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# Recent problems solved by 'robertb'

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 Triangles/456884: The sides of a length of a triangle are x, x+4, and 20, where 20 is the longest side. For which range of values is x an acute triangle1 solutions Answer 313550 by robertb(4012)   on 2011-06-02 22:12:03 (Show Source): You can put this solution on YOUR website!For the triangle to be acute, , where c is the longest side of the triangle. Note that it is given that the longest side has length 20. Hence, we must have , or , after simplifying, , or (x+16)(x - 12) >0. Since x must have positive values only, x > 12. From the triangle inequality, we get the relation x +(x+4) > 20, or x > 8. Also, since 20 is the longest side, we must have x + 4 < 20, or x < 16. Hence from the initial conditions, we must have 8 < x < 16. Intersect the preceding interval with the interval x > 12. Therefore, for the triangle to be acute, we must have 12 < x < 16.
 Travel_Word_Problems/456921: How many feet would be covered at 245.36mph in .351 seconds?1 solutions Answer 313539 by robertb(4012)   on 2011-06-02 21:49:45 (Show Source): You can put this solution on YOUR website! = 126.311 feet.
 Probability-and-statistics/456914: what percentage of the area of the standard normal distribution is between z = -2.00 and z = +2.00? How do you know this?1 solutions Answer 313532 by robertb(4012)   on 2011-06-02 21:33:05 (Show Source): You can put this solution on YOUR website!95%. This is based on the empirical, or 68-95-99.7, rule for normal distributions.
 Surface-area/456855: The area of a regualr Octogon is 50 Cm2. How do you find the area of a regular octogon with sides 3 times as large?1 solutions Answer 313510 by robertb(4012)   on 2011-06-02 20:33:53 (Show Source): You can put this solution on YOUR website! ==> ==> ==> , the area of the bigger octagon.
 Probability-and-statistics/456894: What is the variance of the following data? 600, 470, 170, 430, 3001 solutions Answer 313504 by robertb(4012)   on 2011-06-02 20:27:56 (Show Source): You can put this solution on YOUR website! ==>
 logarithm/456887: log4 4^(2/3)=?1 solutions Answer 313502 by robertb(4012)   on 2011-06-02 20:20:48 (Show Source):
 Sequences-and-series/456892: How to you find the fourth term of an arithmetic series, given a1 = 20 and the sum (S subroot 10) = 335?1 solutions Answer 313501 by robertb(4012)   on 2011-06-02 20:20:00 (Show Source): You can put this solution on YOUR website! ==> ==> 335 = 5(40 + 9d) ==> 67 = 40 + 9d ==> 27 = 9d ==> d = 3. ==>
 Quadratic-relations-and-conic-sections/456555: find the equation of a parabola with the focus (-1,-4) and directrix y=-31 solutions Answer 313334 by robertb(4012)   on 2011-06-02 01:00:58 (Show Source): You can put this solution on YOUR website!The equation of the parabola has the form From the given, the x-coordinate of the vertex must be -1. The y-coordinate must be midway between y = -3 and y = -4. Hence, k = -7/2. Also, a = -4 - (-7/2) = -1/2, the directed distance from the focus to the vertex. ==> , or
 Quadratic-relations-and-conic-sections/456554: find the equation of a parabola with vertex (-3,1) and directrix y=21 solutions Answer 313333 by robertb(4012)   on 2011-06-02 00:54:51 (Show Source): You can put this solution on YOUR website!The form of the equation is , where (h,k) is the vertex. ==> a = directed distance from the focus to the vertex (which in absolute value is equal to the distance between the vertex and the directrix.) Hence a = -1, and therefore, the equation is .
