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# Recent problems solved by 'nerdybill'

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 Percentage-and-ratio-word-problems/464633: The population of a city was 127 thousand in 1992. The exponential growth rate was 1.3% per year. Find the exponential growth function in terms of t, where t is the number of years since 1992. P(t)=?1 solutions Answer 318296 by nerdybill(6962)   on 2011-06-26 17:00:09 (Show Source): You can put this solution on YOUR website!The population of a city was 127 thousand in 1992. The exponential growth rate was 1.3% per year. Find the exponential growth function in terms of t, where t is the number of years since 1992. P(t)=? The general exponential growth/decay model is: A = Pe^(rt) where A is the amount after time t P is the initial amount r is the rate of growth or decay t is time . Plugging in what was given by the problem: P(t)= 127e^(.013t)
 Bodies-in-space/464636: I'm trying to the determine the base of a right hand triangle that has a base of 4 and height 4 - I was told the answer is b-5.66 where does the 5.66 come from?1 solutions Answer 318294 by nerdybill(6962)   on 2011-06-26 16:55:59 (Show Source): You can put this solution on YOUR website!They are applying the Pythagorean theorem: a^2 + b^2 = c^2 where 'a' and 'b' are the legs of a right triangle and 'c' is the hypotenuse (longest side) 4^2 + 4^2 = c^2 16 + 16 = c^2 32 = c^2 sqrt(32) = c 5.66 = c
 Linear-equations/464640: Find the slope,if it exists,of the line containing the pair of points. (2,10) and (8,-4) The slope m=1 solutions Answer 318292 by nerdybill(6962)   on 2011-06-26 16:51:04 (Show Source): You can put this solution on YOUR website!Find the slope,if it exists,of the line containing the pair of points. (2,10) and (8,-4) The slope m=(y2-y1)/(x2-x1) m=(-4-10)/(8-2) m=(-14)/(6) m=-7/3
 test/464574: If it takes Steve 5 hours to mow the lawn, and it takes Jane 3 hours to mow the same lawn, how long does it take them to mow the lawn together?1 solutions Answer 318275 by nerdybill(6962)   on 2011-06-26 13:22:17 (Show Source): You can put this solution on YOUR website! If it takes Steve 5 hours to mow the lawn, and it takes Jane 3 hours to mow the same lawn, how long does it take them to mow the lawn together? . Let x = time (hours) it takes for both then x(1/5 + 1/3) = 1 multiplying both sides by 15: x(3 + 5) = 15 x(8)=15 x = 1.875 hours or x = 1 hour and 53 minutes
 Polynomials-and-rational-expressions/464388: Dal and Kim can assemble a swing set in 1 1/2 hr. Working alone, it takes Kim 4 hr longer than Dal to assemble the swing set. How long would it take Dal, working alone, to assemble the swing set? 1 solutions Answer 318123 by nerdybill(6962)   on 2011-06-25 17:44:27 (Show Source): You can put this solution on YOUR website!Dal and Kim can assemble a swing set in 1 1/2 hr. Working alone, it takes Kim 4 hr longer than Dal to assemble the swing set. How long would it take Dal, working alone, to assemble the swing set? . Let d = time it takes for Dal alone then d+4 = time it takes for Kim . 1.5(1/d + 1/(d+4)) = 1 multiplying both sides by d(d+4): 1.5(d+4 + d) = d(d+4) 1.5(2d+4) = d^2+4d 3d+6 = d^2+4d 6 = d^2+d 0 = d^2+d-6 0 = (d+3)(d-2) d = {-3, 2} toss out the negative solution leaving: d = 2 hours (Dal's time working alone)
