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# Recent problems solved by 'Alan3354'

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 Graphs/250648: How do i graph the equation y=-tan 2x+11 solutions Answer 184804 by Alan3354(30993)   on 2009-12-30 18:17:21 (Show Source): You can put this solution on YOUR website!How do i graph the equation y=-tan 2x+1 ---------------------- The same as any other function. You pick values of x and find y, then plot the points. You can use Excel to generate the points, and to make a graph. A better way is to dl the FREE software from http://www.padowan.dk.com and do it there.
 Complex_Numbers/252737: 9) the expression i to the 25 power is eqivalen to? a) -i b)1 c)i d)-1 10) What does the expression i to 100th power + i to the 101 power + i to the 102 power equal? a) 1 b)i c)-i d)-1 11) What is the sum of 5-3i and the conjugate of 3+2i? 12) The expression 3i(2isquared-5i) is eqivalent to? a)15-5i b)-15-5i c)8+5i d)2-5i 1 solutions Answer 184803 by Alan3354(30993)   on 2009-12-30 18:10:05 (Show Source): You can put this solution on YOUR website!9) the expression i to the 25 power is eqivalen to? a) -i b)1 c)i d)-1 The powers of i are cyclic mod 4, meaning there are 4 possibilities. exp...value 1....i 2....-1 3....-i 4....+1 Then it repeats. For the 25th power, divide 25 by 4 and get the remainder. That's 25 mod 4, or in Excel, mod(25,4) and the remainder is 1. i^1 = i -------- 10) What does the expression i to 100th power + i to the 101 power + i to the 102 power equal? a) 1 b)i c)-i d)-1 i^100 = 1 1^101 = i i^102 = -1 ---------- Add = i --- 11) What is the sum of 5-3i and the conjugate of 3+2i? The conjugate of 3+2i is 3-2i 5-3i 3-2i ----- Add 8-5i -------------- 12) The expression 3i(2isquared-5i) is eqivalent to? a)15-5i b)-15-5i c)8+5i d)2-5i 3i*(2i^2 - 5i) = 3i*(-2 - 5i) = -6i - 15i^2 = -6i - 15*(-1) = 15 - 6i
 Linear-equations/252734: find the slope of the line that passes through the given points. Ok are book a little messed up. we are learning about SLopes in Algebra andGeometry A(5,8) B(7,11) E(-1,-2), F(-6,-4) if you could please help me. I need a lot of help. 1 solutions Answer 184798 by Alan3354(30993)   on 2009-12-30 17:59:43 (Show Source): You can put this solution on YOUR website!find the slope of the line that passes through the given points. Ok are book a little messed up. we are learning about SLopes in Algebra andGeometry Slope = diff of y/diff of x. Slope is also the rise over the run. For example, a ramp at a loading dock has a slope of the vertical change divided by its horizontal length. ------------------------------ Usually m is used for slope. ---------------- A(5,8) B(7,11) m = (11-8)/(7-5) m = 3/2 ------------------------- E(-1,-2), F(-6,-4) m = (-2 - (-4))/(-1 - (-6)) = (-2 + 4)/(-1 + 6) m = 2/5 ------------- It makes no difference which point is 1st or 2nd as long as you use the same order for x and y.
 Radicals/252735: What is the Pythagorean theorem? How is it used? 1 solutions Answer 184797 by Alan3354(30993)   on 2009-12-30 17:55:49 (Show Source): You can put this solution on YOUR website!try google
 Triangles/252698: How do you figure the sides of an Isosceles Triangle with a perimeter of 2 1/4"1 solutions Answer 184730 by Alan3354(30993)   on 2009-12-30 11:12:13 (Show Source): You can put this solution on YOUR website!How do you figure the sides of an Isosceles Triangle with a perimeter of 2 1/4" ------------------- You need to know at least one angle, or one of the sides. Just the perimeter is not sufficient info for an isosceles triangle.
 Trigonometry-basics/252655: Find the area of the triangle ABC if a=40ft, b=25ft and c=30degrees.1 solutions Answer 184729 by Alan3354(30993)   on 2009-12-30 11:05:26 (Show Source): You can put this solution on YOUR website!Find the area of the triangle ABC if a=40ft, b=25ft and c=30degrees. ------------------ Area = bh/2 h = 40*sin(30) if side b is taken to be the base h = 20 Area = 25*25/2 = 250 sq units ----------------------------- If you take the other side to be the base, the results are the same.
