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# Recent problems solved by 'nerdybill'

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Linear_Equations_And_Systems_Word_Problems/166879: A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in t seconds is given by s(t)=-16(t^2)+142t. At what time(s) will the ball be 172 ft from the ground?
1 solutions

Answer 122989 by nerdybill(7012)   on 2008-11-10 22:49:25 (Show Source):
You can put this solution on YOUR website!
s(t)=-16(t^2)+142t
.
In this case, they are saying that if s(t) equals 172 feet what is t?
.
Simply set s(t) to 172 and solve for 't':
s(t)=-16(t^2)+142t
172=-16(t^2)+142t
16(t^2)-142t+172=0
8(t^2)-71t+86=0
.
Since it is difficult to factor, we use the quadratic equation.
Doing so will yield:
x = {7.428, 1.447}
Units are in seconds
.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=2289 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 7.42771842847642, 1.44728157152358. Here's your graph:

 Expressions-with-variables/166925: Hello :) Please simplify the expression: 9-3(-4+3x)+12x Thanks!1 solutions Answer 122986 by nerdybill(7012)   on 2008-11-10 22:41:37 (Show Source): You can put this solution on YOUR website!9-3(-4+3x)+12x = 9+12-9x+12x = 21-9x+12x = 21+3x . Or, you could factor out a 3 to get: 3(7+x)
 Miscellaneous_Word_Problems/166927: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Solving Polynomial Equations. Solve. Identify all multiple roots. (x^2-3x+2)^3=01 solutions Answer 122982 by nerdybill(7012)   on 2008-11-10 22:34:44 (Show Source): You can put this solution on YOUR website!(x^2-3x+2)^3=0 x^2-3x+2=0 (x-1)(x-2)=0 . x = {1,2}
 Numbers_Word_Problems/166945: help me solve: The sum of 2 numbers is 40 and their difference is 181 solutions Answer 122980 by nerdybill(7012)   on 2008-11-10 22:22:09 (Show Source): You can put this solution on YOUR website!The sum of 2 numbers is 40 and their difference is 18 . Let x = one of two numbers and y = the second number . x + y = 40 x - y = 18 . Using the "elimination method" add the two equations together: x + y = 40 x - y = 18 ----------- 2x = 58 x = 29 . Substitute the above into: x + y = 40 29 + y = 40 y = 40 - 29 y = 11 . The two numbers are 29 and 11
 Quadratic_Equations/166950: 2x^2-3x+1=0 Solve by completing the square. 1 solutions Answer 122977 by nerdybill(7012)   on 2008-11-10 22:07:51 (Show Source): You can put this solution on YOUR website!2x^2-3x+1=0 2x^2-3x = -1 2(x^2 - (3/2)x) = -1 2(x^2 - (3/2)x + 9/16) = -1 + 9/8 2(x-(3/4))^2 = -8/8 + 9/8 2(x-(3/4))^2 = 1/8 (x-(3/4))^2 = 1/16 x-(3/4) = (+-)1/4 x = (3/4)(+-)1/4 . x = {2/4, 4/4} x = {1/2, 1}
 Age_Word_Problems/166952: This question is from textbook Cassidy is 3 times as old as Drew. In 8 years, Cassidy will only be twice as old as Drew. How old is cassidy right now?1 solutions Answer 122976 by nerdybill(7012)   on 2008-11-10 21:58:52 (Show Source): You can put this solution on YOUR website! Cassidy is 3 times as old as Drew. In 8 years, Cassidy will only be twice as old as Drew. How old is cassidy right now? . Let x = Drew's age then 3x = Cassidy's age . 3x+8 = 2(x+8) 3x+8 = 2x+16 x+8 = 16 x = 8 years . Cassidy is 8 years old
 Miscellaneous_Word_Problems/166953: This question is from textbook I am thinking of a number that, when you multiply it by 9, it is the same as adding 8 to 7 times the number. What is the number?1 solutions Answer 122975 by nerdybill(7012)   on 2008-11-10 21:57:00 (Show Source): You can put this solution on YOUR website! I am thinking of a number that, when you multiply it by 9, it is the same as adding 8 to 7 times the number. What is the number? . Let x = the number . 9x = 7x + 8 2x = 8 x = 4 . The number is 4
