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nerdybill answered: 7001 problems
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 Rate-of-work-word-problems/453460: if it take 4 hours to fill a pool with the drain closed and 5 hours to empty a pool with the drain open, how long does it take to fill a pool with the drain open1 solutions Answer 311552 by nerdybill(7003)   on 2011-05-24 11:24:06 (Show Source): You can put this solution on YOUR website!if it take 4 hours to fill a pool with the drain closed and 5 hours to empty a pool with the drain open, how long does it take to fill a pool with the drain open. . Let x = time (hours) it takes to fill pool w/drain open then x(1/4 - 1/5) = 1 multiplying both sides by 20: x(5 - 4) = 20 x(1) = 20 x = 20 hours
 Surface-area/453467: the total area of a sphere is 144 pie square centimeters. what is the diameter?1 solutions Answer 311551 by nerdybill(7003)   on 2011-05-24 11:20:11 (Show Source): You can put this solution on YOUR website!the total area of a sphere is 144 pie square centimeters. what is the diameter? . since the area of a sphere is given as: 4(pi)r^2 . We set the above equal to 144 to find the radius: 4(pi)r^2 = 144(pi) dividing both sides by pi: 4r^2 = 144 dividing both sides by 4: r^2 = 36 take the square root of both sides: r = 6 cm . But, the problem wanted the diameter... diameter = 2r diameter = 2(6) diameter = 12 cm (answer)
 Pythagorean-theorem/453437: A 15 m pole is leaning against a wall. The foot of the pole is 10 m from the wall. What is the angle that the pole makes with the ground?1 solutions Answer 311548 by nerdybill(7003)   on 2011-05-24 10:01:15 (Show Source): You can put this solution on YOUR website!A 15 m pole is leaning against a wall. The foot of the pole is 10 m from the wall. What is the angle that the pole makes with the ground? . Apply Trigonometry... Let x = angle then cos x = 10/15 x = cos^(-1)(10/15) x = cos^(-1)(2/3) x = 48.2 degrees
 Triangles/453127: If a right triangle has legs of 6 cm and 8 cm, then the hypotenuse is ?1 solutions Answer 311344 by nerdybill(7003)   on 2011-05-23 14:08:13 (Show Source): You can put this solution on YOUR website!If a right triangle has legs of 6 cm and 8 cm, then the hypotenuse is ? Apply Pythagorean theorem: Let h = hypotenuse then 6^2 + 8^2 = h^2 36 + 64 = h^2 100 = h^2 10 cm = h
logarithm/453069: Determine the positive root of the following equation:
log3(c - 4) + log3(c + 6) = 4.

1 solutions

Answer 311307 by nerdybill(7003)   on 2011-05-23 12:05:47 (Show Source):
You can put this solution on YOUR website!
log3(c - 4) + log3(c + 6) = 4
log3(c - 4)(c + 6) = 4
(c - 4)(c + 6) = 3^4
c^2 + 6c - 4c -24 = 81
c^2 + 2c -105 = 0
apply the quadratic formula to find the roots:
c = {9.3, -11.3}
throw out the negative root leaving:
c = 9.3
.