 Percentage-and-ratio-word-problems/252694: The ratio of boys to girls in a class is 11 to 7. The difference between the number of boys and girls is 12. How many students are in the class?1 solutions Answer 184720 by Alan3354(30993)   on 2009-12-30 10:23:06 (Show Source): You can put this solution on YOUR website!The ratio of boys to girls in a class is 11 to 7. The difference between the number of boys and girls is 12. How many students are in the class? ----------------- b - g = 12 --> b = g + 12 11:b::7:g 11g = 7b 11g = 7(g+12) 11g = 7g+84 g = 21 b = 33 Total = 54
 decimal-numbers/252677: 0 -5 -5 3 -4 (x ) (x y )1 solutions Answer 184718 by Alan3354(30993)   on 2009-12-30 10:16:46 (Show Source): You can put this solution on YOUR website!It's not clear what you want, or what this is about.
 Miscellaneous_Word_Problems/252696: A soup filling machine rejects cans of soup if they are less than 18 ½ ounces or greater than 19 ½ ounces. This machine is programmed to REJECT a can of soup weighing x ounces if: A) | 19 – x | < 19 B) | x – 19 | < 19 C) | 19 – x | < ½ D) | 19 – x | > ½ E) | 19 + x | < 19 1 solutions Answer 184717 by Alan3354(30993)   on 2009-12-30 10:15:04 (Show Source): You can put this solution on YOUR website! A soup filling machine rejects cans of soup if they are less than 18 ½ ounces or greater than 19 ½ ounces. This machine is programmed to REJECT a can of soup weighing x ounces if: A) | 19 – x | < 19 B) | x – 19 | < 19 C) | 19 – x | < ½ D) | 19 – x | > ½ E) | 19 + x | < 19 ------------------- D If the weight is more than 1/2 oz from the "center", 19 ounces.
 Volume/252658: what is the diameter of the tank if the length of tank is 6metre and the capacity of oil that is in the tank weigh 25 tonnes, plz help, thickness of the tank is 6mm1 solutions Answer 184715 by Alan3354(30993)   on 2009-12-30 10:04:53 (Show Source): You can put this solution on YOUR website!what is the diameter of the tank if the length of tank is 6metre and the capacity of oil that is in the tank weigh 25 tonnes, plz help, thickness of the tank is 6mm ----------------- Not enough info. What is the volume of the oil?
 Travel_Word_Problems/252684: a speed boat travels 200km in 2hours 30 minutes.calculate its average speed in kilometers per hour1 solutions Answer 184714 by Alan3354(30993)   on 2009-12-30 10:03:40 (Show Source): You can put this solution on YOUR website!a speed boat travels 200km in 2hours 30 minutes.calculate its average speed in kilometers per hour ------------ 200 km/2.5 hr = 80 km/hr ------------------------ Boats (and planes) use knots for speed, not km/hr. 80 km/hr = ~48 mph = ~42 knots. Not "knots per hour", knots. 1 knot = 1 nautical mile per hour.
 Travel_Word_Problems/252685: a metal block has mass 200g and volume 40cm3(cubed). calculate its density. 1 solutions Answer 184713 by Alan3354(30993)   on 2009-12-30 09:59:28 (Show Source): You can put this solution on YOUR website!a metal block has mass 200g and volume 40cm3(cubed). calculate its density ------------- = 200 gm/40 cc = 5 gm/cc
 Numbers_Word_Problems/252691: the sum of two consecutive odd intergers equals 40?1 solutions Answer 184712 by Alan3354(30993)   on 2009-12-30 09:58:18 (Show Source): You can put this solution on YOUR website!the sum of two consecutive odd intergers equals 40? --------------- Are you sure? You seem to question it. 40/2 = 20. One is above, one below --> 19 and 21. --------------------------------------- You can do it the hard way: n + (n+2) = 40 2n + 2 = 40 2n = 38 n = 19 --> 19 & 21 ------------------- PS They're integers, only one R.
 Exponents/249719: 27 1/3 (EXPONENT) - 125 1/21 solutions Answer 184711 by Alan3354(30993)   on 2009-12-30 09:54:07 (Show Source): You can put this solution on YOUR website!Is 1/3 the exponent? If so, say 27^(1/3). ------------------ What about the 1/2, is that also an exponent? And, do you have a question?
 Exponents/249586: The equation 2^x^2 = = 16 ^2x−3 has two solutions. What is their sum? (A)−2 (B) 0 (C) 2 (D) 6 (E) 8 1 solutions Answer 184710 by Alan3354(30993)   on 2009-12-30 09:37:39 (Show Source): You can put this solution on YOUR website! 2^x^2 = = 16 ^2x−3 -------------- What does that mean? ? It has too many equal signs, too.