 Graphs/464392: Write the slope-intercept equation for the line that passes through (-5, -8) and is perpendicular to 10x – 6y = -11 Please show all of your work. . 1 solutions Answer 318121 by nerdybill(6962)   on 2011-06-25 17:28:26 (Show Source): You can put this solution on YOUR website!Write the slope-intercept equation for the line that passes through (-5, -8) and is perpendicular to 10x – 6y = -11 Please show all of your work. . . Determine slope of: 10x – 6y = -11 By rearranging into "slope-intercept" form: 10x – 6y = -11 10x = 6y -11 10x + 11 = 6y (10/6)x + 11/6 = y (5/3)x + 11/6 = y slope is 5/3 a line perpendicular must have a "negative reciprocal": (5/3)m = -1 m = -3/5 (slope of new line) . using the slope (-3/5) and (-5, -8) plug into the "point-slope" form: y - y1 = m(x - x1) y - (-8) = (-3/5)(x - (-5)) y + 8 = (-3/5)(x + 5) y + 8 = (-3/5)x - 3 y = (-3/5)x - 11 (this is what they're looking for)
 logarithm/464240: What is the real value of x in the equation log345 - log35 = log7x?1 solutions Answer 318010 by nerdybill(6962)   on 2011-06-24 22:47:14 (Show Source): You can put this solution on YOUR website!log345 - log35 = log7x log(345/35) = log7x 345/35 = 7x (345/35)/7 = x 1.41 = x
 Quadratic_Equations/464114: Find the x- and y- intercepts for the graph of the following equation. 5x + 6y = 120 1 solutions Answer 317913 by nerdybill(6962)   on 2011-06-24 11:56:28 (Show Source): You can put this solution on YOUR website!Find the x- and y- intercepts for the graph of the following equation. 5x + 6y = 120 . x-intercept is found by setting y to 0 and solving for x: 5x + 6y = 120 5x + 6(0) = 120 5x = 120 x = 24 x-intercept is at (24,0) . y-intercept is found by setting x to 0 and solving for y: 5x + 6y = 120 5(0) + 6y = 120 6y = 120 y = 20 y-intercept is at (0, 20)
 Linear_Equations_And_Systems_Word_Problems/464079: Please help me to solve this problem. If is a cost function, how fast is marginal cost changing when q=100 ?1 solutions Answer 317912 by nerdybill(6962)   on 2011-06-24 11:54:14 (Show Source): You can put this solution on YOUR website!If is a cost function, how fast is marginal cost changing when q=100 ? . Find the derivative of: c' = . set q to 100 and find c':
 Miscellaneous_Word_Problems/463928: I would appreciate help solving this question: A section of a roller coaster ride is described by the equation y = 0.005x^2 -2x +200 where y represents the vertical distance in feet and x represents the horizontal distance in feet. At what value of x will the track turn upwards?1 solutions Answer 317771 by nerdybill(6962)   on 2011-06-23 18:18:38 (Show Source): You can put this solution on YOUR website!By "looking" at: y = 0.005x^2 -2x +200 we know that it is a parabola that opens upwards (because of the positive coefficient associated with the x^2 term). So, the vertex would be the lowest point and where it would turn upwards: x = -b/(2a) x = -(-2)/(2*0.005) x = 2/0.010 x = 200 (this is what they're looking for)
 logarithm/463917: lorarithmic form 9^4=65611 solutions Answer 317759 by nerdybill(6962)   on 2011-06-23 17:31:34 (Show Source): You can put this solution on YOUR website!lorarithmic form 9^4=6561
 Graphs/463920: Find the y-intercept of the line whose equation is y=(5/3)x+(8/5) 1 solutions Answer 317758 by nerdybill(6962)   on 2011-06-23 17:30:15 (Show Source): You can put this solution on YOUR website!Because: y=(5/3)x+(8/5) is already in "slope-intercept" form of y=mx+b where (0,b) is the y-intecept . From inspection, we know the y-intecept of y=(5/3)x+(8/5) is at (0, 8/5)
 Money_Word_Problems/463895: The value of fraction is 4/7 and its denominator is 15 greater its numerator. Find the fraction. 1 solutions Answer 317754 by nerdybill(6962)   on 2011-06-23 16:55:09 (Show Source): You can put this solution on YOUR website!The value of fraction is 4/7 and its denominator is 15 greater its numerator. Find the fraction. . Let n = numerator then n+15 = denominator . n/(n+15) = 4/7 cross multiplying: 7n = 4(n+15) 7n = 4n+60 3n = 60 n = 20 . fraction is then: n/(n+15) = 20/(20+15) = 20/35