details of quadratic to follow:
 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=424 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 9.295630140987, -11.295630140987. Here's your graph:

 Equations/453073: find vertex of porabola y = 6 x + 7 - x^21 solutions Answer 311306 by nerdybill(7003)   on 2011-05-23 11:59:36 (Show Source): You can put this solution on YOUR website!y = 6 x + 7 - x^2 rearranging: y = -x^2 + 6x + 7 . The x-coordinate of the vertex is at: x = -b/(2a) = -6/(2*(-1)) = -6/(-2) = 3 . The y-coordinate: y = -x^2 + 6x + 7 y = -3^2 + 6(3) + 7 y = -9 + 18 + 7 y = 16 . Answer: (3, 16)
 logarithm/453080: Find the approximate solution to the equation. 5x + 3 = 2x - 6 (If necessary, please round your answer to 4 decimal 1 solutions Answer 311305 by nerdybill(7003)   on 2011-05-23 11:53:25 (Show Source): You can put this solution on YOUR website!Next time, you should write your expression as: 5^(x+3) = 2(x-6) log(5) * (x+3) = log(2) * (x-6) xlog(5) + 3log(5) = xlog(2) - 6log(2) xlog(5) - xlog(2) = -6log(2) - 3log(5) x(log(5) - log(2)) = -6log(2) - 3log(5) x = (-6log(2) - 3log(5)) / (log(5) - log(2)) x = (-3.9) / (.40) x = -9.76
 Numeric_Fractions/452539: 3/8 + 3/5? 1 solutions Answer 311077 by nerdybill(7003)   on 2011-05-22 11:03:03 (Show Source): You can put this solution on YOUR website!3/8 + 3/5 change both terms so they have a common denominator of 40: 15/40 + 24/40 (15 + 24)/40 39/40
 Problems-with-consecutive-odd-even-integers/452484: Find two consecutive negative integers whose product is 90 -thanks1 solutions Answer 311047 by nerdybill(7003)   on 2011-05-22 08:19:21 (Show Source): You can put this solution on YOUR website!Find two consecutive negative integers whose product is 90 . Let x = first negative answer then x+1 = second negative answer x(x+1) = 90 x^2 + x = 90 x^2 + x - 90 = 0 (x+10)(x-9) = 0 x = (-10, 9) Since we're looking for a negative answer, throw out the positive answer leaving: x = -10 (first negative number) . Second negative number" x+1 = -10+1 = -9 . Answer: -10 and -9
 Miscellaneous_Word_Problems/452493: an element decays in such a way that every 50 years the amount of the element of the element has decreased by 15% in the year 1900,120mg of element was present. a)what is amount in 2000 1 solutions Answer 311046 by nerdybill(7003)   on 2011-05-22 08:15:02 (Show Source): You can put this solution on YOUR website!an element decays in such a way that every 50 years the amount of the element of the element has decreased by 15% in the year 1900,120mg of element was present. a)what is amount in 2000 . A = Pe^(rt) where A is amount after time t P is the initial amount r is the rate of growth/decline t is time . first, we determine r... Let x = initial amount then from: "an element decays in such a way that every 50 years the amount of the element of the element has decreased by 15%" x - .15x = xe^(50r) x(1 - .15) = xe^(50r) (1 - .15) = e^(50r) .85 = e^(50r) ln(.85) = 50r ln(.85)/50 = r -0.0033 = r . Our formula then is: A = Pe^(-0.0033t) . Now, we can answer the question: in the year 1900,120mg of element was present. a)what is amount in 2000 t = 2000-1900 = 100 A = 120e^(-0.0033*100) A = 120e^(-0.33) A = 86.7 mg
 Expressions-with-variables/452500: Algebraic expression: 1.Eight less than e 2.Five subtracted from t 3.The sum of x and y 4.one more than a number p 5.The product of v and 4 times i1 solutions Answer 311045 by nerdybill(7003)   on 2011-05-22 08:01:14 (Show Source): You can put this solution on YOUR website!Algebraic expression: 1.Eight less than e 8 - e 2.Five subtracted from t t - 5 3.The sum of x and y x + y 4.one more than a number p p + 1 5.The product of v and 4 times i v(4i) or 4iv
