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# Recent problems solved by 'nerdybill'

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 Exponential-and-logarithmic-functions/731662: when logx=2logA-(1/2)logB, x is equal to1 solutions Answer 447235 by nerdybill(6951)   on 2013-03-28 23:56:06 (Show Source): You can put this solution on YOUR website! when logx=2logA-(1/2)logB, x is equal to . logx=2logA-(1/2)logB logx = logA^2 - logB^(1/2) logx = log(A^2/B^(1/2)) x = A^2/B^(1/2) . or, . . .
 Quadratic-relations-and-conic-sections/730902: what is the equation of a circle with center (2,0) and radius 2 units? 1 solutions Answer 446932 by nerdybill(6951)   on 2013-03-26 20:49:51 (Show Source): You can put this solution on YOUR website!what is the equation of a circle with center (2,0) and radius 2 units? . Equation of a circle: (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center r is the radius . Plug in given data into: (x-h)^2 + (y-k)^2 = r^2 (x-2)^2 + (y-0)^2 = 2^2 (x-2)^2 + y^2 = 4 (this is what they're looking for)
 Unit_Conversion_Word_Problems/730829: 1 hose can fill a goldfish pond in 65 mins, and 2 hoses can the same pond in 40 mins. find how long it takes the second hose alone to fill the goldfish pond1 solutions Answer 446874 by nerdybill(6951)   on 2013-03-26 17:05:19 (Show Source): You can put this solution on YOUR website! 1 hose can fill a goldfish pond in 65 mins, and 2 hoses can the same pond in 40 mins. find how long it takes the second hose alone to fill the goldfish pond . Let x = time (minutes) it takes for second hose alone then 40(1/65 + 1/x) = 1 multiply both sides by 65x: 40(x + 65) = 65x 40x + 2600 = 65x 2600 = 25x 104 minutes = x
 Travel_Word_Problems/730206: a person travels a distance of 72 km in 4 hours then his average speed is ?1 solutions Answer 446550 by nerdybill(6951)   on 2013-03-25 06:50:08 (Show Source): You can put this solution on YOUR website!divide 72 by 4 to get: 18 km/hr
 Miscellaneous_Word_Problems/730192: The sum of the measures of the angles in any triangle is 180°. Jacqueline has a triangular area in her back yard where she intends to create a garden. If the largest angle is five times the smallest and the middle angle is 20° more than twice the smallest, find the measure of each angle. (It may help to draw the triangle and label each angle.)1 solutions Answer 446549 by nerdybill(6951)   on 2013-03-25 06:47:33 (Show Source): You can put this solution on YOUR website! The sum of the measures of the angles in any triangle is 180°. Jacqueline has a triangular area in her back yard where she intends to create a garden. If the largest angle is five times the smallest and the middle angle is 20° more than twice the smallest, find the measure of each angle. (It may help to draw the triangle and label each angle.) . Let x = measure of smallest angle then 5x = largest angle 2x+20 = middle angle . x + 5x + 2x+20 = 180 8x+20 = 180 8x = 160 x = 20 degrees (smallest angle) . largest angle: 5x = 5(20) = 100 degrees . middle angle: 2x+20 = 2(20)+20 = 40+20 = 60 degrees
Miscellaneous_Word_Problems/730161: A ball is thrown upward from the top of a building. The ball's height above the ground after T seconds is given by the function: h(t) = -16t^2+48t+32.
A. What is the initial height (i.e. the height of the building)?
B. How high did the ball go?
C. When does the ball hit the ground?
1 solutions

Answer 446516 by nerdybill(6951)   on 2013-03-24 23:45:25 (Show Source):
You can put this solution on YOUR website!
A ball is thrown upward from the top of a building. The ball's height above the ground after T seconds is given by the function: h(t) = -16t^2+48t+32.
A. What is the initial height (i.e. the height of the building)?
initial height is when t=0:
h(t) = -16t^2+48t+32
h(0) = -16(0)^2+48(0)+32
h(0) = 32 feet
.
B. How high did the ball go?
vertex is at max:
time, at vertex:
t = -b/(2a)
t = -48/(2(-16))
t = -48/(-32)
t = 3/2
.
Height at t=3/2:
h(3/2) = -16(3/2)^2+48(3/2)+32
h(3/2) = -16(9/4)+24(3)+32
h(3/2) = -4(9)+24(3)+32
h(3/2) = -36+72+32
h(3/2) = 68 feet
.
