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# Recent problems solved by 'nerdybill'

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 Polynomials-and-rational-expressions/720580: how must this be executed? 1.)8x^3-12x^2+2x-3=01 solutions Answer 441873 by nerdybill(6959)   on 2013-02-28 22:54:35 (Show Source): You can put this solution on YOUR website!By "grouping" and factoring: 8x^3-12x^2+2x-3=0 (8x^3-12x^2)+(2x-3)=0 4x^2(2x-3)+(2x-3)=0 factoring out the (2x-3): (2x-3)(4x^2+1)=0 . setting each term to zero: 2x-3=0 2x=3 x=3/2 and 4x^2+1 = 0 4x^2 = -1 x^2 = -1/4 x = sqrt(-1/4) x = +-(1/2)i . solution: x = (3/2, (1/2)i, -(1/2)i}
 logarithm/720466: The population of rabbits in an area is modeled by the growth equation P(t)=8e^.26t, where P is in the thousands and t is in years. How long will it take for population to reach 25,000?1 solutions Answer 441853 by nerdybill(6959)   on 2013-02-28 21:29:00 (Show Source): You can put this solution on YOUR website! The population of rabbits in an area is modeled by the growth equation P(t)=8e^.26t, where P is in the thousands and t is in years. How long will it take for population to reach 25,000? . Set P(t) to 25000 and solve for t: P(t)=8e^(.26t) 25000 = 8e^(.26t) 25000/8 = e^(.26t) 3125 = e^(.26t) ln(3125) = .26t ln(3125)/.26 = t 8.047/.26 = t 30.95 = t or approximately 31 years = t
 Rational-functions/720485: 5.​A company that builds phones earns a profit on sales according to the quadratic relation P = -10n2 + 1000n -2500 where P is the profit earned in dollars, and N is the number of crates of phones sold. a. How many crates must be sold to make a maximum profit? b. What is the maximum profit that can be made? c. If you sell 11 crates how will you make a profit or a loss? How much? 1 solutions Answer 441849 by nerdybill(6959)   on 2013-02-28 21:21:42 (Show Source): You can put this solution on YOUR website!5.​A company that builds phones earns a profit on sales according to the quadratic relation P = -10n2 + 1000n -2500 where P is the profit earned in dollars, and N is the number of crates of phones sold. a. How many crates must be sold to make a maximum profit? P = -10n^2 + 1000n -2500 Find derivative: P' = -20n + 1000 Set P' to zero to find critical points: 0 = -20n + 1000 -1000 = -20n 1000 = 20n 100 = 2n 50 = n . b. What is the maximum profit that can be made? plug n=50 and find P: P = -10n^2 + 1000n -2500 P = -10(50)^2 + 1000(50) -2500 P = -10(2500) + 1000(50) -2500 P = -25000 + 50000 -2500 P = 25000 -2500 P = \$22500 . c. If you sell 11 crates how will you make a profit or a loss? How much? plug n=11 and find P: P = -10n^2 + 1000n -2500 P = -10(11)^2 + 1000(11) -2500 P = -10(121) + 11000 -2500 P = -1210 + 11000 -2500 P = 9790 -2500 P = \$7290 (Profit)
 logarithm/720429: In a labatory, a culture increases from 30 to 195 organisms in 5 hours. What is the hourly growth rate in the growth formula y=a(1+r)^t1 solutions Answer 441825 by nerdybill(6959)   on 2013-02-28 19:27:38 (Show Source): You can put this solution on YOUR website! In a labatory, a culture increases from 30 to 195 organisms in 5 hours. What is the hourly growth rate in the growth formula y=a(1+r)^t . y=a(1+r)^t The problem gives us: y as 195 a as 30 t as 5 . 195=30(1+r)^5 195/30 = (1+r)^5 6.5 = (1+r)^5 6.5^(1/5) = 1+r 6.5^(.2) = 1+r 6.5^(.2) - 1 = r 1.454 - 1 = r 0.454 = r 45.4% = r
Quadratic_Equations/720438: During practice, a softball pitcher throws a ball whose height can be modeled by the equation h=-16t^2+24t+1, where h=height in feet and t=time in seconds. How long does it take for the ball to reach a height of 6 feet?
1 solutions

Answer 441823 by nerdybill(6959)   on 2013-02-28 19:23:03 (Show Source):
You can put this solution on YOUR website!
