at as (3,4) and (0,9), but I don't know what type of "equation" they're looking for. Thanks so much!!1 solutions Answer 67745 by venugopalramana(3286)   on 2007-08-17 11:54:12 (Show Source): You can put this solution on YOUR website!Write an equation for the linear function f satisfying the given conditions. f(3) = 4 and f(0) = 9 I know that these would be looked at as (3,4) and (0,9), but I don't know what type of "equation" they're looking for. Thanks so much!! CORRECT...CONTINUE...USE EQN. OF A STRAIGHT LINE(LINEAR) JOINING 2 POINTS (X1,Y1) AND (X2,Y2) IS Y-Y1=[(Y2-Y1)/(X2-X1)][X-X1] Y-4=[(9-4)/(0-3)][X-3] Y-4=-5(X-3)/3 3Y-12=-5X+15 5X+3Y=27...........OR................ Y=(27-5X)/3 IS THE FUNCTION
 Trigonometry-basics/93110: This question is from textbook Algebra and Trigonometry Solve the equation 4^2x+1=2^3x+6.1 solutions Answer 67741 by venugopalramana(3286)   on 2007-08-17 11:46:21 (Show Source): You can put this solution on YOUR website!Solve the equation 4^2x+1=2^3x+6. (4)^(2X+1)= (2^2)^(2X+1)=(2)^{2(2X+1)}=(2)^(4X+2) (2)^(4X+2) = (2)^(3X+6) HENCE 4X+2=3X+6 4X-3X=6-2=4 X=4
 expressions/92939: where is a website I can go on to teach me pre-algebra in step by step lamen terms? I have had no algebra, and I need to learn it fast!!!!!1 solutions Answer 67638 by venugopalramana(3286)   on 2007-08-16 12:21:47 (Show Source): You can put this solution on YOUR website!YOU MAY TRY THESE SITES. THEY WILL NOT TEACH YOU. BUT YOU CAN DO SELF STUDY http://www.sosmath.com/algebra/algebra.html http://academic.sun.ac.za/mathed/MALATI/
 Probability-and-statistics/92936: A list of numbers consists of p positive and n negative numbers. If a number is picked at random from this list, the probability that the number is positive is 3/5. What is the value of n/p?1 solutions Answer 67637 by venugopalramana(3286)   on 2007-08-16 12:18:42 (Show Source): You can put this solution on YOUR website!A list of numbers consists of p positive and n negative numbers. If a number is picked at random from this list, the probability that the number is positive is 3/5. What is the value of n/p? PROBABILITY OF PICKING A POSITIVE NUMBER = P/(N+P)=3/5 HENCE P/{(N+P)-P}= P/N =3/(5-3)=3/2 N/P = 2/3
 Quadratic_Equations/92943: I am not good at these and I am having some problems Find the x- intercepts y=x^2-5x-10 and y=x^2-4x+4 Thanks you1 solutions Answer 67636 by venugopalramana(3286)   on 2007-08-16 12:14:47 (Show Source): You can put this solution on YOUR website!I am not good at these and I am having some problems Find the x- intercepts y=x^2-5x-10 X INTERCEPT MEANS WHERE THE LINE MEETS X AXIS...AT THAT POINT Y COORDINATE=0 HENC X^2-5X-10=0 HENCE X INTERCEPTS ARE AND and y=x^2-4x+4 =0 X^2-2*2X+(2)^2=(X-2)^2=0 HENCE X INTERCEPT IS X=2 Thanks you
 Pythagorean-theorem/92798: In triangle ABC, C is the right angle, B = 30 degrees, and side b = 3. Find the exact value of the missing sides. Thank you for your help.1 solutions Answer 67528 by venugopalramana(3286)   on 2007-08-15 12:24:05 (Show Source): You can put this solution on YOUR website!In triangle ABC, C is the right angle, B = 30 degrees, and side b = 3. Find the exact value of the missing sides. Thank you for your help. WE HAVE SIN(B)=SIN(30)=0.5=AC/AB=b/c=3/c AB = c =3/0.5=6 TAN(B)=TAN(30)=SQRT(3)=1.7321=AC/BC=b/a=3/a BC = a = 3/1.7321=1.7321
 Numbers_Word_Problems/92593: Eight times the first of three consecutive odd integers is ten more than twice the second. 1 solutions Answer 67403 by venugopalramana(3286)   on 2007-08-14 12:29:27 (Show Source): You can put this solution on YOUR website!Eight times the first of three consecutive odd integers is ten more than twice the second. ANY INTEGER IS N EVEN NUMBER IS 2N ODD INTEGER IS 2N+1 NEXT ODD INTEGER IS 2N+1+2=2N+3 THE NEXT ODD INTEGER IS 2N+3+2=2N+5 8 TIMES THE I = 8(2N+1)=16N+8 TWICE THE SECOND = 2(2N+3)=4N+6 TEN MORE =4N+6+10=4N+16.............HENCE 16N+8=4N+16 16N-4N=16-8 12N=8 N=8/12=......THERE IS NO SOLUTION.......PLEASE CHECK THE DATA IN THE PROBLEM FOR ANY MISTAKES IN TYPING.
