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# Recent problems solved by 'Gogonati'

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 Numbers_Word_Problems/451121: absolute value of y2-3y is equal to 4.1 solutions Answer 310233 by Gogonati(809)   on 2011-05-18 08:51:26 (Show Source): You can put this solution on YOUR website!Base on the absolute value deffinition the equation is equivalent to the equations: and . We solve these two equations:1)=>, where y=-1 and y=4. 2) , which has not real solution because the discriminant is negative number. answer: The solution of original equation is the set; {-1, 4}.
 Equations/451119: Find the product..... (4x+3)(6x^2)1 solutions Answer 310229 by Gogonati(809)   on 2011-05-18 08:38:01 (Show Source): You can put this solution on YOUR website!Using the distributive property we get: .
 Equations/451090: (4sqrt(3)-5)(2sqrt(3)+5) (2sqrt(5)-6sqrt(7))(3sqrt(5)+sqrt(7)) Simplify Thank you1 solutions Answer 310228 by Gogonati(809)   on 2011-05-18 08:34:46 (Show Source): You can put this solution on YOUR website!The first is for me the second is for you; 1).
 Exponential-and-logarithmic-functions/451117: (a^4b^3)2/31 solutions Answer 310227 by Gogonati(809)   on 2011-05-18 08:27:10 (Show Source): You can put this solution on YOUR website!Using the properties of power we can write:
 Complex_Numbers/451113: (3+5i)/(8i)1 solutions Answer 310226 by Gogonati(809)   on 2011-05-18 08:17:24 (Show Source): You can put this solution on YOUR website!To divide complex numbers we multiply the nominator and denominator by the conjugate of the denominator:(Don't forget )
 Quadratic_Equations/451111: 10x^2= -100x Please tell me how to solve this problem by factoring and doing 2 checks. Thanks. SAL I think the answer is x=0, x= -10. But, how do you do it?1 solutions Answer 310224 by Gogonati(809)   on 2011-05-18 08:06:28 (Show Source): You can put this solution on YOUR website!First set the equation to zero;, factor 10x out and get: . Use the fact that if ab=0 then a=0 or b=o to find the roots: 10x=0=> x=0 and x+10=0 => x=-10 Answer:The solution is x=0 and x=-10. Check:1)10*0^2=-100*0 => 0=0; 2)10*10^2=-100*(-10)=> 1000=1000.
 Rectangles/449977: If a tv is 24 inches in length and 18 inches wide, how big is the screen? 1 solutions Answer 309553 by Gogonati(809)   on 2011-05-16 08:26:51 (Show Source): You can put this solution on YOUR website!The screen will be 30 inches:.
 Miscellaneous_Word_Problems/449981: The sum of the base and the height of a parallelogram is 24 in. Find the base and the height for which the area is a maximum.1 solutions Answer 309551 by Gogonati(809)   on 2011-05-16 08:22:25 (Show Source): You can put this solution on YOUR website!Let the base of parallelogram x inches, then the height will be 24-x inches, and the area is , which represent a downward parabola with vertex (12, 144), and the maximum area is 144 square inches. If you have knowledges about derivatives, find the maximum value of the function . Its derivative is -2x+24, and the maximum value will be: -2x+24=0 for x=12. Answer:The maximum area of the parallelogram will be, where the base and height are equal with 12 inches.
 Equations/449983: IF x+y=4 y=x-8, what is the value of x?1 solutions Answer 309545 by Gogonati(809)   on 2011-05-16 07:57:50 (Show Source): You can put this solution on YOUR website!To find the value of x, substitute in the first equation y=x-8, and solve for x: +>=>.