 Problems-with-consecutive-odd-even-integers/166955: The sum of 2 consecutive intergers is 118. Define a variable for the smaller interger? and What must you add to an even interger to get the next greater even interger? Write an expression for the second interger?1 solutions Answer 122974 by nerdybill(7012)   on 2008-11-10 21:55:40 (Show Source): You can put this solution on YOUR website!The sum of 2 consecutive intergers is 118. Define a variable for the smaller interger? and What must you add to an even interger to get the next greater even interger? Write an expression for the second interger? . Let x = smaller even integer then x+2 = next consecutive even integer . x + x+2 =118 2x + 2 = 118 2x = 116 x = 58 x+2 = 60 . The integers are 58 and 60
 logarithm/166958: how do I solve log(5x-1)=2+log(x-2)1 solutions Answer 122973 by nerdybill(7012)   on 2008-11-10 21:53:05 (Show Source): You can put this solution on YOUR website!log(5x-1)=2+log(x-2) log(5x-1) - log(x-2) = 2 log[(5x-1)/(x-2)] = 2 (5x-1)/(x-2) = 10^2 (5x-1)/(x-2) = 100 (5x-1) = 100(x-2) 5x-1 = 100x-200 199 = 95x 199/95 = x 2.0526 = x
 Quadratic_Equations/166949: x^2-6x=16 Solve by completing the square. this is what I did...but it isn't the correct way to do it. (x-8)(x+2) x=8, x=-2 1 solutions Answer 122972 by nerdybill(7012)   on 2008-11-10 21:50:17 (Show Source): You can put this solution on YOUR website!This site explains the entire process: http://www.purplemath.com/modules/sqrquad.htm . x^2-6x=16 Divide the -6 by 2 and square it to get 9. Add it to both sides: x^2-6x+9=16+9 (x-3)^2 = 25 take the square root of both sides: x-3 = (+-)5 x = 3(+-)5 . x = {-2, 8}
 logarithm/166858: rewrite the following Expression using one or more Logarithms and evaluate without a calculator. Log ( 1/10^-3) + log 10^4 = 1 solutions Answer 122938 by nerdybill(7012)   on 2008-11-10 16:10:02 (Show Source): You can put this solution on YOUR website!Log ( 1/10^-3) + log 10^4 = Log 10^3 + log 10^4 = Log 10^3 + log 10^4 = 3 + 4 = 7
 logarithm/166882: So here is my problem: Solve: log(base 7)4x-log(base7)(x+3)=log(base 7)x1 solutions Answer 122937 by nerdybill(7012)   on 2008-11-10 16:07:26 (Show Source): You can put this solution on YOUR website!log(base 7)4x-log(base7)(x+3)=log(base 7)x You can rewrite the left (based on log rules): log(base 7)(4x/(x+3)) = log(base 7)x log(base 7)(4x/(x+3)) - log(base 7)x = 0 log(base 7)(4x/x(x+3)) = 0 (4x/x(x+3)) = 7^0 4x/x(x+3) = 1 4x = x(x+3) 4x = x^2+3x 0 = x^2-x 0 = x(x-1) . x = {0,1}
 Surface-area/166791: How many litres does a cylindrical tank of height 37.8 m with radius 5.80 m hold? (1 m3 = 1000 L) Please enter your answer as a number without units, rounded to three significant digits.1 solutions Answer 122907 by nerdybill(7012)   on 2008-11-10 07:31:38 (Show Source): You can put this solution on YOUR website!How many litres does a cylindrical tank of height 37.8 m with radius 5.80 m hold? (1 m3 = 1000 L) Please enter your answer as a number without units, rounded to three significant digits. . (height)(pi)r^2 =(37.8)(3.14)(5.80^2) =(118.692)(5.80^2) =(118.692)(33.64) = 3992.79888 . Converting to liters: 3992.79888 * 1000 = 3992798.88
 logarithm/166799: log2(x)+log8(x) = 81 solutions Answer 122906 by nerdybill(7012)   on 2008-11-10 07:23:40 (Show Source): You can put this solution on YOUR website!log2(x)+log8(x) = 8 Convert the base: log(x)/log(2) + log(x)/log(8) = 8 Factor out the log(x): log(x)[1/log(2) + 1/log(8)] = 8 log(x)[4.429] = 8 log(x) = 1.806 x = 10^1.806 x = 64
logarithm/166806: log5(x^2+x+4)=2
1 solutions