 Linear-equations/92588: Solve each system by substitution method. Indicate whether each system is independent, inconsistent or dependent. 3y=y+5 3x-9y= -10 and x=1/8y-1 y=1/4x +391 solutions Answer 67389 by venugopalramana(3286)   on 2007-08-14 11:40:16 (Show Source): You can put this solution on YOUR website!Solve each system by substitution method. Indicate whether each system is independent, inconsistent or dependent. 3y=y+5...............IS THIS 3X=Y+5?CHECKUP..ASSUMING SO.PUTTING THIS IN THE EQN. 3x-9y= -10 Y+5-9Y=-10 -8Y=-10-5=-15 Y=15/8 3X=15/8 + 5 = (15+40)/8 =55/8 X=55/24 SYSTEM IS INDEPENDENT
 Quadratic-relations-and-conic-sections/90858: Here'e the question that I can't fiqure out. I might be using the wrong equation or system of equations? A Semielliptical window has a height of 28 in and a length of 64 inches. Find the height of the window 25 inches from one end. Thanks1 solutions Answer 65925 by venugopalramana(3286)   on 2007-07-30 12:40:30 (Show Source): You can put this solution on YOUR website!Here'e the question that I can't fiqure out. I might be using the wrong equation or system of equations? A Semielliptical window has a height of 28 in and a length of 64 inches. Find the height of the window 25 inches from one end. Thanks EQN.OF ELLIPSE WITH CENTER AS O(0,0), MAJOR AXIS=POQ =2A AND MINOR AXIS=ROS=2B IS [X^2/A^2] + [Y^2/B^2]=1 WE HAVE POQ = 2A=64....PO=OQ=A=32 AND RO=OS=B=28 HENCE EQN. IS (X^2/32^2) + (Y^2/28^2) = 1 POINT P' IS 28" FROM ONE END MEANS PP'=28 OP'=32-28=4"=X FROM CENTER. HENCE WE GET 4^2/32^2 + (Y^2/28^2)=1 Y^2/28^2 = 1-16/32^2=1-(1/64)= 63/64 Y^2=28^2(63/64) Y=28*SQRT(63/64) IS ALMOST EQUAL TO 28"
 Rational-functions/90859: In this question, to find the answer I know I need to find a vertex, but can't seem to get a quadratic type equation to figure the points: A wholesaler of appliances finds that she can sell (1200-p) televisions when the price is p dollars. What price will maximize revenue? What is the maximum revenue?1 solutions Answer 65924 by venugopalramana(3286)   on 2007-07-30 12:29:11 (Show Source): You can put this solution on YOUR website!In this question, to find the answer I know I need to find a vertex, but can't seem to get a quadratic type equation to figure the points: A wholesaler of appliances finds that she can sell (1200-p) televisions when the price is p dollars. What price will maximize revenue? What is the maximum revenue? REVENUE = R = ITEMS SOLD * PRICE/ITEM=P(1200-P)=1200P-P^2 R=-[P^2-1200P]=-[P^2-2P*600+600^2-600^2] R= 600^2 - [P-600]^2 AT P=600, WE GET MAXIMUM REVENUE R MAX = 600^2=360000 \$ HENCE VERTEX IS AT (600,360000) PRICE OF 600 \$ WILL MAXIMISE THE REVENUE.