C. When does the ball hit the ground?
set h(t) to zero and solve for t:
h(t) = -16t^2+48t+32
0 = -16t^2+48t+32
0 = t^2-3t-2
solve by applying the "quadratic formula" to get:
t = {3.56, -0.56}
throw out the negative solution (extraneous) leaving
t = 3.56 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=17 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3.56155281280883, -0.56155281280883. Here's your graph:

 Equations/729980: A lot is in the shape of a right triangle. The shorter leg measures 150m. The hypotenuse is 50m longer than the length of the longer leg. How long is the longer leg?1 solutions Answer 446381 by nerdybill(6951)   on 2013-03-24 17:37:46 (Show Source): You can put this solution on YOUR website! A lot is in the shape of a right triangle. The shorter leg measures 150m. The hypotenuse is 50m longer than the length of the longer leg. How long is the longer leg? Let x = length (m) of longer leg then x+50 = length of hypotenuse . applying Pythagorean theorem: 150^2 + x^2 = (x+50)^2 150^2 + x^2 = (x+50)(x+50) 22500 + x^2 = x^2+100x+2500 22500 = 100x+2500 20000 = 100x 200 m = x (longer leg)
 Polynomials-and-rational-expressions/729870: Please help me to solve this problem it's called division of polynomials(-9x3squared+3x2squared-15x)divided by (-3x)1 solutions Answer 446275 by nerdybill(6951)   on 2013-03-24 11:02:18 (Show Source): You can put this solution on YOUR website!(-9x3squared+3x2squared-15x)divided by (-3x) . . we can "distribute" thus: . . . .
 Distributive-associative-commutative-properties/729843: SOLVE THE PROBLEM L=NE/RT+NR FOR N 1 solutions Answer 446273 by nerdybill(6951)   on 2013-03-24 10:54:09 (Show Source): You can put this solution on YOUR website!L=NE/RT+NR factoring out an 'N' on the right side: L=N(E/RT+R) multiplying both sides by (RT+R): L(RT+R) = NE LR(T+1) = NE dividing both sides by E: LR(T+1)/E = N
 Mixture_Word_Problems/729856: How many quarts of pure antifreeze must be added to 2 quarts of a 10% antifreeze solution to obtain a 40% antifreeze solution? and round to the nearest tenth as needed. My email is golittlediva@yahoo.com1 solutions Answer 446272 by nerdybill(6951)   on 2013-03-24 10:49:33 (Show Source): You can put this solution on YOUR website!How many quarts of pure antifreeze must be added to 2 quarts of a 10% antifreeze solution to obtain a 40% antifreeze solution? and round to the nearest tenth as needed. My email is golittlediva@yahoo.com . Let x = amount (quarts) of pure antifreeze added then x + .10(2) = .40(x+2) x + .20 = .40x+.80 x = .40x+.60 .60x = .60 x = 1.0 quart
 Quadratic_Equations/729822: The diagonal of a rectangle is 1m less than twice the length of one of the sides. The other side is 5m long. What is the diagonal1 solutions Answer 446252 by nerdybill(6951)   on 2013-03-24 04:15:53 (Show Source): You can put this solution on YOUR website! The diagonal of a rectangle is 1m less than twice the length of one of the sides. The other side is 5m long. What is the diagonal . Let d = diagonal then d/2 = length of one side . applying Pythagorean theorem: d^2 = (d/2)^2 + 5^2 d^2 = d^2/4 + 25 4d^2 = d^2 + 100 3d^2 = 100 d^2 = 100/3 d = sqrt(100/3) d = sqrt(100)/sqrt(3) d = 10/sqrt(3) d = 10/sqrt(3) * sqrt(3)/sqrt(3) d = 10sqrt(3)/3 meters
 Percentage-and-ratio-word-problems/729819: Gina has to spend 3/10 of her weekly income on food and board and 1/5 on travel to and from university and 1/8 on text books. What fraction of her income does she spend? If Gina can save one third of her remaining income what fraction of her income does she save? 1 solutions Answer 446251 by nerdybill(6951)   on 2013-03-24 04:10:29 (Show Source): You can put this solution on YOUR website!Gina has to spend 3/10 of her weekly income on food and board and 1/5 on travel to and from university and 1/8 on text books. What fraction of her income does she spend? 3/10 + 1/5 + 1/8 12/40 + 8/40 + 5/40 (12+8+5)/40 25/40 5/8 (answer) . If Gina can save one third of her remaining income what fraction of her income does she save? Amount remaining: 1-5/8 = 3/8 . (1/3)(3/8) 3/24 1/8 (answer)
 Polynomials-and-rational-expressions/729774: Help find the factory y^3-11y^2+28y1 solutions Answer 446249 by nerdybill(6951)   on 2013-03-24 04:00:29 (Show Source): You can put this solution on YOUR website!y^3-11y^2+28y y(y^2-11y+28) y(y-4)(y-7)