During practice, a softball pitcher throws a ball whose height can be modeled by the equation h=-16t^2+24t+1, where h=height in feet and t=time in seconds. How long does it take for the ball to reach a height of 6 feet?
.
Set h to 6 and solve for t:
h=-16t^2+24t+1
6=-16t^2+24t+1
0 = -16t^2+24t-5
0 = 16t^2-24t+5
solve the above using the "quadratic formula" which yields:
t = {0.25, 1.25}
The ball reaches the height of 6 feet "on the way up" at
0.25 seconds
and again, "on the way down" at
1.25 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=256 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.25, 0.25. Here's your graph:

 Complex_Numbers/720430: what is the conjugate of 8i in a+bi form and the conjugate for 6.??1 solutions Answer 441819 by nerdybill(6959)   on 2013-02-28 19:16:11 (Show Source): You can put this solution on YOUR website!The form: a+bi where 'a' is the "real" part and 'b' is the "imaginary" part . what is the conjugate of 8i in a+bi form 8i in complex form is 0 + 8i The conjugate is then 0+(-8)i or 0-8i or, simply -8i . and the conjugate for 6.?? 6 in complex form is 6 + 0i conjugate is 6 - 0i but, that's simply: 6
 Square-cubic-other-roots/720137: hi, I'm doing a math program I'm instructed to do, and I'm wondering if you could help me please. This counts towards whether I will get into accel. Algebra. Thanks so much!! 24x to the 14th power square rooted. 1 solutions Answer 441685 by nerdybill(6959)   on 2013-02-28 08:10:48 (Show Source): You can put this solution on YOUR website! 24x to the 14th power square rooted. . Looks like: we can break up the x's like this: now, we can take "pairs" out from underneath the radical: factoring the 24 to prime numbers: now, take out one pair of 2's: final answer:
 Graphs/718341: I'm trying to graph y=6 and x=-5, and I can't seem to find a website that can actually graph this. If you can help that would be great.1 solutions Answer 440866 by nerdybill(6959)   on 2013-02-24 18:18:28 (Show Source): You can put this solution on YOUR website! I'm trying to graph y=6 and x=-5, and I can't seem to find a website that can actually graph this. If you can help that would be great. . y=6 is a horizontal line that crosses the 6 on the y-axis . x=-5 is a vertical line that crosses the -5 on the x-axis
 Graphs/718306: which of the following equation represents a horizontal line through (5,-3)?1 solutions Answer 440861 by nerdybill(6959)   on 2013-02-24 16:39:51 (Show Source): You can put this solution on YOUR website! which of the following equation represents a horizontal line through (5,-3)? y = -3
 Money_Word_Problems/717686: the interest on Rs3000 for one year is Rs210. what is the interest on RS 4500 for one year.1 solutions Answer 440465 by nerdybill(6959)   on 2013-02-22 19:52:21 (Show Source): You can put this solution on YOUR website! the interest on Rs3000 for one year is Rs210. what is the interest on RS 4500 for one year. . I = PRT where I is interest P is principal R is rate T is time . From:"interest on Rs3000 for one year is Rs210" 210 = 3000R(1) 210 = 3000R 210/3000 = R .07 = R 7% = R . Now, we can answer: what is the interest on RS 4500 for one year. I = PRT I = 4500(.07)(1) I = 4500(.07) I = Rs315
 Percentage-and-ratio-word-problems/717687: Principal \$500 Rate 13% Time 1yr I need to simplify and round to the nearest cent.1 solutions Answer 440464 by nerdybill(6959)   on 2013-02-22 19:46:24 (Show Source): You can put this solution on YOUR website!Principal \$500 Rate 13% Time 1yr . A = P(1+r)^t where A is amount after time t (what we're looking for) P is principal r is rate t is time (years) . A = 500(1+.13)^1 A = 500(1.13)^1 A = 500(1.13) A = \$565.00
 Geometry_Word_Problems/717111: 5. A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical form. 1 solutions Answer 440091 by nerdybill(6959)   on 2013-02-21 09:59:24 (Show Source): You can put this solution on YOUR website!5. A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical form. . Let d = diagonal then applying Pythagorean theorem we get
 Functions/717110: f(x)=x+3 and g(x)= x^2-1 I need help with these 2 problems. (f+g)(3) and (f*g)(-2) Thanks for all the help!1 solutions Answer 440089 by nerdybill(6959)   on 2013-02-21 09:56:25 (Show Source): You can put this solution on YOUR website!f(x)=x+3 and g(x)= x^2-1 . (f+g)(x) = x+3 + x^2-1 (f+g)(x) = x+2 + x^2 (f+g)(x) = x^2+x+2 so, (f+g)(3) = 3^2+3+2 (f+g)(3) = 9+3+2 (f+g)(3) = 14 . (f*g)(x) = (x+3)(x^2-1) (f*g)(x) = x^3-x+3x^2-3 (f*g)(x) = x^3+3x^2-x-3 so, (f*g)(-2) = (-2)^3+3(-2)^2-(-2)-3 (f*g)(-2) = -8+3(4)+2-3 (f*g)(-2) = -8+12+2-3 (f*g)(-2) = 3
 Expressions-with-variables/715760: 1 solutions Answer 439581 by nerdybill(6959)   on 2013-02-18 14:50:45 (Show Source): You can put this solution on YOUR website! . . . . . . .