 Quadratic-relations-and-conic-sections/449974: whats the graphing form for this equation Center(-3,-6) Directrix x=-91 solutions Answer 309544 by Gogonati(809)   on 2011-05-16 07:54:01 (Show Source): You can put this solution on YOUR website!First you need to find the equation of the parabola, where based on the data is in the standard form:, and directrix x=-c or c=9. Since its vertex is (-3, -6) the equation will be: This parabola opens right because c=9>0, the vertex is (-3, -6), the axis is the line y=-6 , the focus is (9, -6) and the directrix x=9.
 Quadratic-relations-and-conic-sections/449665: write an equation of the given conic section with the givin informaton. ellipse with center (1,-3) and vertices (1,2) and (1,-8) and co verticies (4,-3)and (-2,-3) Thank you so much for all your help i really appreciate it! 1 solutions Answer 309315 by Gogonati(809)   on 2011-05-15 16:26:30 (Show Source): You can put this solution on YOUR website!The equation of the ellipse with center (1, -3) is: Since we have the endpoints of major and minor axis we can find their lengths: , thus a=5 , thus b=3 The equation of ellipse is:.
 Quadratic-relations-and-conic-sections/449573: Find the equation of the parabola with its vertex at the origin if its directrix is y=31 solutions Answer 309310 by Gogonati(809)   on 2011-05-15 16:05:51 (Show Source): You can put this solution on YOUR website!As you know the directrix of the parabola is y=-c, since y=3, we get 3=-c or c=-3, and the equation of parabola will be: . .
 test/449609: 2zy over y2 =14 over y1 solutions Answer 309306 by Gogonati(809)   on 2011-05-15 15:50:04 (Show Source): You can put this solution on YOUR website!,reducing the first term we get:=>=> =>, substituting z=7 we find y=1.
 Polygons/449626: How many sides does a regular polygon have if the measure of an exterior angle is 24.1 solutions Answer 309301 by Gogonati(809)   on 2011-05-15 15:39:32 (Show Source): You can put this solution on YOUR website!As you know the sum of exterior angels of a regular polygon is 360 degree. Let n the number of angels of polygon, then =>. Answer:The polygon has 15 sides.
 logarithm/449645: which of the following is equivalent to log base 4 of 64^x ? 1) 4^3x 2) 3^x 3) 4x 4) .25x 5) 3x1 solutions Answer 309298 by Gogonati(809)   on 2011-05-15 15:32:06 (Show Source): You can put this solution on YOUR website!Based on the definition of logarithmic and exponential functions we write: => =>=>. Answer:, is equivalent to 3x.
 Polynomials-and-rational-expressions/449634: simplify by removing factors of 1 z^2-9z+20/z^2+z-301 solutions Answer 309295 by Gogonati(809)   on 2011-05-15 15:24:13 (Show Source): You can put this solution on YOUR website!First we factor the nominator and denominator of the rational expression and after reduce the same factors: =
 Trigonometry-basics/449325: solve for theta in teh intervals 0 - 360 sin x cos x = cos x 1 solutions Answer 309102 by Gogonati(809)   on 2011-05-14 16:09:17 (Show Source): You can put this solution on YOUR website!Dividing both sides by cosx we get , and its solution is .
 Polynomials-and-rational-expressions/449321: Find the volume of a cube if its surface area is 6x^2 + 36x + 54 square meters1 solutions Answer 309101 by Gogonati(809)   on 2011-05-14 16:05:50 (Show Source): You can put this solution on YOUR website!First we factor the polynomial of the surface area: , from this expression we conclude that the dimension of the cube is (x+3) m, because the area of one side of the cube is square meter, and the volume will be:
 Trigonometry-basics/449320: Prove that it is an identity 1) tan (1/2) A = csc A - cot A1 solutions Answer 309100 by Gogonati(809)   on 2011-05-14 15:48:26 (Show Source): You can put this solution on YOUR website!We know from trigonometry that , assuming x=A and transforming the right side of the identity we get the left side:
 Trigonometry-basics/448398: verify sinx+cotxcosx=cscx1 solutions Answer 308572 by Gogonati(809)   on 2011-05-12 07:05:01 (Show Source): You can put this solution on YOUR website!To verify this trigonometric identity we transform the left side until reach the same expression as the right side: =.
