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# Recent problems solved by 'Alan3354'

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 Quadratic-relations-and-conic-sections/370308: How do you graph the following: y+1=-1/20(x-1)^2 y+1= 1/20(x-1)^2 y+1=-1/12(x-1)^2 x+1=-1/20(y-1)^21 solutions Answer 263972 by Alan3354(30959)   on 2010-11-13 06:50:42 (Show Source): You can put this solution on YOUR website!How do you graph the following: y+1=-1/20(x-1)^2 Solve for y y = -1 - (1/20)(x-1)^2 Pick values for x and find y. Plot the points, draw a curve thru them. ------------------- y+1= 1/20(x-1)^2 same y+1=-1/12(x-1)^2 same x+1=-1/20(y-1)^2 same, except solve for x and pick values of y. -------------------- dl the FREE graph software at http://www.padowan.dk.com
 Graphs/370257: How do I graph slope: -2; y-intercept (0,3)1 solutions Answer 263970 by Alan3354(30959)   on 2010-11-13 06:45:21 (Show Source): You can put this solution on YOUR website!It's a straight line, so you need only 2 points. One point is given, the y-int is (0,3) Slope = -2 Add 1 to x and -2 to y --> (1,1), the 2nd point. Draw a line thru them.
 Percentage-and-ratio-word-problems/370267: A large cube is dipped into red paint and divided into 216 smaller congruent cubes. one of the smaller cube is then randomly selected. What is the probability that the cube selected will have at least 25% of its surface area painted red? express answers as a common fraction1 solutions Answer 263969 by Alan3354(30959)   on 2010-11-13 06:32:40 (Show Source): You can put this solution on YOUR website!The surface are of a cube with sides of 3 = 6*3^2 = 54, so after the division, 54 of the cubes will have some paint on them. The center cube of each face will have only one of its faces painted, 6 of those, so 48 cubes will have 2 or 3 faces painted, giving them more than 25% coverage. 48/216 = 2/9
 Quadratic-relations-and-conic-sections/370260: find the vertex the line of symmetry the maximum and minimum value of the quadratic function. F(x)=x^2-12x-31 solutions Answer 263944 by Alan3354(30959)   on 2010-11-12 23:06:06 (Show Source): You can put this solution on YOUR website!The line of symmetry is x = -b/2a x = 12/2 x = 6 ------ The minimum is F(6) = 36 - 72 - 3 = -39
 Radicals/370121: Why do we divide by 2 when solving problems involving gravity, 32 feet per second per second?1 solutions Answer 263940 by Alan3354(30959)   on 2010-11-12 22:59:05 (Show Source): You can put this solution on YOUR website!We don't always. v = 32t See? ---- To find the distance an object falls in, eg, 1 second, tho: Its speed at the end of 1 second = 32 ft/sec, but its starting speed was zero. That makes its average speed for that 1 second 16 ft/sec. So, s = at^2/2 = 32*1^2/2 = 16 feet. Or, s = 16t^2
 Complex_Numbers/370271: (2-3i)(5i)/2 + 311 solutions Answer 263916 by Alan3354(30959)   on 2010-11-12 22:20:09 (Show Source): You can put this solution on YOUR website!(2-3i)(5i)/2 + 31 = (10i + 15)/33 = (15 + 10i)/33
 Complex_Numbers/370272: 1+i/i - 3/4-i1 solutions Answer 263910 by Alan3354(30959)   on 2010-11-12 21:47:13 (Show Source): You can put this solution on YOUR website! 1+i/i - 3/4-i = 1 + 1 - (3/4) - i = (5/4) - i ------------- It's ambiguous. It's your job to present the problem clearly.
 Complex_Numbers/370269: 8+20i/2i1 solutions Answer 263908 by Alan3354(30959)   on 2010-11-12 21:44:53 (Show Source): You can put this solution on YOUR website!If you mean (8+20i)/2i = (4 + 10i)/i Multiply by i = (4i - 10)/-1 = 10 - 4i ------------ If you mean 8 + (20i/2i) = 8 + 10 = 18 ----- Parentheses are free, use some.
