Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'richard1234'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399, >>Next

 Geometry_proofs/431819: Prove nCr = n/(n-r) * n-1Cr using an analytic and combinatoial proof1 solutions Answer 299569 by richard1234(5390)   on 2011-04-05 23:06:03 (Show Source): You can put this solution on YOUR website!The right hand side is equal to Since , and the right hand side is equal to , same as the left hand side.
 Equations/431771: Can you please explain how you would work this problem out I just don't understand the whol please excuse my dear aunt sally, but since multiplication goes before division why is it that on this equation you will have to divide before you do your multiplication. Im so confused....please help me understand this.... 35(41-33)÷8-11+17 1 solutions Answer 299568 by richard1234(5390)   on 2011-04-05 23:03:28 (Show Source): You can put this solution on YOUR website!Actually you have to multiply first before dividing: 35(41 - 33) ÷ 8 - 11 + 17 35(8) ÷ 8 - 11 + 17 35 - 11 + 17 = 41 Multiplying and dividing typically take equal precedence over each other, and in such a case you would simply go from left to right (I checked WolframAlpha for its answer, it seemed as if it divided first, but both WolframAlpha and I got 41. This is mainly because the order of these operations usually doesn't matter, i.e. ).
 Complex_Numbers/431787: If i=the square root of _1, what is then 4i(6i)= SHOW ME THE STEPS SO THAT I CAN DO THE OTHERS BY MY SELF1 solutions Answer 299566 by richard1234(5390)   on 2011-04-05 22:57:07 (Show Source):
 Square-cubic-other-roots/431789: I can't find this answer anywhere please help what is the inverse of raising a quantity to a power?1 solutions Answer 299560 by richard1234(5390)   on 2011-04-05 22:41:48 (Show Source): You can put this solution on YOUR website!The inverse of taking a quantity to the nth power is taking the nth root of that quantity.
 Geometry_proofs/431252: I am having trouble with this proof If given a line segment like ab Construct a perpendicular line (i can do) Prove that the line is perpendicular (i can't figure out) I need a proof for a perpendicular bisector of a line. Thank you!! Mary1 solutions Answer 299535 by richard1234(5390)   on 2011-04-05 21:01:10 (Show Source): You can put this solution on YOUR website!Two perpendicular lines simply mean that one line is perpendicular to the other.
 Complex_Numbers/431744: Can you please tell me the answer to 5i to the fourth power? I think it is 625. My thought is, if "i" is involved, and a number is to an even power, then it is a positive number. If it is to an odd power, then it is a negative number.1 solutions Answer 299533 by richard1234(5390)   on 2011-04-05 20:58:18 (Show Source): You can put this solution on YOUR website!It is 625. But i to an even power is not always positive, and i to an odd number is always imaginary. Basically, and so on.
 sets-and-operations/431739: Given these sets: A = {3, 4, 5, 6, 7} B = {6, 7, 8, 9} C = {2, 4, 6, 8} List the elements of this set C ∩ (AUB) Do not skip to the answer. Show your work1 solutions Answer 299522 by richard1234(5390)   on 2011-04-05 20:43:22 (Show Source): You can put this solution on YOUR website!A U B = {3, 4, 5, 6, 7, 8, 9} (simply take all elements in either A or B) C ∩ (A U B) = {4, 6, 8} (these are the elements in both C and A U B)
 Complex_Numbers/431413: Why does ei*pi+1=0 other than the fact that my calculator says so, and so I believe it?1 solutions Answer 299519 by richard1234(5390)   on 2011-04-05 20:41:07 (Show Source): You can put this solution on YOUR website!Apparently it seems like the other tutor taught you this...:) From Euler's formula, . By substituting you will obtain , . Euler's formula itself is derived using the Maclaurin series for , namely (you will learn this sometime in calculus).
 Trigonometry-basics/431693: how do you solve this help show me please so i can understand 1 solutions Answer 299513 by richard1234(5390)   on 2011-04-05 20:35:28 (Show Source): You can put this solution on YOUR website!"how do you solve this help show me please so i can understand" What is "this?"
 absolute-value/431711: how do you find the absolute value when it is on a number line ?1 solutions Answer 299512 by richard1234(5390)   on 2011-04-05 20:33:58 (Show Source): You can put this solution on YOUR website!The absolute value is the positive distance between that number and zero.
