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# Recent problems solved by 'Gogonati'

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 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! =.
 Polynomials-and-rational-expressions/447736: (x^6-x^5+x^4)/x^21 solutions Answer 308192 by Gogonati(809)   on 2011-05-10 18:54:31 (Show Source): You can put this solution on YOUR website!=.
 Numbers_Word_Problems/446477: The sum of the squares of two consecutive natural numbers is 85. Determine the number.1 solutions Answer 307482 by Gogonati(809)   on 2011-05-08 08:16:20 (Show Source): You can put this solution on YOUR website!Solve the equation:. Set the equation to zero: =>=> The solution is: x=-7 which is rejected because it is not natural number, and x=6 which is the right solution. Answer:Two consecutive natural numbers are 6 and 7.
 Permutations/446479: A cow costs seven times as much as goat for 84000 i can buy 18 more goats than cows,How much does a goat cost?1 solutions Answer 307480 by Gogonati(809)   on 2011-05-08 08:00:15 (Show Source): You can put this solution on YOUR website!Let x the price of a goat, then the price of a cow is 7x. With \$84000 we can buy goats or cows Now write the equation;, solving this equation find: =>=> Answer:The price of a goat is \$4000.
 Square-cubic-other-roots/446475: hey my name is farah i want help in my homework i want to know how can you solve those square root cubic y^3-64 and 1000x^3-271 solutions Answer 307477 by Gogonati(809)   on 2011-05-08 07:47:04 (Show Source):
 Sequences-and-series/445978: simplify : 2i+7/8-3i 1 solutions Answer 307153 by Gogonati(809)   on 2011-05-06 15:33:03 (Show Source):
 Rational-functions/446018: The asymptotes of the function g(x)= x+2/x^2+2x-3 are?1 solutions Answer 307152 by Gogonati(809)   on 2011-05-06 15:30:43 (Show Source): You can put this solution on YOUR website!, and its asymptotes are: x=1 and x=-3, because and
 Triangles/446020: A 15 ft ladder is leaning against a house at a 60 degree angle with the ground. How far is the ladder from the house1 solutions Answer 307148 by Gogonati(809)   on 2011-05-06 15:22:20 (Show Source): You can put this solution on YOUR website!The leg of the right triangle opposite to the angel 30 degree is half of the length of hypotenuse. In our case the distance of the ladder from the house is 15/2 ft=7.5 ft.
 Rational-functions/446023: Solve: (x^2 - 1)^1/2 + (x^2 - 1)^-1/2 = 2 Any help would be very much appreciated. Thank you1 solutions Answer 307141 by Gogonati(809)   on 2011-05-06 15:11:01 (Show Source): You can put this solution on YOUR website!,multiply both sides by =>. Raise to the second power both sides of equation:, set the equation to zero:, substitute and get a quadratic equation: , solving this equation we find:y=5 and y=5/4. Knowing that, , get and Also from , we get and Thus, the solution set is:[ , , , ]
 Quadratic_Equations/445946: 6^2+3x-18=01 solutions Answer 307073 by Gogonati(809)   on 2011-05-06 09:21:37 (Show Source): You can put this solution on YOUR website! You easy can solve the equivalent equation: and find the solution: x=-2 and x=2/3.
 Points-lines-and-rays/445924: The equation of a circle is (x - 3)2 + (y + 2)2 = 25. The point (8, -2) is on the circle. What is the equation of the line that is tangent to the circle at (8, -2)? 1 solutions Answer 307072 by Gogonati(809)   on 2011-05-06 09:11:11 (Show Source): You can put this solution on YOUR website!First we find the slope of the line which passes through the (8, -2) and center of the circle (3,-2). This line contains the radius and is perpendicular to the tangent line at (8, -2). The slope is:, since its slope is zero the line is parallel to the x-axis, and its equation is: y=-2. The equation of the tangent line at (8, -2) will be: x=8. Answer:The equation of the line is x=8.
 Polynomials-and-rational-expressions/445940: Can someone please help me with the problem below? Thank you very much. Solve (2+ √5) (2-√5) 1 solutions Answer 307070 by Gogonati(809)   on 2011-05-06 08:47:30 (Show Source):
 Polygons/445920: The measures of 5 of the interior angles of a hexagon are: 130°, 120°, 80°, 160°, and 155°. What is the measure of the largest exterior angle? 1 solutions Answer 307069 by Gogonati(809)   on 2011-05-06 08:44:12 (Show Source): You can put this solution on YOUR website!The sum of interior angels of hexagon is 720 degree, the measure of the unknown angel of hexagon will be:720-645=75 degree. The supplement of 75 degree will be the largest exterior angle of our hexagon thus,180-75=105 degree.
 expressions/445911: Given that 8^x-1/3^2x = 2^3x+1/54^x , evaluate 6^x .1 solutions Answer 307068 by Gogonati(809)   on 2011-05-06 08:33:33 (Show Source): You can put this solution on YOUR website!=> Dividing both sides by:, we get:=> =>=>=>.
