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# Recent problems solved by 'Alan3354'

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 Trigonometry-basics/669058: Help me prove csc^2+sec^2x = csc^2x sec^2x, by doing it step by step so I can understnd. Thanks. 1 solutions Answer 416048 by Alan3354(31528)   on 2012-10-19 18:21:38 (Show Source): You can put this solution on YOUR website!Help me prove csc^2+sec^2x = csc^2x sec^2x, by doing it step by step so I can understnd. ------------ Change to sines and cosines, then eliminate fractions.
 Linear-equations/669066: A line through the points (9,2) and (7,x) has a slope of 7/3. Find x. I think this is how to start. (7-2/7-x)=7/3 (7/7-x)=7/3 7-x-=7 -7 -7 _________ -x=0 -- -- - 1 -1 x=o1 solutions Answer 416047 by Alan3354(31528)   on 2012-10-19 18:17:59 (Show Source): You can put this solution on YOUR website!A line through the points (9,2) and (7,x) has a slope of 7/3. Find x. I think this is how to start. (7-2/7-x)=7/3 (7/7-x)=7/3 7-x-=7 -7 -7 _________ -x=0 -- -- - 1 -1 x=o ================== A line through the points (9,2) and (7,x) has a slope of 7/3. Find x. --------- Not a well posed problem, it has x in the y position. If it said: "A line through the points (9,2) and (7,y) has a slope of 7/3. Find y." it would make more sense. ------------- Slope m = diffy/diffx = (2-y)/(9-7) = 7/3 (2-y)/(9-7) = 7/3 Cross multiply 3(2-y) = 2*7 6-3y = 14 -3y = 8 y = -8/3
 Trigonometry-basics/669044: Help me prove cscx/1+cscx - cscx/1-cscx = 2 sec^2x. Thanks.1 solutions Answer 416029 by Alan3354(31528)   on 2012-10-19 17:14:38 (Show Source): You can put this solution on YOUR website!Help me prove cscx/1+cscx - cscx/1-cscx = 2 sec^2x. ---------- Eliminate fractions. Change it all to sines and cosines.
 Equations/669015: Find all the zeros of the equation. -4x4 - 44x2 + 3600 = 0 A. 5, -5, 6i, -6i B. 5, 6i C. 5, -5, 6i, 0 D. -5, -6i1 solutions Answer 416028 by Alan3354(31528)   on 2012-10-19 17:02:55 (Show Source): You can put this solution on YOUR website!duplicate
 Equations/669041: Find all the zeros of the equation. -4x4 - 44x2 + 3600 = 0 A. 5, -5, 6i, -6i B. 5, 6i C. 5, -5, 6i, 0 D. -5, -6i1 solutions Answer 416027 by Alan3354(31528)   on 2012-10-19 17:00:32 (Show Source): You can put this solution on YOUR website!Find all the zeros of the equation. -4x4 - 44x2 + 3600 = 0 A. 5, -5, 6i, -6i B. 5, 6i C. 5, -5, 6i, 0 D. -5, -6i ============== B, C & D don't work, the complex root has no conjugate. A might work. Try it.
 Travel_Word_Problems/669034: How far would a skier travel in 30 minutes is he were moving at a speed of 8 kilometers per hour?1 solutions Answer 416025 by Alan3354(31528)   on 2012-10-19 16:19:43 (Show Source): You can put this solution on YOUR website!How far would a skier travel in 30 minutes is he were moving at a speed of 8 kilometers per hour? ------ 30 minutes = 0.5 hours d = r*t
 Matrices-and-determiminant/668944: if 𝑓(𝑥) =𝑥^(1/3)/50 and 𝑔(𝑥) = 50 log 𝑥 . Which function dominates as 𝑥 → ∞?1 solutions Answer 415989 by Alan3354(31528)   on 2012-10-19 14:18:55 (Show Source): You can put this solution on YOUR website!if 𝑓(𝑥) =𝑥^(1/3)/50 and 𝑔(𝑥) = 50 log 𝑥 . Which function dominates as 𝑥 → ∞? ------------- What does that mean?
�t�e�s�t/668900: If x^3 + 1/x^3 = 110, then find x + 1/x.
1 solutions