 Word_Problems_With_Coins/152564: how many ways to make change for one dollar using nickels, dimes and quarters1 solutions Answer 299461 by richard1234(5390)   on 2011-04-05 16:12:32 (Show Source): You can put this solution on YOUR website!You can compute the number of ways to make change for \$1 using a bijection. We let n, d, q be the number of nickels, dimes, and quarters, and , which implies . Hence, this is equivalent to finding the number of ways to make 20 "cents" using one-, two-, and five-cent pieces. Suppose we want to find the number of ways to make 20 cents *without* using a five cent piece. Case 0: We wish to make 0 cents --> 1 way (just use no coins) Case 1: We wish to make 1 cent --> 1 way 2*0 + 1*1 Case 2: We wish to make 2 cents --> 2 ways 2*1 + 1*0; 2*0 + 1*2 Case 3: We wish to make 3 cents --> 2 ways 2*1 + 1*1; 2*0 + 1*3 Case 4: We wish to make 4 cents --> 3 ways 2*2 + 1*0; 2*1 + 1*2, 2*0 + 1*4 Case 5: We wish to make 5 cents --> 3 ways 2*2 + 1*1, 2*1 + 1*3, 2*0 + 1*5 We can prove using either induction or modular arithmetic that the number of ways to make n cents in this way is , where denotes the floor value of x. We can evaluate this at n = 20 to get , or 11. Similarly, we can count the number of ways to obtain 20 cents using one five-cent piece. However, we can subtract off the five-cent piece and say that this is analogous to computing the number of ways to obtain 15 cents. Hence, this is equal to . For 10, 5, and 0 cents, we have , and . Therefore the total number of ways is 11 + 8 + 6 + 3 + 1 = 29 ways. Note: the other tutor counted 293 ways, however this included pennies and half dollars, which was not stated in the question. To count the number of ways using pennies, nickels, dimes, and quarters, you can also use a bijection, but instead of counting the number of ways to obtain 20 cents, you evaluate at 20, 19, 18, ..., 0 since this will uniquely determine the number of pennies. We do the same with 15, 10, 5, and 0 to obtain sums: Then, if you want half dollars involved, it is equal to where is the number of ways to make a dollar using i half dollars, equivalently, the number of ways to make 50 cents and 0 cents without half dollars (here you should get 293!).
 Volume/431466: what does it mean to say that an object has a volume of 6 cubic inches?1 solutions Answer 299460 by richard1234(5390)   on 2011-04-05 15:45:39 (Show Source): You can put this solution on YOUR website!It can hold six cubic inches of something, say water. One cubic inch is the volume of water in a 1" x 1" x 1" container.
 Trigonometry-basics/431469: Derive the half angle formula for sin( u/2 ) by following the steps below. (a) Use the sum angle formula to write cos(2x) in terms of powers of sin(x) and cos(x) . (b) Use a trig identity to rewrite cos(2x) in terms of just powers of sin(x): (c) Solve the formula in part (b) in terms of sin(x), and not a power of sin(x). (d) Substitute x = u/2 into the formula in part (c).1 solutions Answer 299459 by richard1234(5390)   on 2011-04-05 15:43:05 (Show Source): You can put this solution on YOUR website! Replacing x with u/2, (however you must be careful what quadrant u and u/2 are in, because it could be positive or negative).
 Linear-equations/431524: Why should we clear fractions when solving linear equations and inequalities? Can you give me an example? Why should we clear decimals when solving linear equations and inequalities? Can you give me an example.1 solutions Answer 299456 by richard1234(5390)   on 2011-04-05 15:36:48 (Show Source): You can put this solution on YOUR website!If you're given an equation or inequality such as , it helps to clear the fraction or decimal since we are trying to find the value of , not .
 Inequalities/431528: Why does the inequality sign change when both sides are multiplied or divided by a negative number? 1 solutions Answer 299455 by richard1234(5390)   on 2011-04-05 15:34:38 (Show Source): You can put this solution on YOUR website!Suppose , and . From we obtain . We can subtract from both sides to get --> --> . Finally, we can scale both sides by the same positive number to get .
 Expressions-with-variables/431476: Use the commutative law of addition to write an equivalent expression. f + 6g 1 solutions Answer 299454 by richard1234(5390)   on 2011-04-05 15:30:35 (Show Source): You can put this solution on YOUR website!6g + f
 test/431296: whar is the probability that a ramdomly selected day in january is after the 20th?1 solutions Answer 299376 by richard1234(5390)   on 2011-04-05 00:11:18 (Show Source): You can put this solution on YOUR website!Out of the days {21, 22, ..., 31} there are 11 days (inclusive). Therefore the probability is 11/31.
 Equations/431282: Find the quadratic equation with integral coefficients having the given roots. 4 + 2i, 4 - 2i Thanks!!1 solutions Answer 299375 by richard1234(5390)   on 2011-04-05 00:10:20 (Show Source): You can put this solution on YOUR website!The quadratic will have and as factors. Hence, the quadratic is equal to (applying the difference of two squares) Expanding and simplifying, this is equal to .