 Polynomials-and-rational-expressions/90860: Can I please get some help with this word problem? The price of an item is given by p = 2x^2 - 100. Find the polynomial that represents the rvenue generated from the sale of x items. Thanks.1 solutions Answer 65923 by venugopalramana(3286)   on 2007-07-30 12:24:34 (Show Source): You can put this solution on YOUR website!Can I please get some help with this word problem? The price of an item is given by p = 2x^2 - 100. Find the polynomial that represents the rvenue generated from the sale of x items. Thanks. REVENUE=R= NO.OF ITEMS SOLD*PRICE/ITEM = X[2X^2-100]=2X^3-100X R = 2X^3 - 100X
 Age_Word_Problems/88942: Ruffy is 3/4 as old as Orlie.Four years ago,Ruffy was 1year more than 1/2 old as Orlie.How old is each1 solutions Answer 64643 by venugopalramana(3286)   on 2007-07-18 09:50:45 (Show Source): You can put this solution on YOUR website!Ruffy is 3/4 as old as Orlie.Four years ago,Ruffy was 1year more than 1/2 old as Orlie...........ORLIE NOW ? OR ORLIE 4 YEARS AGO?...TAKING IT AS 4 YEARS AGO. .How old is each LET ORLIE BE O YEARS RUFFY IS R YEARS = 3*O/4 YEAR 4 YERS AGO ORLIE WAS = O-4 YEARS 4 YEARS AGO RUFFIE WAS =3*O/4 -4=(3*O-16)/4 YEARS HALF AS OLD AS ORLIE = (O-4)2 YEARS MORE BY 1 YEAR = (O-4)/2 +1=(O-2)/2 HENCE (O-2)/2 = (3*O-16)/4 4*O-4*2=2*3*O-2*16 32-8=6*O-4*O 2*O=24 O=12 R=3*12/4=9 YEARS
 Graphs/88789: Sketch the graph of the hyperbola y^2/25- x^2/4= 1. Draw the fundamental rectangle. Find the equations of the asymptotes and label the asymptotes on your graph. 1 solutions Answer 64524 by venugopalramana(3286)   on 2007-07-17 12:39:13 (Show Source): You can put this solution on YOUR website!Sketch the graph of the hyperbola y^2/25- x^2/4= 1. Draw the fundamental rectangle. Find the equations of the asymptotes and label the asymptotes on your graph STD. EQN IS (Y-K)^2/B^2 - (X-H)^2/A^2 =1 COMPARING H=K=0....A=2......B=5 CENTER IS (H,K)=(0,0) TRANSVERSE AXIS IS X=H=0 LENGTH OF TRANSVERSE AXIS = 2B=10 CONJUGATE AXIS IS Y=K=0 LENGTH OF CONJUGATE AXIS = 2A =4 VERTICES ARE [H,K+-B]=(0,5) AND (0,5) USE THIS DATA TO SKETCH.IF NECESSARY GIVE SOME VALUES TO X AND FIND Y AND PLOT CURVES ARE SYMMETRIC ABOUT AXES ASYMPTOTES ARE GIVEN BY Y^2/25 - X^/4 = 0 [(Y/5)+(X/4)][(Y/5)-(X/4)]=0 Y/5 = X/4 AND Y/5 = -X/4 GRAPH IS SHOWN BELOW
 Miscellaneous_Word_Problems/88786: two boys who live 14 miles apart start at noon to walk toward each other at rates of 3 mph and 4 mph respectively . in how many hours will they meet?1 solutions Answer 64523 by venugopalramana(3286)   on 2007-07-17 12:24:51 (Show Source): You can put this solution on YOUR website!two boys who live 14 miles apart start at noon to walk toward each other at rates of 3 mph and 4 mph respectively . in how many hours will they meet? RELATIVE VELOCITY WHILE TRAVELING IN OPPOSITE DIRECTIONS =V1+V2=3+4=7 MPH DISTANCE OF SEPARATION=14 TIME NEEDED TO MEET =14/7 = 2 HRS
 Polynomials-and-rational-expressions/86379: I need help with this: find a polynomial with integer coefficients that has the given zeros -4, -1+i, -1-i1 solutions Answer 62488 by venugopalramana(3286)   on 2007-06-25 08:09:04 (Show Source): You can put this solution on YOUR website!I need help with this: find a polynomial with integer coefficients that has the given zeros -4, -1+i, -1-i CONJUGATE ROOTS ARE -1+I AND -1-I SO EQN. FOR THESE 2 ROOTS IS [X-(-1+I)][X-(-1-I)]=0=(X+1)^2-I^2=X^2+2X+1+1=0=X^2+2X+2=0 NOW THIRD ROOT IS REAL -4 SO MULTIPLY THE ABOVE WITH X+4 TO GET THE POLYNOMIAL (X+4)(X^2+2X+2)=0 X^3+2X^2+2X+4X^2+8X+8=0 X^3+6X^2+10X+8=0