Answer 415967 by Alan3354(31528)   on 2012-10-19 12:35:22 (Show Source):
You can put this solution on YOUR website!
If x^3 + 1/x^3 = 110, then find x + 1/x.
-------------
x^6 - 110x^3 + 1 = 0
Sub y for x^3
y^2 - 110y + 1 = 0
 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=12096 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 109.99090833947, 0.0090916605299185. Here's your graph:

=================
Find the cube root of the 2 answers.
--> x + 1/x = 5

 Square-cubic-other-roots/668953: 81+3y^31 solutions Answer 415964 by Alan3354(31528)   on 2012-10-19 12:25:07 (Show Source): You can put this solution on YOUR website!81+3y^3 ------------- Do you have a question?
 Graphs/668927: I'm sorry if I had broken any rules, but I couldn't find a way to put this on the website directly. The link directs you to the problem. Sorry for that. Thank you so much. http://postimage.org/image/gnmyisjw9/1 solutions Answer 415951 by Alan3354(31528)   on 2012-10-19 11:14:13 (Show Source): You can put this solution on YOUR website!http://postimage.org/image/gnmyisjw9/ ---------------- The vertex is (-3,4) Sub -3 for x and see which equation gives 4 for y (if any).
 Trigonometry-basics/668916: Which quadrant is arccos(cot(5)) in? Is there anyway to figure this out mathematically (solving for arccos(cot(5))). On the calculator I get 1.87 but I don't know if there is a way to do this with identities.1 solutions Answer 415945 by Alan3354(31528)   on 2012-10-19 10:54:28 (Show Source): You can put this solution on YOUR website!Which quadrant is arccos(cot(5)) in? Is there anyway to figure this out mathematically (solving for arccos(cot(5))). On the calculator I get 1.87 but I don't know if there is a way to do this with identities. ---------------- You're not asked for the value, just the quadrant. cot(5) is positive whether it's degrees or radians -------------- Quadt 1 2 3 4 cosine + - - + -------------- Could be Q1 or Q4
 Numeric_Fractions/668922: 3/4(X-12)=31 solutions Answer 415943 by Alan3354(31528)   on 2012-10-19 10:45:29 (Show Source): You can put this solution on YOUR website!3/4(X-12)=3 Multiply by 4 3(x-12) = 12 Divide by 3 x-12 = 4 Add 12 x = 16
Trigonometry-basics/668858: what is the least value of 4sec^2x+9cosec^2x ?
1 solutions

Answer 415939 by Alan3354(31528)   on 2012-10-19 09:55:42 (Show Source):
You can put this solution on YOUR website!
what is the least value of 4sec^2x+9cosec^2x ?
----------------
f(x) = 4sec^2 + 9csc^ = 4cos^-2 + 9sin^-2
f'(x) = 4*-2cos^-3*(-sin) + 9*-2sin^-3*cos = 0
8sin/cos^3 -18cos/sin^3 = 0
8sin^4 - 18cos^4 = 0
4sin^4 - 9cos^4 = 0
cos^2 = 1-sin^2 --> cos^4 = sin^4 - 2sin^2 + 1
-----
4sin^4 - 9sin^4 + 18sin^2 - 9 = 0
5sin^4 - 18sin^2 + 9 = 0
Sub x for sin^2
 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=144 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3, 0.6. Here's your graph:

---------------
Ignore the 3 solution, tho sin(x) = sqrt(3) has a complex solution.
-----------------------
sin^2(x) = 0.6 --> cos^2(x) = 0.4
sec^2(x) = 2.5
csc^2(x) = 5/3
===========================
4*2.5 + 9*(5/3) = 10 + 15
= 25