 Square-cubic-other-roots/370276: Can a cubic equation have only two roots? 1 solutions Answer 263905 by Alan3354(30959)   on 2010-11-12 21:32:59 (Show Source): You can put this solution on YOUR website!In a sense it can, and it can have only 1. eg (x-2)^3 has x = 2 as its only solution, but it's multiplicity 3. (x-2)^2 is a quadratic that has 2 as the only zero, but it's multiplicity 2. -------------- It's a matter of semantics.
 Matrices-and-determiminant/370212: Solve the system of equations if possible. 2x-3y-z=15 2x+3y+z=1 2x+3y-z=31 solutions Answer 263880 by Alan3354(30959)   on 2010-11-12 19:35:29 (Show Source): You can put this solution on YOUR website!2x-3y-z=15 2x+3y+z=1 2x+3y-z=3 ------------- Use elimination 2x-3y-z=15 2x+3y+z=1 ---------- Add 4x = 15 x = 4 ------ 2x-3y-z=15 2x+3y-z=3 ----------- Add 4x - 2z = 18 16 - 2z = 18 z = -1 -------- 2x+3y+z=1 8 + 3y - 1 = 1 3y = -6 y = -2 ------- Most are not this easy.
 Quadratic_Equations/370229: A model for the path of a toy rocket is given by 68t-4.9t(squared), where h is the altitude in meters and t is the time in seconds. Explain how to find both the maximum altitude of the rocket and how long it takes to reach that altitude.1 solutions Answer 263878 by Alan3354(30959)   on 2010-11-12 19:30:59 (Show Source): You can put this solution on YOUR website!It's a parabola. h(t) = -4.9t^2 + 68t The time to max height is the line of symmetry, -b/2a t = -b/2a = -68/-9.8 t = 340/49 seconds = ~ 6.939 seconds ----------- Max ht = h(340/49) = 566440/2401 meters =~ 235.9 meters ------------------
 Polynomials-and-rational-expressions/370225: Find all of the real zeros of the polynomial P(x)=12x^3-129x^2+342x-189. 1 solutions Answer 263866 by Alan3354(30959)   on 2010-11-12 18:49:00 (Show Source): You can put this solution on YOUR website!12x^3-129x^2+342x-189 4x^3-43x^2+114x-63 63 has a factor of 7, try that. Then it's a quadratic. --> 0.75, 3, 7
 Linear-equations/370214: My problem is -2 3/4 x 1/71 solutions Answer 263865 by Alan3354(30959)   on 2010-11-12 18:43:08 (Show Source): You can put this solution on YOUR website!My problem is -2 3/4 x 1/7 = -11/4 * 1/7 = -11/28
 Polynomials-and-rational-expressions/370226: x^2 - 7x 30=0, solve equation1 solutions Answer 263864 by Alan3354(30959)   on 2010-11-12 18:41:52 (Show Source): You can put this solution on YOUR website!There's a sign missing
 Linear-equations/370123: write an equation in standard form line passing through the pair of points for(-4,5) and (0,-2).1 solutions Answer 263833 by Alan3354(30959)   on 2010-11-12 14:37:49 (Show Source): You can put this solution on YOUR website!Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ Another approach using determinants: |x y 1| |2 1 1| = 0 |3 5 1| -------- x(1-5) - y(2-3) + 1(10-3) = 0 -4x + y + 7 = 0 y = 4x - 7 --------- For further assistance, or to check your work, email me via the thank you note or at Moral Loophole@aol.com
 Proportions/370143: An airplane took 3hrs to fly 1800 miles against a headwind. The return trip with the wind took 2 hours. Find the speed of the plane in still air and the speed of the wind. 1 solutions Answer 263816 by Alan3354(30959)   on 2010-11-12 14:10:31 (Show Source): You can put this solution on YOUR website!The "speed in still air" is the airspeed. It's the average of the 2 groundspeeds. The windspeed is the difference between the airspeed and the groundspeed.
