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Quadratic_Equations/301883: An object is propelled vertically upward from the top of a 272-foot building. The quadratic function models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. After how many seconds does the object reach its maximum height? Round to the nearest tenth of a second if necessary. 1 solutions Answer 216483 by nerdybill(6962)   on 2010-05-08 01:38:00 (Show Source): You can put this solution on YOUR website! . From inspection, we see that the function describes a parabola that opens downwards. As such, finding the axis of symmetry will give us our answer. . The axis of symmetry is found by: x = -b/2a x = -144/(2*(-16)) x = 144/(2*(16)) x = 72/16 x = 4.5 seconds

Miscellaneous_Word_Problems/301757: A certain species of bacteria in a laboratory begins with 200 cells and has a half life every 20 minutes. How many cells of the bacteria will be left after 1 hour (60 minutes)? Write an equation to model the problem and then solve your equation for the given value. 1 solutions Answer 216378 by nerdybill(6962)   on 2010-05-07 16:56:19 (Show Source): You can put this solution on YOUR website! A certain species of bacteria in a laboratory begins with 200 cells and has a half life every 20 minutes. How many cells of the bacteria will be left after 1 hour (60 minutes)? Write an equation to model the problem and then solve your equation for the given value. . Use the exponential growth/decay formula: Where P(t) is amount after t time Po is the initial amount r is the rate of growth/decay t is time . Using the first sentence we can determine r: (1/2)(200) = 200e^(r*20) 1/2 = e^(r*20) ln(.5) = r*20 ln(.5)/20 = r -.03466 = r . Our equation then is: Now, we can answer: How many cells of the bacteria will be left after 1 hour (60 minutes)? 25 cells left after 60 minutes

Rate-of-work-word-problems/301708: I have a problem but cannot figure out the equation (formnula) necessary to find the answer. All the examples I can find give me the rates but not the total time, but this one is the opposite. Working together, Jenny and Natalie can mop a warehouse in 5.14 hours. Had she done it alone it would have taken Natalie 12 hours. How long would it take Jenny to do it alone? Thank you for your help. Jonathan 1 solutions Answer 216318 by nerdybill(6962)   on 2010-05-07 12:12:05 (Show Source): You can put this solution on YOUR website! Working together, Jenny and Natalie can mop a warehouse in 5.14 hours. Had she done it alone it would have taken Natalie 12 hours. How long would it take Jenny to do it alone? . Let x = number of hours if Jenny worked alone then 5.14(1/x + 1/12) = 1 Multiplying both sides by 12x we have: 5.14(12 + x) = 12x 61.68 + 5.14x = 12x 61.68 = 6.86x 9 hours = x

logarithm/301624: i need to solve for g 4.48=2.40(1+g)^5 1 solutions Answer 216255 by nerdybill(6962)   on 2010-05-07 00:37:41 (Show Source): You can put this solution on YOUR website! 0.133 = g

Quadratic_Equations/301613: The height of a ball in feet is modeled as f(x)=-16x^2+96x, where x is the time in seconds after it is hit. How long is the ball in the air? 1 solutions Answer 216254 by nerdybill(6962)   on 2010-05-07 00:30:47 (Show Source): You can put this solution on YOUR website! The height of a ball in feet is modeled as f(x)=-16x^2+96x, where x is the time in seconds after it is hit. How long is the ball in the air? . The time it is in the air is equivalent to the time it hits the ground -- so, set f(x) to 0 and solve for t: f(x)=-16x^2+96x 0=-16x^2+96x 0=16x^2-96x 0=x^2-6x 0=x(x-6) x = {0,6} Solution: 6 seconds

Rate-of-work-word-problems/301609: Barney can build a barn in 15 hours. david can build a barn in 10 hours. How long will it take for the barn to be built if they work together? 1 solutions Answer 216253 by nerdybill(6962)   on 2010-05-07 00:27:47 (Show Source): You can put this solution on YOUR website! Barney can build a barn in 15 hours. david can build a barn in 10 hours. How long will it take for the barn to be built if they work together? . Barney's rate: 1/15 David's rate: 1/10 . Let t = time it takes for both then t(1/15 + 1/10) = 1 Multiply both sides by 150: t(10 + 15) = 150 25t = 150 t = 6 hours