 Travel_Word_Problems/463898: This is a problem from my summer homework that should be really easy, but I'm completely blanking out on how to solve it! "Christy drove at 50 miles per hour for h hours but arrived g hours late. How fast should Christy have driven to have arrived on time?" I started some of my own work, but I really had no idea what I was doing, so it was rather pointless, but thanks to anyone who can help!1 solutions Answer 317753 by nerdybill(6962)   on 2011-06-23 16:51:58 (Show Source): You can put this solution on YOUR website!"Christy drove at 50 miles per hour for h hours but arrived g hours late. How fast should Christy have driven to have arrived on time?" . Applying the distance formula of d=rt Distance needed to travel: 50h miles Time needed to make it in: h-g . since: r = d/t r = (50h)/(h-g) . Therefore, your answer is (relative to h and g): (50h)/(h-g) mph
 test/463696: 2=(1.07)^t1 solutions Answer 317680 by nerdybill(6962)   on 2011-06-22 23:55:30 (Show Source): You can put this solution on YOUR website! applying "change of base":
 logarithm/463692: log(2-x)=.05 Find X1 solutions Answer 317679 by nerdybill(6962)   on 2011-06-22 23:52:31 (Show Source): You can put this solution on YOUR website!log(2-x)=.05 (2-x)= 10^(.05) 2-x= 1.122 -x= 1.122-2 -x= -0.878 x= 0.878
 Equations/463716: Please help me to solve this problem. For the cost function c=0.4q^2+4q+5 , find the rate of change of c with respect to q when q=2 .1 solutions Answer 317678 by nerdybill(6962)   on 2011-06-22 23:48:11 (Show Source): You can put this solution on YOUR website!For the cost function c=0.4q^2+4q+5 , find the rate of change of c with respect to q when q=2 . Begin by finding the first derivative of the function: c=0.4q^2+4q+5 c'=0.8q+4 . The "rate of change" when q=2: c'=0.8(2)+4 c'=1.6+4 c'=5.6
 Triangles/462651: Find the length of the hypotenuse of a right triangle whose legs measure 5 and 71 solutions Answer 317134 by nerdybill(6962)   on 2011-06-19 23:32:51 (Show Source): You can put this solution on YOUR website! Find the length of the hypotenuse of a right triangle whose legs measure 5 and 7 . Applying the Pythagorean Theorem: Let h = hypotenuse then h^2 = 5^2 + 7^2 h^2 = 25 + 49 h^2 = 74 h = sqrt(74) h = 8.6
 Equations/462666: Factor completely: 8x^8 - 64x^7 + 16x^61 solutions Answer 317133 by nerdybill(6962)   on 2011-06-19 23:29:39 (Show Source): You can put this solution on YOUR website! Factor completely: 8x^8 - 64x^7 + 16x^6 factor out 8x^6: (8x^6)(x^2 - 8x + 2)
 Quadratic_Equations/462687: Can 3sqrt(3)+sqrt18 be simplified even more?1 solutions Answer 317132 by nerdybill(6962)   on 2011-06-19 23:27:40 (Show Source): You can put this solution on YOUR website!Can 3sqrt(3)+sqrt18 be simplified even more? Yes... . factoring out the 3:
 Linear-equations/462685: find the slope of y=-4x+81 solutions Answer 317131 by nerdybill(6962)   on 2011-06-19 23:25:30 (Show Source): You can put this solution on YOUR website!because y=-4x+8 is in "slope-intercept" form of: y=mx+b we can immediately tell from inspection that the slope is: -4
 Mixture_Word_Problems/462690: Soymeal contains 16% protein. Cornmeal contains 8% protein. How many pounds of each would you need to make 320 pounds of mixture containing 14% protein? Would you please qive me the equation I need to solve this? I've done them before but I can't remember how to set it up. Thank you.1 solutions Answer 317129 by nerdybill(6962)   on 2011-06-19 23:24:13 (Show Source): You can put this solution on YOUR website!Soymeal contains 16% protein. Cornmeal contains 8% protein. How many pounds of each would you need to make 320 pounds of mixture containing 14% protein? . Let x = amount (lbs) of soymeal then 320-x = amount (lbs) of cornmeal . .16x + .08(320-x) = .14(320) Can you finish from here?