 Rectangles/370119: The perimeter of a rectangle is 52 inches squared. Its area is 153 inches squared. What is its length and width? What I've done so far y=26-x -x^2+ 26x -52 = 0 I get stuck while using the quadratic formula to use numbers to substitute into the next equation... Your help would greatly be appreciated. 1 solutions Answer 263774 by Alan3354(30959)   on 2010-11-12 12:20:59 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 52 inches squared. Its area is 153 inches squared. What is its length and width? What I've done so far y=26-x -x^2+ 26x -52 = 0 ------------- x + y = 26 x*y = 153 x*(26 - x) = 153 (you had 52) x^2 - 26x + 153 = 0 (x-9)*(x-17) = 0 x = 9, 17 --> 9 by 17 inches
 Problems-with-consecutive-odd-even-integers/370059: A 10-ft wide round water trampoline is floating in a pool measuring x ft by x ft. Find a polynomial for the remaining surface area of the pool im not sure how to get this started1 solutions Answer 263753 by Alan3354(30959)   on 2010-11-12 10:46:46 (Show Source): You can put this solution on YOUR website!A 10-ft wide round water trampoline is floating in a pool measuring x ft by x ft. Find a polynomial for the remaining surface area of the pool ---------------- The radius of the trampoline = 5 ft The area = 25*pi sq feet ------------------ The area of the pool is x*x = x^2 sq ft The difference is x^2 - 25pi sq feet
 Complex_Numbers/369893: what is the real root number to ^4sqrt( 16 )1 solutions Answer 263598 by Alan3354(30959)   on 2010-11-11 21:58:24 (Show Source): You can put this solution on YOUR website!Do you mean 4th root? ± 2 are the real ones.
 Equations/369912: (1/6,-1/3) and (5/6,5) Find an equation of the line containing the given pair of points.1 solutions Answer 263597 by Alan3354(30959)   on 2010-11-11 21:56:49 (Show Source): You can put this solution on YOUR website!Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ Another approach using determinants: |x y 1| |2 1 1| = 0 |3 5 1| -------- x(1-5) - y(2-3) + 1(10-3) = 0 -4x + y + 7 = 0 y = 4x - 7 --------- For further assistance, or to check your work, email me via the thank you note or at Moral Loophole@aol.com
 Equations/369909: (2,-7) 9x+8y=7 Write the equation of the line containing the given points and perpendicular to the given line.1 solutions Answer 263595 by Alan3354(30959)   on 2010-11-11 21:56:14 (Show Source): You can put this solution on YOUR website!A line and a point example. Write in standard form the eqation of a line that satisfies the given conditions. Perpendicular to 9x+3y=36, through (1,2) ----------------- Find the slope of the line. Do that by putting the equation in slope-intercept form, y = mx + b. That means solve for y. 9x+3y = 36 3y= - 9x + 36 y = -3x + 12 The slope, m = -3 ------------------ The slope of lines parallel is the same. The slope of lines perpendicular is the negative inverse, m = +1/3 ---------------- Use y = mx + b and the point (1,2) to find b. 2 = (1/3)*1 + b b = 5/3 The equation is y = (1/3)x + 5/3 (slope-intercept form) x - 3y = -5 (standard form) ------------------------ For further assistance, or to check your work, email me via the thank you note, or at Moral Loophole@aol.com
 Graphs/369879: Hi guys, it's me again. I need your help on this one. Find an equation of the line passing through the pair of points. Write the equation in slope-intercept form. (5, -3) and (1, -4)1 solutions Answer 263594 by Alan3354(30959)   on 2010-11-11 21:55:21 (Show Source): You can put this solution on YOUR website!Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ Another approach using determinants: |x y 1| |2 1 1| = 0 |3 5 1| -------- x(1-5) - y(2-3) + 1(10-3) = 0 -4x + y + 7 = 0 y = 4x - 7 --------- For further assistance, or to check your work, email me via the thank you note or at Moral Loophole@aol.com