Exponential-and-logarithmic-functions/301569: Carbon-14 has a half-life of 5700 yrs. Scientists use this fact to determine the age of things made of organic material. Suppose the average page of a book containing approximately 0.5 mg of carbon-14 is put into a time capsule. How much c-14 will each page contain after 5700 yrs. 1 solutions Answer 216221 by nerdybill(6962)   on 2010-05-06 22:23:52 (Show Source): You can put this solution on YOUR website! Carbon-14 has a half-life of 5700 yrs. Scientists use this fact to determine the age of things made of organic material. Suppose the average page of a book containing approximately 0.5 mg of carbon-14 is put into a time capsule. How much c-14 will each page contain after 5700 yrs. . Since 5700 years is the "half-life" exactly 0.25 mg will remain.

logarithm/301576: how long will it take for the population of a certain country to triple if its annual growth rate is 2.8%? (round to the nearest year.) Use this exponontial growth model P(t) = P0ekt 1 solutions Answer 216218 by nerdybill(6962)   on 2010-05-06 22:15:28 (Show Source): You can put this solution on YOUR website! how long will it take for the population of a certain country to triple if its annual growth rate is 2.8%? (round to the nearest year.) Use this exponontial growth model P(t) = P0ekt . Let x = initial population then Dividing both sides by x: 39 years = t

Money_Word_Problems/301425: How long does it take $1,150 to double if it is invested at 9% interest compounded monthly? Round your answer to the nearest tenth. 1 solutions Answer 216150 by nerdybill(6962)   on 2010-05-06 18:03:56 (Show Source): You can put this solution on YOUR website! How long does it take $1,150 to double if it is invested at 9% interest compounded monthly? Round your answer to the nearest tenth. . Compound interest formula: Regular Compound Interest Formula . P = principal amount (the initial amount you borrow or deposit) r = annual rate of interest (as a decimal) t = number of years the amount is deposited or borrowed for. A = amount of money accumulated after n years, including interest. n = number of times the interest is compounded per year . 7.7 years = t

Human-and-algebraic-language/301460: Having trouble with this. Can some please help me ·Translate and solve this equation? Twice an unknown number and 3 is 18. 1 solutions Answer 216148 by nerdybill(6962)   on 2010-05-06 17:57:17 (Show Source): You can put this solution on YOUR website! Twice an unknown number and 3 is 18. . Let x = unknown number then 2(x+3) = 18 x+3 = 9 x = 6

logarithm/301449: Please simplify log 10 0.1 1 solutions Answer 216145 by nerdybill(6962)   on 2010-05-06 17:51:35 (Show Source): You can put this solution on YOUR website! Please simplify log 10 0.1 . (this is your answer)

Functions/301455: (3,5);x+8y=9 Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b. This is my problem. I have serious difficulties trying to solve these types of equations. This is for Algebra 1 in Axia College online degree program. 1 solutions Answer 216143 by nerdybill(6962)   on 2010-05-06 17:49:08 (Show Source): You can put this solution on YOUR website! (3,5);x+8y=9 . First, we find the slope of: x+8y=9 Do this by putting it into the "slope-intercept" form: y = mx +b where m is the slope . x+8y=9 8y= -x+9 y = (-1/8)x + 9/8 From above, we know our new line has slope of -1/8 and it crosses: (3,5) . Plug the above data into the "point-slope" form: y - y1 = m(x - x1) y - 5 = (-1/8)(x - 3) y - 5 = (-1/8)x + 3/8 y = (-1/8)x + 3/8 + 5 y = (-1/8)x + 3/8 + 40/8 y = (-1/8)x + 43/8 (this is what they're looking for)