 Polynomials-and-rational-expressions/456589: i need to factor this out the problem is 6a^2+7a-3 and im just getting stuck1 solutions Answer 313329 by robertb(4012)   on 2011-06-02 00:45:30 (Show Source):
 Functions/456582: Find dy/dx of y = (x^3 - 2x)^(ln x) using the method of logarithmic differentiation1 solutions Answer 313326 by robertb(4012)   on 2011-06-02 00:32:57 (Show Source): You can put this solution on YOUR website! ==> ==> , after applying the product rule. ==>
 Quadratic-relations-and-conic-sections/456562: Identify conic section x^2+25y^2=251 solutions Answer 313316 by robertb(4012)   on 2011-06-01 23:50:26 (Show Source): You can put this solution on YOUR website!An ellipse.
 Surface-area/456153: what is the lateral surface area of a right prism the perimeter of whose base is 34cm and whose height is 8cm?1 solutions Answer 313113 by robertb(4012)   on 2011-06-01 02:38:17 (Show Source): You can put this solution on YOUR website!34 cm x 8 cm = 272 square cm.
 Travel_Word_Problems/456143: a man goes to a place at the rate of 4kmph.he comes back on a bicycle at 16kmph.his average speed for the entire journey. 1 solutions Answer 313112 by robertb(4012)   on 2011-06-01 02:34:25 (Show Source): You can put this solution on YOUR website!Find the harmonic mean of the two rates: kmph.
 Matrices-and-determiminant/456150: find ab if, A=7 3 1 4 2 5 b=6 -3 0 -4 2 -11 solutions Answer 313111 by robertb(4012)   on 2011-06-01 02:28:49 (Show Source):
 Permutations/456128: A poker hand consists of five cards from a standard deck of 52. How many poker hands are there that don't have any spades in them?1 solutions Answer 313110 by robertb(4012)   on 2011-06-01 02:23:44 (Show Source): You can put this solution on YOUR website!39C5 = 575,757 poker hands.
 Probability-and-statistics/456123: a set of 12 cards is numbered 1,2,3...,12. suppose you pick a card at random without looking . find the probability of each event. P (a multiple of 3) P(a multiple of 4) P(an even number)1 solutions Answer 313109 by robertb(4012)   on 2011-06-01 02:17:25 (Show Source): You can put this solution on YOUR website!P(a multiple of 3) = 4/12 = 1/3. P(a multiple of 4) = 3/12 = 1/4. P(an even number) = 6/12 = 1/2.
 Money_Word_Problems/455441: Find the equation of the circle with C(-4,2) an is the tangent to the linne 3x+4y-16=01 solutions Answer 313107 by robertb(4012)   on 2011-06-01 01:48:41 (Show Source): You can put this solution on YOUR website!The distance of the center (-4,2) from the line 3x + 4y - 16 = 0 can be found from the formula . This distance becomes the radius of the circle. Hence the radius of the circle is . Therefore the equation of the circle is .
 Evaluation_Word_Problems/455359: The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the z-Score for a student who finishes the test in 45 minutes?1 solutions Answer 313105 by robertb(4012)   on 2011-06-01 01:37:00 (Show Source):
 expressions/456138: Obtain the general solution dr = b(cosx dr + rsinx dx) ANSWER: r= c(1 - bcosx)1 solutions Answer 313104 by robertb(4012)   on 2011-06-01 01:32:38 (Show Source): You can put this solution on YOUR website!dr = b(cosx dr + rsinx dx) <==> <==> <==> ==> ln r = ln(1 - bcosx) + k, k an arbitrary constant. <==> r = C(1 - bcosx), after raising e to both sides of the previous equation. (C an arbitrary constant.)
 Functions/456140: Will you assist me in answering this question. State the degree of the following polynomial 9x^4y^3+6xy-3y. Iam not sure where to begin or how to answer. Thank you 1 solutions Answer 313102 by robertb(4012)   on 2011-06-01 01:21:05 (Show Source): You can put this solution on YOUR website!The degree of the polynomial is 4+3 = 7 (which is the degree of the term ). (The degree of 6xy is 1+1 = 2, while -3y is 1.)
 expressions/456139: Obtain the general solution y lnx lny dx + dy = 01 solutions Answer 313101 by robertb(4012)   on 2011-06-01 01:18:51 (Show Source): You can put this solution on YOUR website!Divide both sides by ylny, to get . <==> Integrate both sides: k an arbitrary constant. After integration by parts (on the first integral), the equation becomes xlnx - x + ln(lny) = k. Simplifying: <==> <==> <==> <==> , where C is an arbitrary constant.