 Polynomials-and-rational-expressions/86380: I have a question that states: find the vertical and horizontal asymptotes for the rational function f(x)=(2x^2-5x-3)/(x^2-4)1 solutions Answer 62486 by venugopalramana(3286)   on 2007-06-25 08:04:41 (Show Source): You can put this solution on YOUR website!I have a question that states: find the vertical and horizontal asymptotes for the rational function f(x)= Y =(2x^2-5x-3)/(x^2-4) FIND LIMIT Y AS X TEND TO INFINITY LIMIT Y = 2/1=2 HENCE Y=2 IS THE HORIZONTAL ASYMPTOTE. FIND WHEN Y TENDS TO INFINITY THIS HAPPENS WHEN D.R=X^2-4=0 X=+2 AND X=-2 THESE ARE THE 2 VERTICAL ASYMPTOTES
 Linear_Equations_And_Systems_Word_Problems/86344: A common mistake when solving equations is the following: The equation: 2(x – 2) = x + 3 First step in solving: 2x – 2 = x + 3 Write a clear explanation of what error has been made. What could be done to avoid this error? 1 solutions Answer 62450 by venugopalramana(3286)   on 2007-06-24 23:16:21 (Show Source): You can put this solution on YOUR website!A common mistake when solving equations is the following: The equation: 2(x – 2) = x + 3 First step in solving: 2x – 2 = x + 3 THE ERROR IS IN LHS IN NOT MULTIPLYING WITH 2 EACH AND EVERY TERM IN THE BRACKET. IT SHOULD BE 2*X-2*2 =2X-4 AND NOT 2X-2 ON LHS THIS IS DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION & SUBTRACTION. ONE SHOULD PAY ATTENTION TO THIS PROPERTY TO AVOID SUCH MISTAKES Write a clear explanation of what error has been made. What could be done to avoid this error?
 Money_Word_Problems/86350: Business and finance. If the total bill at a restaurant, including a 15% tip, is \$65.32, what was the cost of the meal alone?1 solutions Answer 62448 by venugopalramana(3286)   on 2007-06-24 23:10:27 (Show Source): You can put this solution on YOUR website!Business and finance. If the total bill at a restaurant, including a 15% tip, is \$65.32, what was the cost of the meal alone? LET ACTUAL BILL \$ = 100 TIP=15 \$ = 15 TOTAL BILL = 115 HENCE IF TOTAL IS 115..........ORGL....IS 100 IF TOTAL IS 65.32...........ORGL.IS = 65.32*100/115 = 56.80
 Money_Word_Problems/86349: Business and finance. The electricity costs of a business decreased from \$12,000 one year to \$10,920 the next. What is the rate of decrease?1 solutions Answer 62444 by venugopalramana(3286)   on 2007-06-24 23:05:18 (Show Source): You can put this solution on YOUR website!Business and finance. The electricity costs of a business decreased from \$12,000 one year to \$10,920 the next. What is the rate of decrease? ORGL=12000 AFTER 1 YEAR =10920 DECREASE = 12000-10920=1080 RATE OF DECREASE =1080/10920 = 0.0989...OR....9.89%
 Money_Word_Problems/86352: ) Business and finance. The electricity costs of a business decreased from \$12,000 one year to \$10,920 the next. What is the rate of decrease?1 solutions Answer 62442 by venugopalramana(3286)   on 2007-06-24 23:04:01 (Show Source): You can put this solution on YOUR website!) Business and finance. The electricity costs of a business decreased from \$12,000 one year to \$10,920 the next. What is the rate of decrease? ORGL=12000 AFTER 1 YEAR =10920 DECREASE = 12000-10920=1080 RATE OF DECREASE =1080/10920 = 0.0989...OR....9.89%
 Miscellaneous_Word_Problems/86126: If you are rolling a fair die, what is the probability of rolling an even number and then, on a second roll, rolling the very same number that you rolled on the first roll. (even# and same #)=1 solutions Answer 62238 by venugopalramana(3286)   on 2007-06-22 12:28:47 (Show Source): You can put this solution on YOUR website!If you are rolling a fair die, what is the probability of rolling an even number and then, on a second roll, rolling the very same number that you rolled on the first roll. (even# and same #)= TOTAL THERE ARE 6 FACES THEY HAVE 1 TO 6 NUMBERS EVEN NUMBERS ARE 3 SO PROBABILITY OF GETTING AN EVEN NUMBER ON I THROW = 3/6 TO GET SAME NUMBER IN II THROW PROBABILITY=1/6 HENCE COMBINATION PROBABILITY = (3/6)(1/6)=1/12