 Quadratic_Equations/252662: Write the equation of the quadratic function with roots 0 and 2 and a vertex at (1, 5). 1 solutions Answer 184708 by Alan3354(30993)   on 2009-12-30 09:21:32 (Show Source): You can put this solution on YOUR website!y = x*(x-2) gives the 2 roots, but the vertex is below the x-axis. y = -x*(x-2) inverts it. y = -x^2 + 2x gives the 2 roots, but the vertex is at 1,1. Multiply it by 5: y = -5x^2 + 10x works
 Rate-of-work-word-problems/252648: If Mario can do a piece of work in 3 days and Joey in 2 days, in how many days can they do the same work together?1 solutions Answer 184705 by Alan3354(30993)   on 2009-12-30 08:42:37 (Show Source): You can put this solution on YOUR website!If Mario can do a piece of work in 3 days and Joey in 2 days, in how many days can they do the same work together? -------------------------------- Realistically, about 7 days, since they'll waste time together. Using math, tho: M does 1/3 of the work per day. J does 1/2 of the work per day. Together, 1/3 + 1/2 = 5/6 of the work per day. --> 6/5 days to do the work, or 1.2 days. ----------------------------- Use the shortcut, product/sum 3*2/(3+2) = 6/5
 Miscellaneous_Word_Problems/252683: If x^2 + y^2 = 2xy, then x must equal ? A) –1 B) 0 C) 1 D) –y E) y1 solutions Answer 184699 by Alan3354(30993)   on 2009-12-30 08:13:41 (Show Source): You can put this solution on YOUR website!If x^2 + y^2 = 2xy, then x must equal ? A) –1 B) 0 C) 1 D) –y E) y ------------------------- x^2 - 2xy + y^2 = 0 (x-y)^2 = 0 x = y
 Graphs/249566: Graph F=(9/5)C+32 (F on Y-axis, C on x-axis) What is the slope? What is the y-intercept? What is the x-intercept?1 solutions Answer 184676 by Alan3354(30993)   on 2009-12-29 22:04:55 (Show Source): You can put this solution on YOUR website!--> y = (9/5)x + 32 --------------------- Slope = 9/5 y-intercept = 32 (0ºC = 32ºF) x-intercept = -160/9 (0ºF =~ -17.8ºC)
 Travel_Word_Problems/250795: How far does a boat travel in 3 hours at 65 miles per hour? 1 solutions Answer 184644 by Alan3354(30993)   on 2009-12-29 19:28:54 (Show Source): You can put this solution on YOUR website!3 hours * 65 miles/hour = 195 miles For a boat, a fish, an airplane or anything else.
 Linear-equations/250798: In a new company, after three months of employement, you earn 2 days of sick leave, and after 9 months, you earn 6 days1 solutions Answer 184571 by Alan3354(30993)   on 2009-12-29 14:47:41 (Show Source): You can put this solution on YOUR website!That's good to know. Do you have a question?
 Quadratic_Equations/252575: Which of the following quadratic equations has solutions x=6a and x=-3b? A. x^2 - 18ab=0 B. x^2 - x(3b-6a)-18ab=0 C. x^2 - x(3b+6a) +18ab= 0 D. x^2 + x(3b-6a)- 18ab=0 E. x^2 + x(3b+6a) + 18ab=0 1 solutions Answer 184569 by Alan3354(30993)   on 2009-12-29 14:40:33 (Show Source): You can put this solution on YOUR website!Which of the following quadratic equations has solutions x=6a and x=-3b? A. x^2 - 18ab=0 B. x^2 - x(3b-6a)-18ab=0 C. x^2 - x(3b+6a) +18ab= 0 D. x^2 + x(3b-6a)- 18ab=0 E. x^2 + x(3b+6a) + 18ab=0 --------------------- Multiply it and see. (x-6a)*(x+3b) = x^2 + x(6a-3b) - 18ab it's B
 Quadratic_Equations/252536: How many different values of n are there such that n is a natural number and n^2 - 20 is a perfect square? (a) 1 (b) 2 (c) 3 (d) 4 (e) infinitely many1 solutions Answer 184531 by Alan3354(30993)   on 2009-12-29 11:17:22 (Show Source): You can put this solution on YOUR website!How many different values of n are there such that n is a natural number and n^2 - 20 is a perfect square? (a) 1 (b) 2 (c) 3 (d) 4 (e) infinitely many There are 2, +6 and -6. ------------------------ a^2 - b^2 = 20 (a-b)*(a+b) = 20 This is one eqn in two variables, but restricted to integers. 20 = 1*20, 2*10 or 4*5 1 and 20 a-b = 1 a+b = 20 Not integers ------------------------ 2 and 10 a-b = 2 a+b = 10 --> 4 and 6 which works ------------------------ 4 and 5 no integer solution 6^2 - 20 = 4^2 (-6)^2 - 20 = 4^2 No other solutions.
