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Polynomials-and-rational-expressions/433594: what does descrates rule of signs tell me about number of real positive zeros and negative real zeros of this function. 5x raised to the 6th-3x raised to the 3rd+x squared-x?
1 solutions
Answer 300579 by robertb(4012)   on 2011-04-09 22:25:45 (Show Source):
You can put this solution on YOUR website!Descartes' rule of signs only gives insight on whether a root is positive or negative, not whether a root is zero.
The polynomial  has a root of 0. Thus apply Descartes' rule only on  . Hence, there might 3 positive roots or 1 positive root. (3 variation of signs.)
Considering  , (replacing x by -x), we see that there are no negative roots. (No variation of signs.)
Hence the original polynomial have 0 as a root, 3 positive roots, and 2 complex roots,
OR
have 0 as a root, 1 positive root, and 4 complex roots.
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Inequalities/433306: Prove the following inequality. Then state for which values the LHS equals the RHS.
Please show and explain (in simple terms) every step in the solution.
a^2 + b^2 >= 2 (a-b-1)
Thank you.
1 solutions
Answer 300360 by robertb(4012) on 2011-04-08 21:04:55 (Show Source):
You can put this solution on YOUR website!I begin with a generally true statement, which is
<==> 
<==> 
<==>  .
Equality holds only if a = 1 and b = -1. (This is obvious if you look at the first inequality in this proof.)
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logarithm/433014: Find the domain of f and write it in set builder or interval notation.
f(x) = log(4 - √(2-x))
1 solutions
Answer 300134 by robertb(4012) on 2011-04-08 07:52:26 (Show Source):
You can put this solution on YOUR website!First we must have  .
<==>  after squaring both sides.
<==>  .
Intersect this with  , or  , to get the interval
(-14, 2]. This is the domain.
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Probability-and-statistics/432856: Assume the probability of a girl being born is the same as the probability of a boy being born. In a family of four children, find the probability of two boys and two girls.
1 solutions
Answer 300125 by robertb(4012) on 2011-04-08 07:28:26 (Show Source):
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test/432964: Show that x^4 +(plus) 4 is prime only for one value of x,where x belongs to set of natural no.s
1 solutions
Answer 300120 by robertb(4012) on 2011-04-08 07:17:52 (Show Source):
You can put this solution on YOUR website!
For all natural numbers  , each of the two factors above is a positive integer greater than 1, hence the number itself is composite. If x = 1, the number itself is  , which is prime. The solution is complete.
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Travel_Word_Problems/432926: Ms. Driva Reck drove from her home to a service station at 48 km/h. She returned home by bicycle at 16 km/h. The entire trip took 4 hours. How far was the service station from Ms. Reck's home?
1 solutions
Answer 300116 by robertb(4012) on 2011-04-08 06:42:38 (Show Source):
You can put this solution on YOUR website!From the formula D = RT, we get T = D/R, so that
letting x = distance from her home to the service station, we get
x = 48 kilometers.
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test/432963: The positive integers p,q & r are all prime no.s if p^2-q^2=r,then find all posible values of r?
1 solutions
Answer 300115 by robertb(4012) on 2011-04-08 06:37:05 (Show Source):
You can put this solution on YOUR website! , where p,q, and r are all prime.
Now p and q cannot both be odd primes at the same time, because by then p-q and p+q will both be even, and their product will be even, not prime. (Neither can we assume that p = q = 2. why?)
Hence we can assume that q is equal to 2 (the only even prime), whence
==> p - 2 = 1 and p + 2 = r ==> p = 3 and r = 5.
OR
==> p - 2 = r and p + 2 = 1 ==> p = -1, which is not acceptable.
Thus, the only possible value of r is 5.
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Probability-and-statistics/433000: A national survery showed that 65% of kids hate veies. If 3 kids are chosen from random, what is the probability that all 3 will hate veggies? write as a percent to the nearest tenth
1 solutions
Answer 300111 by robertb(4012) on 2011-04-08 05:58:33 (Show Source):
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Triangles/432942: Find the length of the altitude to the hypotenuse of a right triangle whose sides have lengths 7, 24, and 25
1 solutions
Answer 300082 by robertb(4012) on 2011-04-07 22:59:34 (Show Source):
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Geometry_Word_Problems/432898: a wheel of one car has a diameter of 20 in, the wheel of another car has a diameter of 24 in. About how many more revolution must the smaller wheel make than the larger wheel to travel 100ft?
1 solutions
Answer 300080 by robertb(4012) on 2011-04-07 22:50:21 (Show Source):
You can put this solution on YOUR website!The circumference of the bigger wheel =  feet.
The circumference of the smaller wheel =  feet.
==> Revolutions of larger wheel in 100 ft =  revolutions.
==> Revolutions of smaller wheel in 100 ft =  revolutions.
==> the smaller wheel makes  more revolutions than the larger wheel to travel 100ft.
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Probability-and-statistics/432909: Ten lines in the table contain 400 digits. The count of 0's in these lines is approximately Normal with
a.) mean 40 and standard deviation 36.
b.) mean 40 and standard deviation 6.
c.) mean 36 and standard deviation 6.
1 solutions
Answer 300077 by robertb(4012) on 2011-04-07 22:36:24 (Show Source):
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test/432927: What's the answer, exact value of cot[sin^(-1) (-1/2)] ? I did it but want to make sure I got the right answer! Thanks!
1 solutions
Answer 300076 by robertb(4012) on 2011-04-07 22:30:56 (Show Source):
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logarithm/432348: Is this solvable?
log of 9 to the base of x equals log of 6 to the base of x
1 solutions
Answer 299788 by robertb(4012) on 2011-04-06 23:01:33 (Show Source):
You can put this solution on YOUR website!Assuming  and  , (the parameters for the logarithmic base), the expression  is one-to-one, and so by property of inverses,
 <==>  , or 9=6, which is false. Hence the equation has no real solution.
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