 Miscellaneous_Word_Problems/729821: PLEASE, SOMEONE HELP ME !!! Two mortgage companies want to hire you as a consultant. Firm A offers you \$60 plus rate of \$50 per hour. Firm B offers you a flat rate of \$65 per hour. A) Find the "break-even" point - the point where both companies would pay the same amount. B) If you work for 10 hours, which firm would give you the most money? *You "Like" to solve this wrd. problem, and I will "Like" you on your website and Facebook . . Excellent !!! 1 solutions Answer 446248 by nerdybill(6951)   on 2013-03-24 03:54:32 (Show Source): You can put this solution on YOUR website!Two mortgage companies want to hire you as a consultant. Firm A offers you \$60 plus rate of \$50 per hour. Firm B offers you a flat rate of \$65 per hour. . Let x = hours worked then Firm A: 60x+50 Firm B: 65x . A) Find the "break-even" point - the point where both companies would pay the same amount. "break-even" is when they amount earned is the same for either Firm: 60x+50 = 65x 50 = 5x 10 hours = x . B) If you work for 10 hours, which firm would give you the most money? From part A, working 10 hours is the "break-even" point. This is when both firms will pay exactly the same amount. . You could plug it in and verify: Firm A: 60x+50 = 60(10)+50 = 600+50 = \$650 Firm B: 65x 65x = 65(10) = \$650 Answer: both firms will give exactly the same amount
 Rate-of-work-word-problems/729664: It takes Bob 4 hours longer to repair a car than it takes Ken. Working together, they can complete the job in 1.5 hours. How long would each of them take working alone.1 solutions Answer 446160 by nerdybill(6951)   on 2013-03-23 14:02:19 (Show Source): You can put this solution on YOUR website! It takes Bob 4 hours longer to repair a car than it takes Ken. Working together, they can complete the job in 1.5 hours. How long would each of them take working alone. . Let x = time (hours) it takes ken to do job alone then x+4 = time it takes bob . 1.5(1/(x+4) + 1/x) = 1 multiplying both sides by x(x+4): 1.5(x + x+4) = x(x+4) 1.5(2x+4) = x^2+4x 3x+6 = x^2+4x 6 = x^2+x 0 = x^2+x-6 0 = (x+3)(x-2) x = {-3, 2} throw out negative solution (extraneous) leaving: x = 2 hours (Ken) . Bob: x+4 = 2+4 = 6 hours
 Money_Word_Problems/729619: 1)find the break-even point for the firm whose cost function C and revenue function R are given. round the intermediate calculation to nearest integer. C(x)=210x+20,000 ; R(x)=240x1 solutions Answer 446064 by nerdybill(6951)   on 2013-03-23 10:08:15 (Show Source): You can put this solution on YOUR website!1)find the break-even point for the firm whose cost function C and revenue function R are given. round the intermediate calculation to nearest integer. C(x)=210x+20,000 ; R(x)=240x . Breakeven is when C(x) = R(x) 210x+20000 = 240x 20000 = 30x 666.66 = x rounded to nearest integer: 667 = x
 Miscellaneous_Word_Problems/729606: Hi I need help on this question Sasha is planning to put a patio around her new pool which has dimensions of 20m by 30m. she wants the patio to have a uniform width,x,and to surround the entire pool. Her budget is \$6000 and she knows it will cost \$10/m^2 to construct the patio. How wide can she afford for the patio to be?1 solutions Answer 446062 by nerdybill(6951)   on 2013-03-23 10:06:09 (Show Source): You can put this solution on YOUR website! Sasha is planning to put a patio around her new pool which has dimensions of 20m by 30m. she wants the patio to have a uniform width,x,and to surround the entire pool. Her budget is \$6000 and she knows it will cost \$10/m^2 to construct the patio. How wide can she afford for the patio to be? . Let x = width of patio then area of "pool and patio" is: (2x+20)(2x+30) 4x^2+60x+40x+600 . our equation: 10((2x+20)(2x+30)- (20)(30))= 6000 10(4x^2+60x+40x+600 - 600)= 6000 10(4x^2+100x)= 6000 (4x^2+100x)= 600 4x^2+100x-600 = 0 x^2+25x-150 = 0 x^2+25x-150 = 0 (x+30)(x-5) = 0 x = {-30, 5} throw out the negative solution (extraneous) leaving x = 5 m