 Circles/452433: A circle has a radius of 5 cm ..what is the length of an arc measuring 80 degrees1 solutions Answer 311044 by nerdybill(7003)   on 2011-05-22 07:59:31 (Show Source): You can put this solution on YOUR website! A circle has a radius of 5 cm ..what is the length of an arc measuring 80 degrees . circumference of a circle = d(pi) circumference of a circle = 2r(pi) circumference of a circle = 2(5)(3.14) circumference of a circle = 31.4 cm . Since there is 360 deg in a circle: length of the arc must be: 80/360 * 31.4 = 6.98 cm
 Triangles/452472: a right triangle has a leg that measures 5 meters, the angle at the intersection of that same leg and the hypoteneuese is 35 degrees.... How do you find the measure of the hypoteneuese?1 solutions Answer 311029 by nerdybill(7003)   on 2011-05-22 00:22:47 (Show Source): You can put this solution on YOUR website!a right triangle has a leg that measures 5 meters, the angle at the intersection of that same leg and the hypoteneuese is 35 degrees.... How do you find the measure of the hypoteneuese? . You apply trigonometry. cos = adjacent/hypotenuse . Let h = hypotenuse then cos 35 = 5/h h*cos 35 = 5 h = 5/cos 35 h = 6.10 meters
 Equations/452471: how do you solve t^2-8t+15=0 1 solutions Answer 311028 by nerdybill(7003)   on 2011-05-22 00:09:26 (Show Source): You can put this solution on YOUR website!t^2-8t+15=0 factoring the left: (t-3)(t-5) = 0 t = {3, 5}
 Linear_Equations_And_Systems_Word_Problems/452262: I hope this is a linear equation and that someone can help me convert it from words to and equation and graph. I need to illustrate the decline in the herring population over the years and estimate what will happen if the trend continues. I've spent all day researching the information and now I have no idea how to put it together, or even if it belongs together :0 Every year the herring returning to the Stonybrook Run to spawn is declining as overfishing, water pollution, and loss of habit takes a toll on their numbers. In 2000, you could count 100 herring go through the run in 1 minute, but by 2005, it took 5 minutes to count the same number. The count in 2010 took 10 minutes to count the 100 fish. If the trend continues how long will it take count 100 herring in 2015? 1 solutions Answer 310934 by nerdybill(7003)   on 2011-05-21 09:19:07 (Show Source): You can put this solution on YOUR website!Create a table of data: year time 2000 1 2005 5 2010 10 . Plot the above three points on graph paper. Because the dots appears to be in a straight line, you can assume it is linear. . Determine slope: m = (y2-y1)/(x2-x1) using first and last points m = (10-1)/(2010-2000) m = (9)/(10) m = 9/10 . using the slope above and one point (2000,1) plug it into the "point-slope" form: y - y1 = m(x - x1) y - 1 = (9/10)(x - 2000) y - 1 = (9/10)x - (9/10)2000 y - 1 = (9/10)x - (9)200 y - 1 = (9/10)x - 1800 y = (9/10)x - 1801 (this is your equation) . For, 2015: y = (9/10)x - 1801 y = (9/10)2015 - 1801 y = (9)201.5 - 1801 y = (9)201.5 - 1801 y = 1813.5 - 1801 y = 12.5 minutes
 Equations/452199: Find the slope, if one exists, of the line containing the pair of points. (8,7) and (9,-9)1 solutions Answer 310843 by nerdybill(7003)   on 2011-05-20 19:52:52 (Show Source): You can put this solution on YOUR website!(8,7) and (9,-9) m (slope) = (y2 - y1)/(x2 - x1) m (slope) = (-9 - 7)/(9 - 8) m (slope) = (-16)/(1) m (slope) = -16
 Quadratic_Equations/452149: what is the y-coordinate of the y-intercept of y=-9x^2+5x-71 solutions Answer 310841 by nerdybill(7003)   on 2011-05-20 19:46:18 (Show Source): You can put this solution on YOUR website!Set x equal to zero to find the y-intercept: y=-9x^2+5x-7 y=-9(0)^2+5(0)-7 y=-7 So, your y-coordinate is -7
 Exponential-and-logarithmic-functions/452158: Solve for each variable: 2500=4e^58t1 solutions Answer 310832 by nerdybill(7003)   on 2011-05-20 18:22:48 (Show Source): You can put this solution on YOUR website! I'm assuming the 't' is part of the exponent... if not, write back. 2500=4e^(58t) divide both sides by 4: 625 = e^(58t) take the natural log (ln) of both sides: ln(625) = 58t divide both sides by 58: ln(625)/58 = t .111 =t