Polynomials-and-rational-expressions/301209: Solve: x^3-3x^2-x+3=0 Looking for the roots. Thank you 1 solutions Answer 216014 by nerdybill(6962)   on 2010-05-06 09:22:11 (Show Source): You can put this solution on YOUR website! x^3-3x^2-x+3=0 Solve by "grouping": (x^3-3x^2)-(x-3)=0 x^2(x-3)-(x-3)=0 (x-3)(x^2-1) = 0 x = {3,-1,1} .

logarithm/301264: 2log(x^2+4x)=1 Professor says there are two answers? 1 solutions Answer 216008 by nerdybill(6962)   on 2010-05-06 09:11:16 (Show Source): You can put this solution on YOUR website! 2log(x^2+4x)=1 log(x^2+4x)^2=1 (x^2+4x)^2=10^1 (x^2+4x)^2=10 x^2+4x=sqrt(10) x^2+4x-sqrt(10) = 0 x^2+4x-3.162 = 0 Using the quadratic formula we get: x={0.676, -4.676} . Details of 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=28.6491106406735 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.676243198995259, -4.67624319899526. Here's your graph:

Finance/301265: Ten liters of a 4% acid solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? 1 solutions Answer 216003 by nerdybill(6962)   on 2010-05-06 09:01:28 (Show Source): You can put this solution on YOUR website! Ten liters of a 4% acid solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? . Let x = liters of 10% solution needed then .04(10) + .10x = .06(10+x) .4 + .10x = .6+.06x .4 + .04x = .6 .04x = .2 x = 5 liters

Reduction-of-unit-multipliers/301249: how do I find how many hours it took to make 3510 products when it took only 36 minutes to make 1. whats the conversion please many thanks Kay 1 solutions Answer 216002 by nerdybill(6962)   on 2010-05-06 08:58:41 (Show Source): You can put this solution on YOUR website! how do I find how many hours it took to make 3510 products when it took only 36 minutes to make 1. . Since it takes 36 minutes for each: 36*3510 = 126360 minutes . Converting to hours: 126360/60 = 2106 hours . Converting to days: 2106/24 = 87.75 days or 87 days and 18 hours

Miscellaneous_Word_Problems/301267: A picture 19 inches by 24 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 188 square inches? 1 solutions Answer 215999 by nerdybill(6962)   on 2010-05-06 08:42:23 (Show Source): You can put this solution on YOUR website! A picture 19 inches by 24 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 188 square inches? . Let w = width of border then "area of border" = "area of mat" - "area of picture" 188 = (19+2w)(24+2w) - 19(24) 188 = 456+38w+48w+4w^2 - 456 188 = 38w+48w+4w^2 188 = 4w^2+86w 0 = 4w^2+86w-188 0 = 2w^2+43w-94 Solve using the quadratic formula. Doing so yields: w = {2, -23.5} Of course, we can toss out the negative solution leaving: w = 2 inches . Details of 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=2601 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2, -23.5. Here's your graph:

Quadratic_Equations/301003: Quadratic application If the cost ,C(x) for manufactoring x units of a certain product is given by C(x)=x^2-125x+50, find thye units manufactored at a cost of $9500 1 solutions Answer 215865 by nerdybill(6962)   on 2010-05-05 18:35:20 (Show Source): You can put this solution on YOUR website! If the cost ,C(x) for manufactoring x units of a certain product is given by C(x)=x^2-125x+50, find thye units manufactored at a cost of $9500 . The given quadratic: C(x)=x^2-125x+50 where C(x) is the cost x is the number of units . Simply plug in the given cost and solve for x: C(x)=x^2-125x+50 9500 = x^2-125x+50 0 = x^2-125x-9450 Apply the quadratic formula when then yields: x = {178.07, -53.07} . Throw out the negative solution leaving: x = 178 units . Details of quadratic formula follows: 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=53425 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 178.069243313262, -53.0692433132622. Here's your graph:

Pythagorean-theorem/300752: Two planes take off from an airport at the same time. They fly at right angles to each other and one hour later they are 390km apart. If one plane travels 210km/hr faster than the other, what is the speed of the two planes? I tried to apply Pythagoras Theorem, making the hypotenuse 390, and the sides x and x+210. I squared 390 = the sum of the squares of x and x+210, but my answers always come out wrong. 1 solutions Answer 215727 by nerdybill(6962)   on 2010-05-05 06:10:41 (Show Source): You can put this solution on YOUR website! Two planes take off from an airport at the same time. They fly at right angles to each other and one hour later they are 390km apart. If one plane travels 210km/hr faster than the other, what is the speed of the two planes? . Let x = speed of slower plane then x+210 = speed of faster plane . x^2 + (x+210)^2 = 390^2 x^2 + (x+210)(x+210) = 390^2 x^2 + x^2+420x+44100 = 152100 2x^2+420x+44100 = 152100 x^2+210x+22050 = 76050 x^2+210x-54000 = 0 (x+360)(x-150) = 0 x={150, -360} Throw out the negative: x = 150 km/hr (slower plane) . faster plane: x+210 = 150+210 = 360 km/hr

Miscellaneous_Word_Problems/300724: bill has a collection of 65 nickels and dimes. their total worth is $5.50. find how many nickels and dimes bill has 1 solutions Answer 215720 by nerdybill(6962)   on 2010-05-05 01:24:14 (Show Source): You can put this solution on YOUR website! bill has a collection of 65 nickels and dimes. their total worth is $5.50. find how many nickels and dimes bill has . Let n = number of nickels then 65-n = number of dimes . .05n + .10(65-n) = 5.50 .05n + 6.5 - .10n = 5.50 6.5 - .05n = 5.50 -.05n = -1 n = 20 (number of nickels) . number of dimes: 65-n = 65-20 = 45

Rectangles/300727: The area of a square is 5 more times than its perimeter. Find the length of a side. 1 solutions Answer 215719 by nerdybill(6962)   on 2010-05-05 01:20:55 (Show Source): You can put this solution on YOUR website! The area of a square is 5 times than its perimeter. Find the length of a side. . Let x = length of one side of square then "area of square" = "5 more times than its perimeter" x^2 = 5(4x) x^2 = 20x x^2 - 20x = 0 x(x - 20) = 0 x = {0, 20} . length of side must be 20

Polynomials-and-rational-expressions/300713: Solve by factoring and using the principle of zero products. 9t^2=25 1 solutions Answer 215718 by nerdybill(6962)   on 2010-05-05 00:07:56 (Show Source): You can put this solution on YOUR website! 9t^2=25 9t^2-25 = 0 (3t)^2 - 5^2 = 0 The above is a "difference of squares": (3t-5)(3t+5) = 0 t = {-5/3, 5/3}

logarithm/300705: How long will it take for the population of a certain country to double if its annual growth rate is 3.5%? (Round to the nearest year) Use the exponential growth modle P(t) = poe kt 1 solutions Answer 215717 by nerdybill(6962)   on 2010-05-04 23:26:49 (Show Source): You can put this solution on YOUR website! How long will it take for the population of a certain country to double if its annual growth rate is 3.5%? (Round to the nearest year) Use the exponential growth modle P(t) = poe kt . P(t) = poe^kt . Let x = initial population then 2x = xe^(.035t) dividing both sides by x: 2 = e^(.035t) ln(2) = .035t ln(2)/.035 = t 19.80 = t round to nearest year: 20 years = t

Mixture_Word_Problems/300675: To reduce 16 ounces of a 18% saline solution to a 10% solution, how much distilled water (to the nearest tenth oz.) should a nurse add? The nurse should add ________ oz. of distilled water. 1 solutions Answer 215693 by nerdybill(6962)   on 2010-05-04 22:00:04 (Show Source): You can put this solution on YOUR website! To reduce 16 ounces of a 18% saline solution to a 10% solution, how much distilled water (to the nearest tenth oz.) should a nurse add? . Let x = ounces of distilled water to add then .18(16) = .10(16+x) 2.88 = 1.6+.10x 1.28 = .10x 12.8 = x . The nurse should add 12.8 oz. of distilled water.