 Quadratic_Equations/252549: If a and b are roots of 7x^2 − 2002x +182 = 0 , find the value of 1/a + 1/b1 solutions Answer 184525 by Alan3354(30993)   on 2009-12-29 10:41:48 (Show Source): You can put this solution on YOUR website!If a and b are roots of 7x^2 − 2002x +182 = 0 , find the value of 1/a + 1/b ------------------ 7x^2 − 2002x +182 = 0 x^2 - 286x + 26 = 0 The roots are: (-b + sqrt(b^2 - 4ac))/2a and (-b - sqrt(b^2 - 4ac))/2a ---------------------------- The inverses give: 2a/(-b + sqrt(b^2 - 4ac)) and 2a/(-b - sqrt(b^2 - 4ac)) The sum is: 2a*2*(-b)/(b^2 - (b^2 - 4ac) = 4ab/(4ac) = b/c The general solution ----------------- For this eqn it's -11 = -11
 Problems-with-consecutive-odd-even-integers/252546: a. what is the inverse of squaring a number? b. the principal square root of 144 is 12. what is the other square root of 144?______ please help 1 solutions Answer 184517 by Alan3354(30993)   on 2009-12-29 09:55:04 (Show Source): You can put this solution on YOUR website!a. what is the inverse of squaring a number? It's finding the square root, the number that when squared gives the result. As in part b of your post. ------------------------------ b. the principal square root of 144 is 12. what is the other square root of 144? It's -12 12*12 = 144 (-12)*(-12) = 144 ------------------- There are always 2 square roots.
 Distributive-associative-commutative-properties/252544: Actually I wanted to favtorize: So I multiplied 8 with 15 and got 120. The factors came as and Then I split the into these 2 numbers, so I got: Then what do I do next? Please help I have no clue!1 solutions Answer 184516 by Alan3354(30993)   on 2009-12-29 09:49:43 (Show Source): You can put this solution on YOUR website! ----------------- It's a trial and error thing. The 1st term, 15, can be: 1*15 or 3*5 The last term, 8, can be 1*8 or 2*4. It's +8, so the signs are the same. Start with 1 and 15, ignore the sign but try to get 22 for the middle term: (x - 1)*(15x - 8) --> 23x NG (3x - 1)*(5x - 8) --> 29x NG ------------------------------ (x - 2)*(15x - 4) --> 34x NG (3x - 2)*(5x - 4) --> 22x That's it. The 22x is negative, so it's factored. ------------------------------------ The best approach is to use the quadratic equation, but students are usually subjected to factoring before learning the quadratic equation.
 Miscellaneous_Word_Problems/252534: The measure of an angle formed by the hands of a clock at 2:15 is: (a) 7.5 degrees (b) 22.5 degrees (c) 27.5 degrees (d) 30 degrees (e) 37.5 degrees1 solutions Answer 184512 by Alan3354(30993)   on 2009-12-29 08:57:35 (Show Source): You can put this solution on YOUR website!The measure of an angle formed by the hands of a clock at 2:15 is: (a) 7.5 degrees (b) 22.5 degrees (c) 27.5 degrees (d) 30 degrees (e) 37.5 degrees ---------------------- Using 12 as zero degrees: The minute hand is at 90 degs --------------------------- The hour hand moves 30 degs/hour, so it's at 30*2.25 degs = 67.5 90-67.5 = 22.5 degrees
 absolute-value/252542: Help me Find each product. I really don't know where to begin. I am trying hard but none of this is making since to me. I want to grow a love for math so please help me (3x -5) (2x + 1) 1 solutions Answer 184510 by Alan3354(30993)   on 2009-12-29 08:49:15 (Show Source): You can put this solution on YOUR website!(3x -5) (2x + 1) ------------------- Expand one of the binomials: = 3x*(2x + 1) - 5*(2x + 1) Do the multiplication: = (6x^2 + 3x) - (10x + 5) Collect like terms, which are the x terms: = 6x^2 (+3x - 10x) - 5 = 6x^2 - 7x - 5 That's all
2 tan y + 5 cosy y = 0 for 0 < y < 6
Thank You.
1 solutions

Answer 184506 by Alan3354(30993)   on 2009-12-29 08:29:17 (Show Source):
You can put this solution on YOUR website!
2 tan y + 5 cosy y = 0 for 0 < y < 6
---------------------
Do you mean 2 tan y + 5 cosy = 0 ??
2sin/cos + 5cos = 0
2sin + 5cos^2 = 0
2sin +5(1-sin^2) = 0
-5sin^2 + 2sin + 5 = 0
Now it's a quadratic in sin(y)
Sub x for sin(y):
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) 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=104 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.819803902718557, 1.21980390271856. Here's your graph:

Ignore the value >1
sin(y) =~-0.819804
y =~ -55 degs
or 305 degs, 235 degs