 Trigonometry-basics/448396: simplify 1/(1-cosx) + 1/(1+cosx)1 solutions Answer 308570 by Gogonati(809)   on 2011-05-12 06:57:29 (Show Source): You can put this solution on YOUR website!=.
 Trigonometry-basics/448400: solve 2sin^2x- square root of 3 sinx=01 solutions Answer 308569 by Gogonati(809)   on 2011-05-12 06:51:30 (Show Source): You can put this solution on YOUR website!, assuming sinx≠0 or x≠n*, divide both sides by sinx and get:=>, where its solution is: and .
 Trigonometry-basics/448402: solve sinxtanx-sinx=01 solutions Answer 308568 by Gogonati(809)   on 2011-05-12 06:37:41 (Show Source): You can put this solution on YOUR website!, assuming sinx≠0 or x≠n*, divide both sides of equation by sinx and get:, where its solution is:.
 Exponents-negative-and-fractional/448461: reduce given fracion to lowest term 15z^(2)/-36z^(8)1 solutions Answer 308567 by Gogonati(809)   on 2011-05-12 06:16:30 (Show Source):
 Numbers_Word_Problems/447881: find the two-digit number whose units' digit is 5 more than its tens' digit and whose value equals 3 times the sum of these digits.1 solutions Answer 308316 by Gogonati(809)   on 2011-05-11 08:18:05 (Show Source): You can put this solution on YOUR website!Let the ten's be x, then its units are x+5 and the sum of digits is x+x+5=2x+5 and the value of a number will be:10x+x+5=11x+5. Since its value equals 3 times the sum of the digits we write the equation: =>=>.The units are 2+5=7. Answer: The two digit number is 27.
 Linear-equations/447918: graph y = -x^2 + 3 1 solutions Answer 308307 by Gogonati(809)   on 2011-05-11 07:55:40 (Show Source):
 Inverses/447941: Suppose f(x) = 2^(x^2) - 5, for x >=0. find f^-1, the inverse of f. Determine the domain of f^-1. compute f^(-11).1 solutions Answer 308305 by Gogonati(809)   on 2011-05-11 07:52:30 (Show Source): You can put this solution on YOUR website!Assume that , solve this equation for x:=> =>, interchange x and y and get the inverse function:. The domain of this function is: (5, ). The value x=-11 is not included in its domain for this value the function is undefined.
 Inverses/447943: simplify ln(1/e)^6-4t1 solutions Answer 308302 by Gogonati(809)   on 2011-05-11 07:34:08 (Show Source): You can put this solution on YOUR website!=.
 Inequalities/447948: i need your help... can you graph this equation? y=-(x-4)^2+3 *state weather the graph opens upward or downwards? *is the vertex of the graph a maximum or minimum point? *find the vertex of the graph of the functon? *what is the axis of symmetry? *identify the transformation of the graph (how did you mave the parabola)?1 solutions Answer 308301 by Gogonati(809)   on 2011-05-11 07:29:53 (Show Source): You can put this solution on YOUR website!The graph is a downward parabola, its vertex is the point (4, 3) and the axis of symmetry is the line x=4. To construct the graph we start from :1) reflect to the x-axis , 2)shift 4 units to the right shift 3 units up . See the graph below:
 logarithm/447732: How do I solve 7^3b = 12^b+2? I don't know how to even start this problem... Thank you! 1 solutions Answer 308201 by Gogonati(809)   on 2011-05-10 19:19:43 (Show Source): You can put this solution on YOUR website!==>=> =>=>=>.
 Exponential-and-logarithmic-functions/447735: 2^(5/2)- 2^(3/2)= ?1 solutions Answer 308196 by Gogonati(809)   on 2011-05-10 19:02:33 (Show Source): You can put this solution on YOUR website! =.