 Proportions/452179: One number is 4 more than 3/8 of another number. Total of both is 427. Please give formula. Thanks1 solutions Answer 310831 by nerdybill(7003)   on 2011-05-20 18:19:10 (Show Source): You can put this solution on YOUR website!One number is 4 more than 3/8 of another number. Total of both is 427. . Let x = one number and y = another number . From: "One number is 4 more than 3/8 of another number." x = 4+ (3/8)y (equation 1) . From: "Total of both is 427" x + y = 427 (equation 2) . Solve equation 2 for y: x + y = 427 y = 427-x . Substitute above into equation 1 to find x: x = 4+ (3/8)y x = 4+ (3/8)(427-x) 8x = 32+ (3)(427-x) 8x = 32+ 1281-3x 11x = 32+ 1281 11x = 1313 x = 119.36 . Substitute above into equation 2 to find y: x + y = 427 119.36 + y = 427 y = 307.64
 test/452036: Evaluate the polynomial ecpression 16x to the second power-16x+4for x=21 solutions Answer 310753 by nerdybill(7003)   on 2011-05-20 10:34:05 (Show Source): You can put this solution on YOUR website!16x to the second power-16x+4for x=2 Given: then they say x=2 substitute it in:
 Quadratic_Equations/452046: The line y=2x-k passes through the point (4,0) work out the value of k1 solutions Answer 310752 by nerdybill(7003)   on 2011-05-20 10:25:12 (Show Source): You can put this solution on YOUR website!The line y=2x-k passes through the point (4,0) . Since the line passes through (4,0) this means that x = 4 y = 0 . plug it in to: y = 2x-k 0 = 2(4)-k 0 = 8-k adding 'k' to both sides: k = 8
 Quadratic_Equations/451729: Hi! This is a fairly simple question: how much can you simplify in this problem using i (square root of - 1): The original problem was Thanks1 solutions Answer 310609 by nerdybill(7003)   on 2011-05-19 15:27:29 (Show Source): You can put this solution on YOUR website!when applying the "quadratic formula" Instead of: It should be: .
 Quadratic_Equations/451697: Find equation of line passing through the point (5,-2) and (-3,4) I got the answer y=(-3/4)x+7/4 but I don't know how Please show me step by step to get the answer. thanks1 solutions Answer 310597 by nerdybill(7003)   on 2011-05-19 14:16:40 (Show Source): You can put this solution on YOUR website!Find equation of line passing through the point (5,-2) and (-3,4) . First, find the slope: m = (y2-y1)/(x2-x1) m = (4-(-2))/(-3-5) m = (4+2)/(-3-5) m = (6)/(-8) m = -3/4 . Next, use one of the two given points (5, -2) and the slope above -- plug it into the "point-slope" form: y - y1 = m(x - x1) y - (-2) = (-3/4)(x - 5) y + 2 = (-3/4)x + 15/4 y = (-3/4)x + 15/4 - 2 y = (-3/4)x + 15/4 - 8/4 y = (-3/4)x + 7/4 . So, YES, you are correct!
 Rate-of-work-word-problems/451656: A stone is thrown directly upward from a height of 30ft with a velocity of 60ft/sec. The height of the stone t seconds after it has been thrown is given by the function s(t)= - 16t^2 + 16t + 30. Find the time at which the stone reaches its maximum height and find that maximum height.1 solutions Answer 310559 by nerdybill(7003)   on 2011-05-19 11:49:39 (Show Source): You can put this solution on YOUR website!A stone is thrown directly upward from a height of 30ft with a velocity of 60ft/sec. The height of the stone t seconds after it has been thrown is given by the function s(t)= - 16t^2 + 16t + 30. Find the time at which the stone reaches its maximum height and find that maximum height. . Time reaching maximum height is at the vertex: t = -b/(2a) t = -16/(2*(-16)) t = -16/(-32) t = 1/2 seconds . Maximum height: s(1/2)= - 16(1/2)^2 + 16(1/2) + 30 s(1/2)= - 16(1/4) + 8 + 30 s(1/2)= - 4 + 8 + 30 s(1/2)= 34 feet