 Equations/462665: factor: c^2 + 4c + 41 solutions Answer 317122 by nerdybill(6962)   on 2011-06-19 22:27:27 (Show Source): You can put this solution on YOUR website!factor: c^2 + 4c + 4 (c+2)(c+2) Or (c+2)^2
 Pythagorean-theorem/462479: leg1: x+2 leg2: x and the hypotenuse is square root of 10. how to find x using the pythagorean theorem?.1 solutions Answer 317044 by nerdybill(6962)   on 2011-06-19 09:21:56 (Show Source): You can put this solution on YOUR website!leg1: x+2 leg2: x and the hypotenuse is square root of 10. how to find x using the pythagorean theorem?. . Pythagorean theorem says: (leg1)^2 + (leg2)^2 = (hypotenuse)^2 plug in what was given: (x+2)^2 + x^2 = (sqrt(10))^2 (x+2)^2 + x^2 = 10 (x+2)(x+2) + x^2 = 10 x^2+4x+4 + x^2 = 10 2x^2+4x+4 = 10 2x^2+4x-6 = 0 x^2+2x-3 = 0 factoring: (x+3)(x-1) = 0 x = {-3,1} throw out the negative solution (extraneous) leaving: x = 1
 Percentage-and-ratio-word-problems/462471: The cost per megabyte of disk storage in 1981 was \$700. In 2010 the cost per megabyte of disk storage was about \$.00012. Assuming that the cost per megabyte is decreasing exponentially, find an exponential model of the form C(t)=Aekt that gives the cost per megabyte C in year t. Use 1981 for t = 0, and round k to the nearest thousandth. According to the model, in what year was the cost per megabyte of storage \$.12? 1 solutions Answer 317043 by nerdybill(6962)   on 2011-06-19 09:17:18 (Show Source): You can put this solution on YOUR website!The cost per megabyte of disk storage in 1981 was \$700. In 2010 the cost per megabyte of disk storage was about \$.00012. Assuming that the cost per megabyte is decreasing exponentially, find an exponential model of the form C(t)=Aekt that gives the cost per megabyte C in year t. Use 1981 for t = 0, and round k to the nearest thousandth. According to the model, in what year was the cost per megabyte of storage \$.12? . C(t)=Ae^(kt) C(t) is .00012 A is 700 k is what we're looking for t is 2010-1981=29 . .00012 = 700e^(k*29) .00012/700 = e^(k*29) ln(.00012/700) = k*29 ln(.00012/700)/29 = k -0.537 = k . our general formula: C(t)=700e^(-0.537t) Set c(t) to .12 and solve for t: .12=700e^(-0.537t) .12/700 = e^(-0.537t) ln(.12/700) = -0.537t ln(.12/700)/(-0.537) = t 16.148 = t . 1981+16.148 = 1997.148 answer: 1997
 Geometry_Word_Problems/462469: Using the formula f(x) = x^2 – 2x + 1, find if it has a maximum or minimum and give that point. Also give x-intercepts.1 solutions Answer 317040 by nerdybill(6962)   on 2011-06-19 09:08:29 (Show Source): You can put this solution on YOUR website! Using the formula f(x) = x^2 – 2x + 1, find if it has a maximum or minimum and give that point. Also give x-intercepts. . f(x) = x^2 – 2x + 1 Examining the coefficient associated with the x^2 term, we see that it is "positive" -- this means the vertex is a MINIMUM. x = -b/(2a) x = -(-2)/(2*1) x = (2)/(2) x = 1 To find the 'y', plug above value back into: f(x) = x^2 – 2x + 1 f(1) = 1^2 – 2(1) + 1 f(1) = 1 – 2 + 1 f(1) = 0 Vertex: (1,0) . x-intercepts: set f(x) to zero and solve for x: f(x) = x^2 – 2x + 1 0 = x^2 – 2x + 1 0 = (x-1)(x-1) x = 1 x-intercept at (1,0) (same as the vertex, in this case)