 Percentage-and-ratio-word-problems/715622: 11% of x = 33 find x1 solutions Answer 439513 by nerdybill(6959)   on 2013-02-18 06:24:15 (Show Source): You can put this solution on YOUR website!11% of x = 33 find x . .11x = 33 x = 33/.11 x = 300
 Coordinate-system/715630: without plotting the points how will you know if the coordinate lies on its quadrant ? 1 solutions Answer 439512 by nerdybill(6959)   on 2013-02-18 06:22:22 (Show Source): You can put this solution on YOUR website!without plotting the points how will you know if the coordinate lies on its quadrant ? By the signs of the x,y coordinates: (+ , + ) : quadrant 1 (- , + ) : quadrant 2 (- , - ) : quadrant 3 (+ , - ) : quadrant 4
 percentage/715594: what is 18% of 491 solutions Answer 439501 by nerdybill(6959)   on 2013-02-18 00:37:56 (Show Source): You can put this solution on YOUR website!18% of 49 18/100 * 49 .18 * 49 8.82
 Length-and-distance/715396: The width of a rectangular field is 8ft. shorter than its length. The length is represented by l. a. Write an expression in terms of l that represents the perimeter of the rectangle. b. Given that the length of the rectangular field is 32 ft., find the perimeter of the field. How many 4 ft. sections of fence are required to enclose the field? c. If the perimeter of the field is 80 ft., find the area enclosed by the fence. Support your answer. I have been doing this all day, please help!!! 1 solutions Answer 439410 by nerdybill(6959)   on 2013-02-17 14:47:49 (Show Source): You can put this solution on YOUR website!The width of a rectangular field is 8ft. shorter than its length. The length is represented by l. a. Write an expression in terms of l that represents the perimeter of the rectangle. Let L = length then L-8 = width . Perimeter = 2(L + L-8) = 2(2L-8) = 4L-16 . b. Given that the length of the rectangular field is 32 ft., find the perimeter of the field. Perimeter = 4L-16 Perimeter = 4(32)-16 Perimeter = 128-16 Perimeter = 112 feet How many 4 ft. sections of fence are required to enclose the field? 112/4 = 108 sections . c. If the perimeter of the field is 80 ft., find the area enclosed by the fence. Support your answer. Perimeter = 4L-16 80 = 4L-16 96 = 4L 24 feet = L (length) . width: L-8 = 24-8 = 16 feet . Area = 24*16 = 384 square feet
 �t�e�s�t/714440: An oil tank has two inlet pipes and one outlet pipe. One inlet pipe can fill the tank in 12 hours, and the other inlet pipe can fill the tank in 20 hours. The outlet pipe can empty the tank in 10 hours. How long would it take to fill the tank with all three pipes open?1 solutions Answer 438800 by nerdybill(6959)   on 2013-02-14 06:00:12 (Show Source): You can put this solution on YOUR website! An oil tank has two inlet pipes and one outlet pipe. One inlet pipe can fill the tank in 12 hours, and the other inlet pipe can fill the tank in 20 hours. The outlet pipe can empty the tank in 10 hours. How long would it take to fill the tank with all three pipes open? Let x = time (hours) it takes to fill then x(1/12 + 1/20 - 1/10) = 1 multiply both sides by 120: common denominator x(10 + 6 - 12) = 120 x(16 - 12) = 120 x(4) = 120 x = 30 hours
 test/714272: Factor 2x squared -1x-11 solutions Answer 438742 by nerdybill(6959)   on 2013-02-13 19:02:48 (Show Source): You can put this solution on YOUR website! Factor 2x squared -1x-1 . we can rewrite the middle term as: grouping:
 Rate-of-work-word-problems/714190: if a tub take 10 min to fill and it takes 12min to drain how long will it take to fill up if the drain was left open ? 1 solutions Answer 438723 by nerdybill(6959)   on 2013-02-13 16:14:40 (Show Source): You can put this solution on YOUR website!if a tub take 10 min to fill and it takes 12min to drain how long will it take to fill up if the drain was left open ? Let x = time (minutes) to fill then x(1/10 - 1/12) = 1 multiplying both sides by 120: x(12 - 10) = 120 x(2) = 120 x = 60 minutes
 Rate-of-work-word-problems/714063: One maid can clean the house three times faster than another. Working together they can clean the entire house in three hours. How long would it take the faster maid cleaning alone?1 solutions Answer 438652 by nerdybill(6959)   on 2013-02-13 08:49:58 (Show Source): You can put this solution on YOUR website! One maid can clean the house three times faster than another. Working together they can clean the entire house in three hours. How long would it take the faster maid cleaning alone? Let x = time (hours) it takes faster maid then 3x = time (hours) it takes slower maid . 3(1/x + 1/(3x)) = 1 3(3 + 1) = 3x 3(4) = 3x 4 hours = x
 logarithm/713994: what is log base6 4 + log base 6 (x+2) = 1? what is log base2 (x+6)- log base2 (x) = 3? 1 solutions Answer 438634 by nerdybill(6959)   on 2013-02-13 00:58:07 (Show Source): You can put this solution on YOUR website!what is log base6 4 + log base 6 (x+2) = 1? log base6 4 + log base 6 (x+2) = 1 log base6 4(x+2) = 1 4(x+2) = 6^1 4x+8 = 6 4x = -2 x = -1/2 . what is log base2 (x+6)- log base2 (x) = 3? log base2 (x+6)- log base2 (x) = 3 log base2 (x+6)/(x) = 3 (x+6)/(x) = 2^3 (x+6)/(x) = 8 (x+6) = 8x 6 = 7x 6/7 = x
 Exponential-and-logarithmic-functions/713626: Solve the following logarithmic equation. log(2x+8)=1+ log(x-5) Thanks so much!!1 solutions Answer 438507 by nerdybill(6959)   on 2013-02-12 10:25:21 (Show Source): You can put this solution on YOUR website!log(2x+8)=1+ log(x-5) log(2x+8) - log(x-5) = 1 log(2x+8)/(x-5) = 1 (2x+8)/(x-5) = 10^1 (2x+8)/(x-5) = 10 (2x+8) = 10(x-5) 2x+8 = 10x-50 8 = 8x-50 58 = 8x 58/8 = x 7.25 = x
 Trigonometry-basics/712880: I need to find the amplitude, period and displacement of y=3cos(2x-pi/2) Thanks1 solutions Answer 438201 by nerdybill(6959)   on 2013-02-10 18:14:05 (Show Source): You can put this solution on YOUR website!General form: y = a cos k(x-b) where amplitude is |a| period is 2(pi)/k phase shift is b . Your equation y=3cos(2x-pi/2) factor out the 2: y=3cos 2(x-pi/4) so, from inspection then amplitude: 3 phase shift: (pi)/4 period: (2(pi))/2 pi
 Quadratic_Equations/712636: I'm having trouble with this one! A rectangular garden has dimensions 3m by 4m. A path is built around the garden. The area of the garden and path is 6 times as great as the area of the garden. What is the width of the path?1 solutions Answer 438085 by nerdybill(6959)   on 2013-02-10 01:16:28 (Show Source): You can put this solution on YOUR website!A rectangular garden has dimensions 3m by 4m. A path is built around the garden. The area of the garden and path is 6 times as great as the area of the garden. What is the width of the path? . Let x = width (m) of path then area of "path+garden" = (2x+3)(2x+4) area of "garden" = 3*4 = 12 . From:"The area of the garden and path is 6 times as great as the area of the garden." we get our equation: (2x+3)(2x+4) = 6*12 4x^2+8x+6x+12 = 72 4x^2+14x+12 = 72 4x^2+14x-60 = 0 2x^2+7x-30 = 0 rewrite middle term: 2x^2+12x-5x-30 = 0 group: (2x^2+12x)-(5x+30) = 0 2x(x+6)- 5(x+6) = 0 (x+6)(2x-5) = 0 x = {-6, 5/2} we can throw out the negative solution (extraneous) leaving: x = 5/2 or x = 2.5 m