 Numbers_Word_Problems/451650: the difference between the tens digit and the unit digit of a two digit number is 3. Suppose the tens digit is one less than twice the units digit. what is the number?1 solutions Answer 310557 by nerdybill(7003)   on 2011-05-19 11:36:03 (Show Source): You can put this solution on YOUR website!the difference between the tens digit and the unit digit of a two digit number is 3. Suppose the tens digit is one less than twice the units digit. what is the number? . Let x = tens digit and y = units digit then from: "the difference between the tens digit and the unit digit of a two digit number is 3" x-y = 3 (equation 1) from: "Suppose the tens digit is one less than twice the units digit" x = 2y-1 (equation 2) . Start with equation 1: x-y = 3 substitute definition of x from equation 2: 2y-1-y = 3 y-1 = 3 y = 4 . Substitute above into equation 1 to find x: x-y = 3 x-4 = 3 x = 7 . Solution: the number is 74
 Angles/451643: Two angles are complementary. they have measures of (7x+2)degree and (3x-2)degree, respectively. what is the value of x? 1 solutions Answer 310549 by nerdybill(7003)   on 2011-05-19 11:09:28 (Show Source): You can put this solution on YOUR website!Two angles are complementary. they have measures of (7x+2)degree and (3x-2)degree, respectively. what is the value of x? . Since the sum of complementary angles is 90 degrees we get: (7x+2) + (3x-2) = 90 7x+2 + 3x-2 = 90 10x+2-2 = 90 10x = 90 x = 9
 logarithm/451625: log3 (x)=1/21 solutions Answer 310544 by nerdybill(7003)   on 2011-05-19 10:45:46 (Show Source):
 Equations/451627: Please help me, I'm getting every solution but the correct one for this problem, thank you! 6x+7-4x=8+7x-261 solutions Answer 310543 by nerdybill(7003)   on 2011-05-19 10:44:08 (Show Source): You can put this solution on YOUR website!6x+7-4x=8+7x-26 combine like-terms: 2x+7=7x-18 subtract 2x from both sides: 7=5x-18 add 18 to both sides: 25=5x divide both sides by 5: 5 = x
 Systems-of-equations/451619: solve equation by completing the square x2 + 4x - 36 = 01 solutions Answer 310535 by nerdybill(7003)   on 2011-05-19 10:07:01 (Show Source): You can put this solution on YOUR website!x^2 + 4x - 36 = 0 x^2 + 4x = 36 half 'b' and square it -- then add to both sides x^2 + 4x + 4 = 36 + 4 (x+2)(x+2) = 40 (x+2)^2 = 40 x+2 = sqrt(40) x+2 = sqrt(2*2*2*5) x+2 = 2*sqrt(2*5) x+2 = 2*sqrt(10) x = 2*sqrt(10) - 2 x = 4.325
 Numbers_Word_Problems/451604: two consecutive numbers are squared and then added to gether to get the result of 113. What is the starting formula?1 solutions Answer 310532 by nerdybill(7003)   on 2011-05-19 10:03:14 (Show Source): You can put this solution on YOUR website!two consecutive numbers are squared and then added to gether to get the result of 113. What is the starting formula? . Let x = first consecutive number then x+1 = second consecutive number . x^2 + (x+1)^2 = 113 (you can probably leave it like this) x^2 + (x+1)(x+1) = 113 x^2 + (x^2+x+x+1) = 113 x^2 + (x^2+2x+1) = 113 2x^2+2x+1 = 113
 Geometry_Word_Problems/451616: Can someone help me with this? Please!! You can use displacement to find the volume of an irregular object, such as a stone. Suppose a tank 1 ft wide and 2 ft long is filled with water to a depth of 8 inches. A stone is placed n the rank so that it is completely covered, causing the water level to rise by 2 inches. Find the volume of the stone. Thank you!! :)1 solutions Answer 310530 by nerdybill(7003)   on 2011-05-19 09:59:30 (Show Source): You can put this solution on YOUR website!You can use displacement to find the volume of an irregular object, such as a stone. Suppose a tank 1 ft wide and 2 ft long is filled with water to a depth of 8 inches. A stone is placed n the rank so that it is completely covered, causing the water level to rise by 2 inches. Find the volume of the stone. . Adding in the stone causes the water to rise 2 inches. 2 inches = 1/6 feet . volume of stone then is: (1/6)(2)(1) (1/3)(1) 1/3 cubic feet or .33 cubic feet