 test/668694: 2+9= =+21 solutions Answer 415783 by Alan3354(31528)   on 2012-10-18 20:51:57 (Show Source): You can put this solution on YOUR website!2+9= =+2 ------------- That makes no sense.
 Numeric_Fractions/668657: what is the answer to 6/5 + 1/6 = 1/x1 solutions Answer 415759 by Alan3354(31528)   on 2012-10-18 20:18:16 (Show Source): You can put this solution on YOUR website!what is the answer to 6/5 + 1/6 = 1/x ------------- It depends on the question.
 Travel_Word_Problems/668668: how many miles is 1 hour and 40 min.1 solutions Answer 415757 by Alan3354(31528)   on 2012-10-18 20:17:23 (Show Source): You can put this solution on YOUR website!how many miles is 1 hour and 40 min. ------------------- Miles is distance. 1:40 is time. ====================== Why is a duck so much alike?
 Systems-of-equations/668675: Solve each system by elimination(show work) 12.-x+3y=-1 x-2y=21 solutions Answer 415747 by Alan3354(31528)   on 2012-10-18 20:02:13 (Show Source): You can put this solution on YOUR website!-x+3y=-1 x -2y =2 --------------- add
 Expressions-with-variables/668625: 5/6 x ? + 1/41 solutions Answer 415718 by Alan3354(31528)   on 2012-10-18 19:01:22 (Show Source): You can put this solution on YOUR website!5/6 x ? + 1/4 ------------ idk
 Permutations/668579: can someone please tell me how many triangles are in this picture??? http://i48.tinypic.com/fwm3bq.png its not 12!1 solutions Answer 415712 by Alan3354(31528)   on 2012-10-18 18:53:18 (Show Source): You can put this solution on YOUR website!can someone please tell me how many triangles are in this picture??? http://i48.tinypic.com/fwm3bq.png ------------ I found 16. I doubt there are any more.
 Quadratic_Equations/668630: How do I find the discriminant for a problem such as 4x^2=3241 solutions Answer 415709 by Alan3354(31528)   on 2012-10-18 18:50:42 (Show Source): You can put this solution on YOUR website!How do I find the discriminant for a problem such as 4x^2=324 -------- Disc = b^2 - 4ac a = 4, b = 0, c = -324 Disc = 5184 -------------- --> Disc = 324
 absolute-value/668572: -5 I 6a + 2 I = -15 I = absolute valu sign I was taught to drop the absolute value sign, set up two equations--one = to -15 and one = to 15 and then solve for a. So for this problem, I wasn't sure if I should drop the absolute value sign and then it would be -5 x 6a + 2 = -15 and -5 x 6a + 2 = 15 OR if I should first distribute the -5 as if the absolute value signs were parentheses. Thanks so much for your help.1 solutions Answer 415680 by Alan3354(31528)   on 2012-10-18 17:23:47 (Show Source): You can put this solution on YOUR website!-5 I 6a + 2 I = -15 I = absolute valu sign --------------- -5|6a + 2| = -15 |6a + 2| = 3 ---- 6a+2 = 3 6a = 1 a = 1/6 ------- 6a+2 = -3 6a = -5 a = -5/6
 Linear-systems/668524: Please help, this one stumps me. Thank you to anyone willing to give it a shot. One apple has 100 calories and 24 grams of carbohydrates. One avocado has 350 calories and 14 grams of carbohydrates. How many of each should be eaten to get exactly 1000 calories and 100 grams of carbohydrates?1 solutions Answer 415647 by Alan3354(31528)   on 2012-10-18 16:11:33 (Show Source): You can put this solution on YOUR website!One apple has 100 calories and 24 grams of carbohydrates. One avocado has 350 calories and 14 grams of carbohydrates. How many of each should be eaten to get exactly 1000 calories and 100 grams of carbohydrates? ----------------- To get 1000 calories, you need an even # of avocadoes. 2 Av's + 3 apples fits.
 Geometric_formulas/668532: I am studying for my chapter 1 test but there is this question i dont understand, i know the distance from -4 to 12 using the formula. But i dont know what the second answer is! Please help me heres the question. "On a number line, the coordinate of A is -4. Find the coordinate of T if T is 12 units away from A. (There are 2 answers)"1 solutions Answer 415646 by Alan3354(31528)   on 2012-10-18 16:08:30 (Show Source): You can put this solution on YOUR website!"On a number line, the coordinate of A is -4. Find the coordinate of T if T is 12 units away from A. -------------------- It's not from -4 to 12, it's 12 units from -4. ---- -4 + 12 = 8 -4 - 12 = -16