 Exponents-negative-and-fractional/455835: what is the simplified answer to this expression? (x^-2)^41 solutions Answer 313099 by robertb(4012)   on 2011-06-01 01:08:47 (Show Source):
 Expressions-with-variables/455759: if x+y=a and xy=b then the value of ?THANK YOU VERY MUCH.1 solutions Answer 312885 by robertb(4012)   on 2011-05-31 03:40:00 (Show Source): You can put this solution on YOUR website! Now . Also, ==> ==> ==>
 Linear_Algebra/455730: Let v1 and v2 be non zero vectors in a vector space V. Show that the following statements are equivalent. a) v1 is not in Rv2=span{v2} b)Rv1 doesn't equals Rv21 solutions Answer 312878 by robertb(4012)   on 2011-05-31 00:58:15 (Show Source): You can put this solution on YOUR website!(a)==>(b): not in ==> for any non-zero real number k. ==> For any non-zero real number m, , and hence no element of span{v1} can be found in span{v2}. (b) ==> (a): ==> there is element in that is not in , or , for any non-zero real number r, or . Hence v1 is not in span{v2}.
 Linear_Algebra/455735: If V={v1,v2,...,vk} is linearly independent, and w is not element of V. Then show that {v1+w,v2+w,...,vk+w} is linearly independent1 solutions Answer 312877 by robertb(4012)   on 2011-05-31 00:38:54 (Show Source): You can put this solution on YOUR website!Let +...+. Now let +...+ = , which for the purpose of contradiction, we assume that not all the a's are 0, (i.e., the set is linearly DEPENDENT). ==> (+...+)* +(+...+)* + ...+(+...+)* = By the hypothesis, {v1, v2, v3,..., vk } is linearly independent, and thus, +...+ +...+ ................................... +...+. We get a homogeneous system of equations. Adding all corresponding sides of the system, we get +...+ OR, +...+. Subtracting this equation from each one of the equations in the system above, we obtain =...=, CONTRARY to the initial assumption that not all a's are 0. Hence {v1+w,v2+w,...,vk+w} must be linearly independent.
 Sequences-and-series/455731: find the 11th term of (b-3)^121 solutions Answer 312874 by robertb(4012)   on 2011-05-31 00:18:21 (Show Source): You can put this solution on YOUR website!13th term --> 12th term --> 11th term -->
 Conjunction/455733: Form the contrapositive: If I do not mow the lawn, the grass grows too tall1 solutions Answer 312873 by robertb(4012)   on 2011-05-31 00:14:25 (Show Source): You can put this solution on YOUR website!If the grass is short, then you have mowed the lawn.
 Complex_Numbers/455727: Compute the special products and write your answer in a+bi form. (-2+5i)^2 I know I should foil this but I am doing something wrong. Could you help me here showing all steps please. David 1 solutions Answer 312872 by robertb(4012)   on 2011-05-31 00:09:59 (Show Source):
 Probability-and-statistics/455623: Is the following a valid probability distribution? x P(X=x) -1 -0.1 0 0.5 1 0.61 solutions Answer 312854 by robertb(4012)   on 2011-05-30 21:55:02 (Show Source): You can put this solution on YOUR website!No, it's not a valid probability distribution. (There's no such thing as a negative probability.)
 logarithm/455693: solve log(x+20)-log(x+2)=logx1 solutions Answer 312847 by robertb(4012)   on 2011-05-30 21:41:45 (Show Source): You can put this solution on YOUR website! ==> ==> ==> ==> ==> 0 = (x +5)(x - 4) ==> x = -5, 4. -5 does not satisfy the original equation. Hence the final answer is x = 4.