Answer 122905 by nerdybill(7012)   on 2008-11-10 07:02:21 (Show Source):
You can put this solution on YOUR website!
log5(x^2+x+4)=2
x^2+x+4 = 5^2
x^2+x+4 = 25
x^2+x-21 = 0
Since we can't factor, we must use the quadratic equation.
Doing so will yield:
x = {4.110, -5.110}
.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=85 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.10977222864644, -5.10977222864644. Here's your graph:

 Volume/166810: This question is from textbook How do you find the volume of a cube?1 solutions Answer 122904 by nerdybill(7012)   on 2008-11-10 06:56:40 (Show Source): You can put this solution on YOUR website!The definition of a "cube" is that all sides have the same length. . The volume then would be: The measure of the length of one side, cubed. . That is: If x = length of a side of the cube then the volume is x^3 or x*x*x
Quadratic_Equations/166813: The hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.5 units longer than the shorter leg. Find the lengths of the sides of the triangle.
1 solutions

Answer 122903 by nerdybill(7012)   on 2008-11-10 06:54:12 (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.5 units longer than the shorter leg. Find the lengths of the sides of the triangle.
.
Let x = length of shorter leg
then from "leg is 1.5 units longer than the shorter leg"
x+1.5 = length of longer leg
.
Applying Pythagorean theorem:
x^2 + (x+1.5)^2 = 2.5^2
x^2 + x^2+3x+2.25 = 6.25
2x^2+3x+2.25 = 6.25
2x^2+3x-4 = 0
.
Since we can't factor, use the quadratic equation. Doing so will produce:
x = {0.851, -2.351}
.
We can toss out the negative solution leaving us with the sides as:
0.851 units and 2.351 units
.
The following is the details of the quadratic:
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=41 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.850781059358212, -2.35078105935821. Here's your graph:

 logarithm/166780: log^2 (x^2-6x) = 3+log^2(1-x)1 solutions Answer 122893 by nerdybill(7012)   on 2008-11-09 22:16:39 (Show Source): You can put this solution on YOUR website!I'm assuming when you say log^2, you mean log base 2. If not, please write back. . log2(x^2-6x) = 3+log2(1-x) log2(x^2-6x) - log2(1-x) = 3 log2[(x^2-6x)/(1-x)] = 3 (x^2-6x)/(1-x) = 2^3 (x^2-6x)/(1-x) = 8 (x^2-6x) = 8(1-x) x^2-6x = 8-8x x^2+2x = 8 x^2+2x-8 = 0 (x+4)(x-2) = 0 . x = {-4, 2}
 logarithm/166781: log(x-3) + log (x) = 11 solutions Answer 122891 by nerdybill(7012)   on 2008-11-09 22:13:00 (Show Source): You can put this solution on YOUR website!log(x-3) + log (x) = 1 log[(x-3)(x)] = 1 (x-3)(x) = 10^1 x^2-3x = 10 x^2-3x-10 = 0 (x-5)(x+2) = 0 . x = {-2, 5}
 logarithm/166775: 3(5)^(-.01x)=61 solutions Answer 122883 by nerdybill(7012)   on 2008-11-09 21:28:09 (Show Source): You can put this solution on YOUR website!3(5)^(-.01x)=6 (5)^(-.01x)=2 -.01x=log5(2) -.01x=log(2)/log(5) -.01x=.4307 x = -43.068 . Note: log5 : log base 5 log : (w/o any number) means log base 10 . This is a good site to review log rules: http://www.purplemath.com/modules/logrules.htm
logarithm/166689: log3(x-2)+log3(x+4)=3
1 solutions

Answer 122882 by nerdybill(7012)   on 2008-11-09 21:23:50 (Show Source):
You can put this solution on YOUR website!
log3(x-2)+log3(x+4)=3
log3[(x-2)(x+4)]=3
(x-2)(x+4)=3^3
x^2+4x-2x-8 = 9
x^2+2x-8 = 9
x^2+2x-17 = 0
.
Since we can't factor, we must use the quadratic equation.
Do so will yield:
x = {3.243, -5.243}
.
Details here:
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=72 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3.24264068711928, -5.24264068711928. Here's your graph:

 logarithm/166757: 5(5)^(-0.08x)=4 please solve for x1 solutions Answer 122879 by nerdybill(7012)   on 2008-11-09 21:06:42 (Show Source): You can put this solution on YOUR website!5(5)^(-0.08x)=4 If so, start by dividing both sides by 5: (5)^(-0.08x)=4/5 (5)^(-0.08x)=.8 Take the LOG5 of both sides: -0.08x = LOG5(.8) -0.08x = LOG(.8)/LOG(5) -0.08x = -.0969/.6990 -0.08x = -.1386 x = 1.733
 logarithm/166748: 5(5)^-.08x=61 solutions Answer 122878 by nerdybill(7012)   on 2008-11-09 21:00:31 (Show Source): You can put this solution on YOUR website!Hey, this sounds familiar... . When you posted: 5(5)^-0.08x=6 I assume you mean: 5(5)^(-0.08x)=6 This means 5 is raised to the power of (-0.08x) If this is incorrect, please write back . If so, start by dividing both sides by 5: (5)^(-0.08x)=6/5 (5)^(-0.08x)=1.2 Take the LOG5 of both sides: -0.08x = LOG5(1.2) -0.08x = LOG(1.2)/LOG(5) -0.08x = .0792/.6990 -0.08x = .1133 x = -1.416
 Polygons/166749: The circumference of the circle is 30.2 cm. Find the radius.1 solutions Answer 122871 by nerdybill(7012)   on 2008-11-09 19:42:20 (Show Source): You can put this solution on YOUR website!circumference of a circle: 2(pi)r . where pi is 3.14 . 30.2 = 2(3.14)r 15.1 = 3.14r 4.81 cm = r (radius)
 Polygons/166750: The area of the circle is 547 m 2. Find the radius.1 solutions Answer 122870 by nerdybill(7012)   on 2008-11-09 19:38:58 (Show Source): You can put this solution on YOUR website!Area of any circle is: (pi)r^2 . They gave you the area as 547 and pi is 3.14. Plug and solve: 547 = (pi)r^2 547 = (3.14)r^2 174.2 = r^2 13.2 m = r (radius)
 logarithm/166740: log(x^2-x-5)= 0 I canot figure out the way to solve this. I looked at the example in my book and it was not clear. Solve for x my guess is to complete the square, but i am not sure how to do this 1 solutions Answer 122869 by nerdybill(7012)   on 2008-11-09 19:36:03 (Show Source): You can put this solution on YOUR website!log(x^2-x-5)= 0 x^2-x-5= 10^0 x^2-x-5= 1 x^2-x-6= 0 (x-3)(x+2)=0 . x = {-2, 3}
 logarithm/166741: 5(5)^-0.08x=6 Please!!! solve for x1 solutions Answer 122868 by nerdybill(7012)   on 2008-11-09 19:33:05 (Show Source): You can put this solution on YOUR website!When you posted: 5(5)^-0.08x=6 I assume you mean: 5(5)^(-0.08x)=6 . If so, start by dividing both sides by 5: (5)^(-0.08x)=6/5 (5)^(-0.08x)=1.2 Take the LOG5 of both sides: -0.08x = LOG5(1.2) -0.08x = LOG(1.2)/LOG(5) -0.08x = .0792/.6990 -0.08x = .1133 x = -1.416
 logarithm/166735: 4log(2x+6)=8 Solve for X. Please1 solutions Answer 122866 by nerdybill(7012)   on 2008-11-09 19:06:32 (Show Source): You can put this solution on YOUR website!4log(2x+6)=8 log(2x+6)=2 2x+6=10^2 2x+6=100 2x=94 x = 47
 Proportions/166699: There is a class. The ratio is 5 boys to 4 girls. There are 65 boys. How many girls are there?1 solutions Answer 122865 by nerdybill(7012)   on 2008-11-09 19:04:47 (Show Source): You can put this solution on YOUR website! There is a class. The ratio is 5 boys to 4 girls. There are 65 boys. How many girls are there? . Let g = number of girls in the class . 4:5 = g:65 or 4/5 = g/65 g = (4*65)/5 g = 260/5 g = 52 (girls in the class)
 Polynomials-and-rational-expressions/166719: how do you simplify this rational expression? (2/k-3)+ (4/k+3)= i was out sick for 3 days and i dont know how to do this.1 solutions Answer 122864 by nerdybill(7012)   on 2008-11-09 19:02:06 (Show Source): You can put this solution on YOUR website! . Common denominator is:(k-3)(k+3) .
 Mixture_Word_Problems/166734: 2/3 divided by x = 1 please help1 solutions Answer 122863 by nerdybill(7012)   on 2008-11-09 18:54:55 (Show Source): You can put this solution on YOUR website!2/3 divided by x = 1 (2/3)/x = 1 multiplying both sides by x: 2/3 = x