 Travel_Word_Problems/668337: Tires: Wheels are 1.25 inches in diameter Fastest speed is 3ft/sec Maximum distance is 16 x (18 cm) 1) How many times does the wheel turn to travel the maximum distance? 2) How long does it take to travel the maximum distance at full speed? 3) What is the acceleration needed to travel the maximum distance when starting from a standstill? 1 solutions Answer 415643 by Alan3354(31528)   on 2012-10-18 16:01:13 (Show Source): You can put this solution on YOUR website!Wheels are 1.25 inches in diameter Fastest speed is 3ft/sec Maximum distance is 16 x (18 cm) 1) How many times does the wheel turn to travel the maximum distance? 1.25 in = 3.175 cm Circum = pi*d = 3.175pi cm # of revs = 288/3.175 =~ 90.709 ----------------- 2) How long does it take to travel the maximum distance at full speed? r = 3ft/sec = 91.44 cm/sec t = d/r = 288/91.443.15 seconds ------------- 3) What is the acceleration needed to travel the maximum distance when starting from a standstill? Any acceleration > 0 will do.
 Money_Word_Problems/668513: My question is how would you show the work for the interest formula a=p(1+r/n)^nt to compare saving accounts if you need to show more than one months work. As if you did say the month of October then the next month and so on? 1 solutions Answer 415627 by Alan3354(31528)   on 2012-10-18 15:39:47 (Show Source): You can put this solution on YOUR website!My question is how would you show the work for the interest formula a=p(1+r/n)^nt to compare saving accounts if you need to show more than one months work. As if you did say the month of October then the next month and so on? -------------- What are you comparing? If you use the same formula, the account with the higher interest rate pays the most interest, regardless of the # of months.
 Number-Line/668517: A friend of mine is having trouble with doing this problem and I have no clue how to help her out. Her teacher is telling her she to take another look at her overtime pay rate calculation..please do help her and me. thanks. She chose option 1: Method 1:(total regular hours X hourly rate) + (overtime hours X overtime rate)=gross pay And this is her information : Pay rate: 14.26 Regular Hours: 80 Overtime hours: 6 Overtime rate: 1.5 (time and a half) (80 x 14.26) + (6 x 1.5) = gross pay 80 x 14.26 = 1140.80 6 x 1.5 = 9 1140.80 + 9 = 1149.801 solutions Answer 415621 by Alan3354(31528)   on 2012-10-18 15:29:30 (Show Source): You can put this solution on YOUR website!She chose option 1: Method 1:(total regular hours X hourly rate) + (overtime hours X overtime rate)=gross pay And this is her information : Pay rate: 14.26 Regular Hours: 80 Overtime hours: 6 Overtime rate: 1.5 (time and a half) (80 x 14.26) + (6 x 1.5) = gross pay *************** OT is 1.5 times \$14.26, not \$1.50 per hour. --------------------- 80 x 14.26 = 1140.80 6 x 1.5 = 9 1140.80 + 9 = 1149.80
 Rate-of-work-word-problems/668437: Find the interior angles of the triangle with vertices A=(3,2), B=(4,5), C=(-1,-1)1 solutions Answer 415600 by Alan3354(31528)   on 2012-10-18 15:05:06 (Show Source): You can put this solution on YOUR website!Find the interior angles of the triangle with vertices A=(3,2), B=(4,5), C=(-1,-1) --------------- One way is to find the lengths of the 3 sides, then use the Cosine Law. Can you do that? -------------- Another is to find the slope of each side and then find the angles. Less work than the 1st method. Do you know how to do that?
 Graphs/668483: Sketch the curve of y=x^2+12x-3, clearly marking on the vetex and y-intercept. Thanks!1 solutions Answer 415581 by Alan3354(31528)   on 2012-10-18 14:21:11 (Show Source): You can put this solution on YOUR website!Sketch the curve of y=x^2+12x-3, clearly marking on the vetex and y-intercept. ----------------- dl the FREE graph software at http://www.padowan.dk Use Insert, the enter the function x^2+12x-3
 Numeric_Fractions/668476: what does the fraction 5/6 + 7/32 equal1 solutions Answer 415578 by Alan3354(31528)   on 2012-10-18 14:02:00 (Show Source): You can put this solution on YOUR website!what does the fraction 5/6 + 7/32 equal -------------- Find a common denominator. The product always works, 6*32 = 192 5/6 + 7/32 = 160/192 + 42/192 = 202/192 = 101/96
 Equations/668396: A^2X^2-B^2Y^21 solutions Answer 415562 by Alan3354(31528)   on 2012-10-18 12:45:45 (Show Source): You can put this solution on YOUR website!A^2X^2-B^2Y^2 ---------------- Do you have a question?
 Complex_Numbers/668409: - (square root) -481 solutions Answer 415528 by Alan3354(31528)   on 2012-10-18 11:36:08 (Show Source): You can put this solution on YOUR website! = =