 Finance/712610: Please help me solve this. An investment of \$11,050 is divided into two accounts, one for stocks and one for mutual funds. The value of the stock account is \$1,700 less than twice the value of the mutual fund account. Find the amount in the stock account. I do appreciate any help you could offer! Thank you for your time!1 solutions Answer 438081 by nerdybill(6959)   on 2013-02-10 01:01:07 (Show Source): You can put this solution on YOUR website!An investment of \$11,050 is divided into two accounts, one for stocks and one for mutual funds. The value of the stock account is \$1,700 less than twice the value of the mutual fund account. Find the amount in the stock account. . Let x = amount (\$) of stock account then 11050-x = amount (\$) in mutual funds . From:"The value of the stock account is \$1,700 less than twice the value of the mutual fund account." we get our equation: x = 2(11050-x) - 1700 x = 22100-2x - 1700 3x = 22100 - 1700 3x = 20400 x = \$6800
 Volume/712608: Hello there I came across this problem set that I dont understand how it came about with the solution. Pls help Find the exact volume of sphere ( looks like half a sphere) with a radius of 8ft the answer is: 1024/3 pi cu ft. How did this happen? Thanks1 solutions Answer 438075 by nerdybill(6959)   on 2013-02-09 23:15:41 (Show Source): You can put this solution on YOUR website!Volume of a sphere is: (4/3)(pi)r^3 if you have HALF of a sphere: (1/2)(4/3)(pi)r^3 (2/3)(pi)r^3 . plug in our radius: (2/3)(pi)(8)^3 (2/3)(pi)(512) (1024/3)(pi) cubic feet
 Systems-of-equations/712424: Solve by the elimination method. 8x-y=69 x+9y=361 solutions Answer 437925 by nerdybill(6959)   on 2013-02-09 11:10:22 (Show Source): You can put this solution on YOUR website!Solve by the elimination method. 8x-y=69 x+9y=36 . Multiply the top equation by 9 and combine both equations: 72x-9y=621 x+9y= 36 ---------- 73x =657 x = 9 . Plug above into: x+9y=36 9+9y=36 9y=27 y = 3 . solution: x=9 and y=3
 Age_Word_Problems/712346: judy is Y years old. in 18 years she will be 3 times as old as she was 2 years ago. how old is she now?1 solutions Answer 437924 by nerdybill(6959)   on 2013-02-09 11:06:57 (Show Source): You can put this solution on YOUR website!judy is Y years old. in 18 years she will be 3 times as old as she was 2 years ago. how old is she now? . Y+18 = 3(Y-2) Y+18 = 3Y-6 18 = 2Y-6 24 = 2Y 12 years old = Y
 Equations/712420: Can you please assist our fourth grade son with his Algebra? Thank you. 1. Which number makes this a true number sentence? Show your work. 397 + m > 412 A. 14 B. 9 C. 16 D. 15 2. Which number does NOT make this a true number sentence? Show your work. 480 - z < 459 A. 25 B. 42 C. 21 D. 221 solutions Answer 437923 by nerdybill(6959)   on 2013-02-09 11:04:22 (Show Source): You can put this solution on YOUR website!1. Which number makes this a true number sentence? Show your work. 397 + m > 412 397 + m - 397 > 412 - 397 m > 15 that is, m has to be "greater than" 15. Looking at the choice: A. 14 B. 9 C. 16 D. 15 The ONLY one that is greater than 15 is is choice C . 2. Which number does NOT make this a true number sentence? Show your work. 480 - z < 459 480 - z - 480 < 459 - 480 -z < -21 z > 21 Looking at available choices: A. 25 B. 42 C. 21 D. 22 The ONLY choice is D