 Graphs/86133: I am so lost doing inequalities. Could someone explain how you would write this? You have at least \$30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer.1 solutions Answer 62237 by venugopalramana(3286)   on 2007-06-22 12:25:01 (Show Source): You can put this solution on YOUR website!I am so lost doing inequalities. Could someone explain how you would write this? You have at least \$30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer. LET NUMBER OF DIMES BE = D..........ITS VALUE =10D CENTS LET NUMBER OF QUARTERS = Q............ITS VALUE =25D CENTS TOTAL VALUE =10D+25Q CENTS THIS IS AT LEAST 30\$=3000 CENTS 10D+25Q>=3000 2D+5Q>=600
 Quadratic_Equations/85444: 1. Find two consecutive integers such that the sum of there square is 85. 2. A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area id 400ft ^2, what is the width of the path?1 solutions Answer 61651 by venugopalramana(3286)   on 2007-06-15 09:06:35 (Show Source): You can put this solution on YOUR website!1. Find two consecutive integers such that the sum of there square is 85. N^2+(N+1)^2=85 N^2+N^2+2N+1=85 2N^2+2N-84=0 N^2+N-42=0 N^2+7N-6N-42=0 N(N+7)-6(N+7)=0 (N-6)(N+7)=0 HENCE N=6 OR -7 THE 2 INTEGERS ARE 6&7 OR -7 AND -6 2. A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area id 400ft ^2, what is the width of the path? GARDEN AREA =400 SQ.FT. IF THE WIDTH OF PATH IS X FEET , THEN LENGTH OF GARDEN = 30-X-X=30-2X WIDTH OF GARDEN =20-X-X=20-2X AREA OF GARDEN =(30-2X)(20-2X)=400 600-60X-40X+4X^2=400 4X^2-100X+200=0 X^2-25X+50=0 =2.2 FT
 Trigonometry-basics/85211: find the determinate of the matrix. Book shows below is 1 set or () (8+4a 4) (5+3a 3)1 solutions Answer 61646 by venugopalramana(3286)   on 2007-06-15 08:47:53 (Show Source): You can put this solution on YOUR website!find the determinate of the matrix. Book shows below is 1 set or () (8+4a 4) (5+3a 3) D=(8+4A)*3-4(5+3A)=24+12A-20-12A=4
 Angles/85283: A swing starts at the angle of 53 degrees to the horizontal swing. Every time the swing stops to turn in the opposite direction, the angle between the chain and the vertical is 1 degree less. How many times did the swing pass the vertical position before it stopped? What amount of degrees did it move through from beginning until it stopped?1 solutions Answer 61645 by venugopalramana(3286)   on 2007-06-15 08:43:32 (Show Source): You can put this solution on YOUR website!A swing starts at the angle of 53 degrees to the horizontal swing. Every time the swing stops to turn in the opposite direction, the angle between the chain and the vertical is 1 degree less. How many times did the swing pass the vertical position before it stopped? What amount of degrees did it move through from beginning until it stopped? ORIGINAL ANGLE =53 ANGLE IN THE I PASS BEYOND THE VERTICAL =53 II PASS =52 III PASS =51 ........ NTH PASS =53-N+1 =0 WHEN IT COMES TO STOP N=54..PASSES TOTAL DEGREES MOVED =53+52+51+.............3+2+1=53(53+1)/2=1431
 Geometry_proofs/85376: I am really confused with this question, please help Use a coordinate geometry to prove that the quadrilateral OPQR with vertices O(0,0), P(9,3),Q(9,8), and R(-3,4) is an isosceles trapezoid1 solutions Answer 61642 by venugopalramana(3286)   on 2007-06-15 08:35:43 (Show Source): You can put this solution on YOUR website!I am really confused with this question, please help Use a coordinate geometry to prove that the quadrilateral OPQR with vertices O(0,0), P(9,3),Q(9,8), and R(-3,4) is an isosceles trapezoid SLOPE OF OP=(3-0)/(9-0)=3/9=1/3 SLOPE OF QR=(4-8)/(-3-9)=-4/-12=1/3 HENCE OP||QR HENCE OPQR IS A TAPEZIUM OR^2=(-3-0)^2+(4-0)^2=9+16=25 PQ^2=(9-9)^2+(3-8)^2=0+25=25 HENCE OR=PQ HENCE IT IS AN ISOSCELES TRAPEZIUM