 Complex_Numbers/369901: 2+3i 7-2i ---- + ---- 3-2i 8+i the answer is 54+42i ------ 65 but i don't know HOW my teacher got that. can you explain? 1 solutions Answer 263592 by Alan3354(30959)   on 2010-11-11 21:52:01 (Show Source): You can put this solution on YOUR website!2+3i 7-2i ---- + ---- 3-2i 8+i ----------- Step 1, get the i's out of the denominators. Multiply NUM and DEN by the conjugate of the DEN --------- (2+3i)*(3+2i) (7-2i)*(8-i) ------------- + ----------- (3-2i)*(3+2i) (8+i)*(8-i) --- (6+13i-6) (56 - 23i - 2) --------- + ----------- (9 + 4) (64 + 1) --- 13i (54 - 23i) --- + ---------- 13 65 = (54 - 23i)/65 + i = (54 - 23i)/65 + 65i/65 = (54 + 42i)/65
 Trigonometry-basics/369832: Find the angle θ. (Use either the Law of Sines or the Law of Cosines, as appropriate.) (Round your answer to one decimal place.) a = 14, b = 3, c = 15 θ = ?1 solutions Answer 263530 by Alan3354(30959)   on 2010-11-11 19:05:37 (Show Source): You can put this solution on YOUR website!You'll have to spec which 2 sides are adjacent to the angle. ------------ Since 3 sides are known, use the Law of Cosines.
 Linear-equations/369772: state the slope of aline parallel to the line passing through the given points E(-1,2), F(5,0) G(2,4), H(-3,1) find the value of k so that the line passing through R(-3,k) and S(0,0) is perpendicular to the line passing through T(0,0) and U(7,7).1 solutions Answer 263529 by Alan3354(30959)   on 2010-11-11 19:03:47 (Show Source): You can put this solution on YOUR website!state the slope of aline parallel to the line passing through the given points E(-1,2), F(5,0) slope m = diffy/diffx m = ( m = (2-0)/(-1-5) m = 2/-6 m = -1/3 ------------ G(2,4), H(-3,1) Do it like the 1st one.
 Graphs/369811: 7x=2y direct variations1 solutions Answer 263521 by Alan3354(30959)   on 2010-11-11 18:41:51 (Show Source): You can put this solution on YOUR website!Do you have a question?
 Angles/369812: estimate the angle to the nearest one half radiam1 solutions Answer 263520 by Alan3354(30959)   on 2010-11-11 18:41:14 (Show Source): You can put this solution on YOUR website!What angle?
 Polynomials-and-rational-expressions/369799: Solve by factoring and using the principle of zero products: x^2+4x-21=01 solutions Answer 263519 by Alan3354(30959)   on 2010-11-11 18:39:28 (Show Source): You can put this solution on YOUR website!Hint: factor 21
 Triangles/369808: the lengths of two sides of a triangle are 15 inches each and the third side measures 10 inches what kind of triangle is that1 solutions Answer 263516 by Alan3354(30959)   on 2010-11-11 18:37:06 (Show Source): You can put this solution on YOUR website!Isosceles, still.
 logarithm/369806: How would you solve the question: 64=x(x-30)1 solutions Answer 263515 by Alan3354(30959)   on 2010-11-11 18:35:39 (Show Source): You can put this solution on YOUR website!I would multiply x by the binomial, collect terms, set it = to zero.
 Triangles/369792: whta kind of triangle is this if two sides are 15 in and the other is 10 in.1 solutions Answer 263514 by Alan3354(30959)   on 2010-11-11 18:34:39 (Show Source): You can put this solution on YOUR website!If 2, but not 3, sides are equal, it's isosceles.