 Rectangles/431308: how do you find the area of a rectangular prism? do i multiply the sides or add?1 solutions Answer 299374 by richard1234(5390)   on 2011-04-04 23:43:32 (Show Source): You can put this solution on YOUR website!multiply
 Radicals/431151: I am trying to simplify radical expressions.. It says Assume that the variables are positive. Write "nonreal" if the expression does not represent a real number. The problem is sqrt( 98 ). I know the answer is 7 sqrt ( 2 ) but I am not sure how I got that answer. How do I get from sqrt ( 98 ) to 7 sqrt (2) ? Thanks!1 solutions Answer 299306 by richard1234(5390)   on 2011-04-04 19:17:57 (Show Source): You can put this solution on YOUR website!Factor out the largest square divisor of 98. Since , .
 logarithm/431013: what is the derivative of: 1. y= tanx + 3 2. y= 7x - 5 sinx - secx ????1 solutions Answer 299304 by richard1234(5390)   on 2011-04-04 19:00:53 (Show Source): You can put this solution on YOUR website!Simply apply the basic rules of differentiation, as well as the derivatives of various trigonometric functions: 1. 2.
 testmodule/430948: how many moles of HCl we get for mixing 1 mole of hydrogen and 1000000 moles of chlorine??1 solutions Answer 299303 by richard1234(5390)   on 2011-04-04 18:54:24 (Show Source): You can put this solution on YOUR website!I would suppose you would get 1 mole, since the other 999,999 moles of chlorine would not react.
 Quadratic_Equations/431049: write a quadratic equation that has the solutions of -2 and 51 solutions Answer 299302 by richard1234(5390)   on 2011-04-04 18:43:22 (Show Source): You can put this solution on YOUR website!If -2 and 5 are roots, then x-(-2) and x-5 are factors of the polynomial. We can write the equation in the form C(x+2)(x-5) = 0, where C is some nonzero constant.
 Polynomials-and-rational-expressions/431173: is y to the 3 over 12x a polynomial1 solutions Answer 299301 by richard1234(5390)   on 2011-04-04 18:40:01 (Show Source): You can put this solution on YOUR website! is not a polynomial, because this the exponent of x is negative.
 Trigonometry-basics/431008: how do i evaluate arccos(cos 7pi/2) using the properties of inverse functions?1 solutions Answer 299299 by richard1234(5390)   on 2011-04-04 18:34:33 (Show Source): You can put this solution on YOUR website!Arccosine and cosine are inverses of each other, so would be equal to . However, since the arccosine function restricts the range (since an infinite number of values are obtained), we say that this . Depending on the context of the problem, either answer could be correct, or even some general answer in the form .
 Quadratic_Equations/431169: What is x with x2-2x-13=0? And x2+12x-64=0? I've tried several times to find out what x is but neither of my solutions to these problems seem correct. 1 solutions Answer 299298 by richard1234(5390)   on 2011-04-04 18:31:48 (Show Source): You can put this solution on YOUR website!Use the quadratic formula. The quadratic formula says that the roots of any quadratic equation in the form (with a,b,c real) are . From here, it's just simply identifying what a,b,c are and then substitution.
 Matrices-and-determiminant/431116: The vertices of a triangle are given below. Use a determinant and the vertices of the triangle to find the area of the triangle. (-3,-7.5), (-1.5,6.5), (1.5,-5.5) ** By the way: I know that the answer is 30, I just don't understand how to get the answer. Thank you1 solutions Answer 299297 by richard1234(5390)   on 2011-04-04 18:21:54 (Show Source): You can put this solution on YOUR website!We have where A = | -3 -7.5 1 | | -1.5 6.5 1 | | 1.5 -5.5 1 | (3x3 matrix) Here, , Therefore, the area is equal to 1/2 of 60, or 30.
 Linear-equations/431130: y+4x=9 and x= y-4 I need to graph these on the computer any ideas ?1 solutions Answer 299295 by richard1234(5390)   on 2011-04-04 18:07:02 (Show Source): You can put this solution on YOUR website!You could go to WolframAlpha (www.wolframalpha.com) and provide your graphs there.
 Evaluation_Word_Problems/431141: A restaurant is open from 2 pm to 2 am on Saturday and a maximum of 80 people are allowed inside. If f(t) is the number of people in the restaurant t hours after 2 pm on Saturday, what is a reasonable domain and range for y=f(t)? Domain= range=1 solutions Answer 299294 by richard1234(5390)   on 2011-04-04 18:05:12 (Show Source): You can put this solution on YOUR website!The restaurant is open up to 12 hours after the opening, so it is reasonable to say . Also, between 0 and 80 people are allowed, so .
 Trigonometry-basics/430780: Please any answer is appreciated for the following: Prove that cos[3*pi/2 + x] = sinx THank You1 solutions Answer 299110 by richard1234(5390)   on 2011-04-03 21:27:47 (Show Source): You can put this solution on YOUR website!Using the addition formula for cosine: Since and , = .
 Triangles/430574: Is a triangle with side lengths of 3,4, and 5 and another triangle with side lengths of 6, 8, and 11 a counterexample of two similar right triangles?1 solutions Answer 299105 by richard1234(5390)   on 2011-04-03 21:19:44 (Show Source): You can put this solution on YOUR website!No, because a triangle with sides 6,8,11 is not a valid counterexample (it is not a right triangle).