 Linear-equations/462472: How do I write the equation of the line that has a y-intercept of (0,-6) and is perpendicular to the line 3x - 6y = 8.1 solutions Answer 317039 by nerdybill(6962)   on 2011-06-19 09:01:23 (Show Source): You can put this solution on YOUR website! How do I write the equation of the line that has a y-intercept of (0,-6) and is perpendicular to the line 3x - 6y = 8. . Remember the "slope-intercept" form: y = mx + b (equation of a line) . From:"the line that has a y-intercept of (0,-6)" we now know: b = -6 . To find 'm', begin by finding slope of: 3x - 6y = 8 -6y = -3x+8 6y = 3x-8 y = (3/6)x-(8/6) y = (1/2)x-(4/3) a line that is perpendicular to the above line MUST have a slope that is the negative reciprocal: (1/2)m = -1 m = -2 . Plug 'm' and 'b' back into: y = mx + b to get your answer: y = -2x + (-6) y = -2x - 6
 Distributive-associative-commutative-properties/462278: Okay, I have looked at this a dozen ways and I am not getting it. I thought I knew it, but not so much. I have checked my answer against the back of the book and keep getting it wrong. Here is is: (x+4)(x-5)-(x+3)(x-6) Tried FOIL and distributive and I am very frustrated...Thanks for your help -Matt1 solutions Answer 316925 by nerdybill(6962)   on 2011-06-18 14:08:23 (Show Source): You can put this solution on YOUR website!(x+4)(x-5)-(x+3)(x-6) Yes, you would begin by FOILing: (x^2-5x+4x-20)-(x^2-6x+3x-18) (x^2-x-20)-(x^2-3x-18) Now, distribute the "negative sign" to each term inside right parenthesis: x^2-x-20-x^2+3x+18 -x-20+3x+18 2x-20+18 2x-2
 Quadratic-relations-and-conic-sections/461883: a ball is thrown from a 180m high cliff> the relation h=-5t^2-5t+180 relates the time in seconds to the height in m. a) What was the intial height of the ball? b) how long does it take the ball to reach a height of 80m? c) determine the maximum height if the ball1 solutions Answer 316662 by nerdybill(6962)   on 2011-06-16 19:51:33 (Show Source): You can put this solution on YOUR website!a ball is thrown from a 180m high cliff> the relation h=-5t^2-5t+180 relates the time in seconds to the height in m. a) What was the intial height of the ball? this is when t=0: h=-5t^2-5t+180 h=-5(0)^2-5(0)+180 h=180 m . b) how long does it take the ball to reach a height of 80m? set h to 80 and solve for t: h=-5t^2-5t+180 80=-5t^2-5t+180 0=-5t^2-5t+100 0=-t^2-t+20 0=t^2+t-20 0=(t+5)(t-4) t={-5,4} throw out the negative solution leaving: t = 4 seconds . c) determine the maximum height if the ball this occurs at the vertex when h=-5t^2-5t+180 t = -b/(2a) t = -(-5)/(2(-5)) t = 5/(-10) t = -1/2 seconds . Note: you probably typed in a wrong equation in your original problem probably should be something like: h=-5t^2+5t+180
Mixture_Word_Problems/461620: Cindy can paint a house in 3 hr less time than Dustin. Together, it takes 18 hrs. How long does it take each to do the job by theirselves?

1 solutions

Answer 316539 by nerdybill(6962)   on 2011-06-16 09:24:00 (Show Source):
You can put this solution on YOUR website!
Cindy can paint a house in 3 hr less time than Dustin. Together, it takes 18 hrs. How long does it take each to do the job by theirselves?
.
Let x = time (hrs) it takes for Dustin
then
x-3 = time it takes for Cindy
.
18(1/x + 1/(x-3)) = 1
multiplying both sides by x(x-3):
18((x-3) + x) = x(x-3)
18(2x-3) = x^2-3x
36x-54 = x^2-3x
-54 = x^2-39x
0 = x^2-39x+54
solve by applying the "quadratic formula" to get:
x = {37.56, 1.44}
throw out the 1.44 (extraneous) to get
x = 37.56 hours (Dustin)
.
Cindy
x-3 = 37.56-3 = 34.56 hours
.