 Travel_Word_Problems/729590: James left home and travelled towards the moumtains.Lisa left 2.1 hours later travelling 35 km/h faster in an effort to catch him. After 1.2 hours Lisa finally caught up with him.What was James average speed?1 solutions Answer 446044 by nerdybill(6951)   on 2013-03-23 06:42:40 (Show Source): You can put this solution on YOUR website! James left home and travelled towards the moumtains.Lisa left 2.1 hours later travelling 35 km/h faster in an effort to catch him. After 1.2 hours Lisa finally caught up with him.What was James average speed? . Let x = james average speed (km/h) then x+35 = lisa's average speed (km/h) . 1.2 hours = Lisa's driving time 1.2+2.1 = 3.3 hours = James' driving time . our equation 1.2(x+35) = 3.3x 1.2x+42 = 3.3x 42 = 2.1x 42/2.1 = x 20 mph = x
 Rate-of-work-word-problems/729529: Working together, it takes two computers 15 minutes to send out a company’s email. If it takes the slower computer 60 minutes to do the job on its own, how long will it take the faster computer to do the job on its own?1 solutions Answer 446043 by nerdybill(6951)   on 2013-03-23 06:37:24 (Show Source): You can put this solution on YOUR website! Working together, it takes two computers 15 minutes to send out a company’s email. If it takes the slower computer 60 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? . Let x = time (minutes) it takes faster computer to do job alone then 15(1/x + 1/60) = 1 multiplying both sides by 60x: 15(60 + x) = 60x 900 + 15x = 60x 900 = 45x 20 minutes = x
 logarithm/728568: Help me please! I'm stuck on this problem: 3^2x=65611 solutions Answer 445504 by nerdybill(6951)   on 2013-03-20 14:52:15 (Show Source):
 logarithm/728456: log6(x-1)+log6(x+4)=21 solutions Answer 445419 by nerdybill(6951)   on 2013-03-20 09:51:41 (Show Source): You can put this solution on YOUR website!log6(x-1)+log6(x+4)=2 log6(x-1)(x+4)=2 (x-1)(x+4)=6^2 x^2+3x-4=36 x^2+3x-40=0 (x+8)(x-5) = 0 x = {-8,5} throw out the -8 (extraneous) leaving: x = 5
 Mixture_Word_Problems/728460: how many liters of a 30% saline solution must be mixed with a 40% saline solution to obtain 25 liters of a 32% saline solution?1 solutions Answer 445418 by nerdybill(6951)   on 2013-03-20 09:49:20 (Show Source): You can put this solution on YOUR website! how many liters of a 30% saline solution must be mixed with a 40% saline solution to obtain 25 liters of a 32% saline solution? . Let x = amount (liters) of 30% then 25-x = amount (liters) of 40% . .30x + .40(25-x) = .32(25) .30x + 10-.40x = 8 10-.10x = 8 -.10x = -2 x = 20 liters (of 30%) . amount of 40%: 25-x = 25-20 = 5 liters
 Miscellaneous_Word_Problems/728349: A rocket shot into the aire has a height of s= 128t - 16t^2 feet, where t is the number of seconds after the rocket is shot. During what time after the rocket is shot is it atleast 240 feet high??1 solutions Answer 445378 by nerdybill(6951)   on 2013-03-20 00:00:40 (Show Source): You can put this solution on YOUR website! A rocket shot into the aire has a height of s= 128t - 16t^2 feet, where t is the number of seconds after the rocket is shot. During what time after the rocket is shot is it atleast 240 feet high?? . set s to 240 and solve for t: s= 128t - 16t^2 240 = 128t - 16t^2 15 = 8t - t^2 t^2 + 15 = 8t t^2 - 8t + 15 = 0 (t-3)(t-5) = 0 t = {3, 5} answer: the entire time between 3 seconds and 5 seconds
 test/728079: Hugo has \$20 . He spends n dollars. How much does he have left ? 1 solutions Answer 445297 by nerdybill(6951)   on 2013-03-19 15:37:46 (Show Source): You can put this solution on YOUR website! Hugo has \$20 . He spends n dollars. How much does he have left ? . He has 20-n dollars left.
 Rate-of-work-word-problems/728073: craig and jim,working together, can clean the house in 2 hours. Working alone, jim takes twice as long as craig. How long does it take craig to clean the house alone?1 solutions Answer 445293 by nerdybill(6951)   on 2013-03-19 15:10:54 (Show Source): You can put this solution on YOUR website! craig and jim,working together, can clean the house in 2 hours. Working alone, jim takes twice as long as craig. How long does it take craig to clean the house alone? . Let x = time (hours) it takes Craig to clean the house alone then 2x = time (hours) it takes Jim to clean the house alone . The equation: 2(1/x + 1/(2x)) = 1 multiplying both sides by 2x: 2(2 + 1) = 2x 2(3) = 2x 6 = 2x 3 hours = x (Time it takes Craig)