Quadratic_Equations/300563: Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 square feet. --They want me to use the quadratic formula, but I don't know how to set the equation up. That's all I'm having trouble with. I know how to use the quadratic formula fairly well. Can you please help me? ~Thanks! 1 solutions Answer 215647 by nerdybill(6962)   on 2010-05-04 19:01:12 (Show Source): You can put this solution on YOUR website! Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 square feet. . Let x = length and y = width . 2(x+y) = 100 (equation 1) xy = 600 (equation 2) . Solve equation 2 for y: xy = 600 y = 600/x . Substitute the above into equation 1 and solve for x: 2(x+y) = 100 2(x+600/x) = 100 x+600/x = 50 x^2+600 = 50x x^2-50x+600 = 0 (x-20)(x-30) = 0 . x = {20,30} . Dimensions are 20 feet by 30 feet

Quadratic_Equations/300547: Suppose you are going to construct a circular fish pond in your garden. You want the pond to cover an area of 300ft^2. What is the radius of the pond? 1 solutions Answer 215645 by nerdybill(6962)   on 2010-05-04 18:51:19 (Show Source): You can put this solution on YOUR website! Suppose you are going to construct a circular fish pond in your garden. You want the pond to cover an area of 300ft^2. What is the radius of the pond? . Since area of a circle is (1/2)(pi)r^2 . 300 = (1/2)(pi)r^2 300 = (1/2)(3.14)r^2 600 = (3.14)r^2 600/3.14 = r^2 191.0828 = r^2 3.72 feet = r

Polynomials-and-rational-expressions/300548: Can someone please solve the below and explain. Thank you so much. Factor Completly. Remember to look first for a common factor. Check by multiplying. If a polynomoal is prime state this. 3y^2-9y-84. Thanks again 1 solutions Answer 215643 by nerdybill(6962)   on 2010-05-04 18:47:32 (Show Source): You can put this solution on YOUR website! 3y^2-9y-84 3(y^2-3y-28) 3(y-7)(y+4)

Polynomials-and-rational-expressions/300489: Reduce the rational expression (please show steps) 1 solutions Answer 215640 by nerdybill(6962)   on 2010-05-04 17:27:59 (Show Source): You can put this solution on YOUR website! Starting with: . Factor numerator and denominator: . Cancel like-terms:

logarithm/300393: How long will it take for the population of a certain country to double if its annual growth rate is 5.1%? I have been dividing ln2 by 5.1%? A)14 yr B)6 yr C) 39 yr D) 1 yr 1 solutions Answer 215573 by nerdybill(6962)   on 2010-05-04 15:03:45 (Show Source): You can put this solution on YOUR website! . Apply: A = Pe^(rt) . Let x = current population then 2x = xe^(.051t) 2 = e^(.051t) ln 2 = .051t ln 2/.051 = t 13.6 years =t . Closest answer would be B

Radicals/300409: what is 2(squareroot)2=(squareroot)u and how do you do it 1 solutions Answer 215568 by nerdybill(6962)   on 2010-05-04 14:55:45 (Show Source): You can put this solution on YOUR website! 2(squareroot)2=(squareroot)u . Square both sides:

percentage/300381: I am terrible at math, can you please help me? Thank you again. A saleswoman is working on a 6% commission basis. If she wants to make $2,400 in one month, how much must she sell? 1 solutions Answer 215564 by nerdybill(6962)   on 2010-05-04 14:33:53 (Show Source): You can put this solution on YOUR website! A saleswoman is working on a 6% commission basis. If she wants to make $2,400 in one month, how much must she sell? . Let x = amount she sells then .06x = 2400 x = 2400/.06 x = $40,000 She must sell $40,000 worth of merchandise