 Polygons/445841: the shape is a pentagon. if you have an apothem of 6 and your area of the the shape is 130.8 cm 2[ squared ] how would you find the perimeter?1 solutions Answer 307063 by Gogonati(809)   on 2011-05-06 07:32:46 (Show Source): You can put this solution on YOUR website!The area of a regular pentagon is given by formula:, where p is the perimeter and a the apothem.Substituting in our formula we have: => cm.
 Polynomials-and-rational-expressions/445447: The area of a triangle is 270. It has a base of 15 and a height of 12x. What is the area of a circle with a radius of 2x? 1 solutions Answer 306923 by Gogonati(809)   on 2011-05-05 14:59:13 (Show Source): You can put this solution on YOUR website!The area of triangle is half of the base and height product. , solving this equation we get: The area of the circle with radius 6cm is: cm^2.
 Trigonometry-basics/445499: find all solutions on the interval 0 ≤x≤2pi : sin^(2)x-3cos^(2)x=01 solutions Answer 306919 by Gogonati(809)   on 2011-05-05 14:47:33 (Show Source): You can put this solution on YOUR website!, substitute , and get: => => . The last equation is equivalent with two equations: and . The solution for the first equation is: and . The solution for the second equation is: and .
 Polynomials-and-rational-expressions/445519: (2s^2 - 9y)(2s^2 + 9y)1 solutions Answer 306913 by Gogonati(809)   on 2011-05-05 14:28:59 (Show Source):
 Expressions-with-variables/445526: 125x^3+2161 solutions Answer 306911 by Gogonati(809)   on 2011-05-05 14:25:52 (Show Source):
 Volume/443127: A sphere and a cube have same volume. Find the ratio of the lenght of the side of the cube to the radius of the sphere.1 solutions Answer 305692 by Gogonati(809)   on 2011-05-01 08:28:24 (Show Source): You can put this solution on YOUR website!As you know the volume of the sphere with radius r is:, and the volume of the cube with length a is:. To find the ratio , we know that , substituting: => => , and, a/r=cubed root of or
 Surface-area/443139: Sean drew a circle with an area of 254.34 square centimeters.What is the diameter of Sean's circle.1 solutions Answer 305689 by Gogonati(809)   on 2011-05-01 08:05:28 (Show Source): You can put this solution on YOUR website!As you know the area of the circle given by the formula:, where r is the radius of the circle.Substitute and get: => , and , where D is the diameter of the circle.
 Volume/443142: what is the length and width of a square prism that`s volume is 0.5L 1 solutions Answer 305683 by Gogonati(809)   on 2011-05-01 07:51:47 (Show Source): You can put this solution on YOUR website!As you know and . The volume of square prism is:, where a is the dimension of square prism: a=cubed root of 500, a=7.94 cm.
 Quadratic_Equations/443133: What is the domain and sketch the graph of the reducible function. f(x) = (x^2 -25) / (2x -10). 1 solutions Answer 305679 by Gogonati(809)   on 2011-05-01 07:41:41 (Show Source): You can put this solution on YOUR website!In my opinion since the function is reducible, first we reduce the function and after find the domain and sketch the graph. , which is the linear function on its slope-intercept form. We know its domain is the set of all real numbers and the graph the line:y=x/2+5/2.
 Quadratic_Equations/443130: Hey guys, So I was on your website, practicing solving quadratics by completing the square (as you do) and I ran in to a problem. I had done this: (where the nines are b/2^2) What do I do now that there's a negative number on the right side? I can't square root both! HELP!! 1 solutions Answer 305674 by Gogonati(809)   on 2011-05-01 07:29:11 (Show Source): You can put this solution on YOUR website!If you find the determinant of this quadratic equation . We answered that this quadratic equation has no real solution. If you know the complex numbers you can find the complex roots. and where .
 Angles/442472: What values are there of the six trigonometric functions of an angle Q in standard position whose terminal side passes through (1,2)?1 solutions Answer 305200 by Gogonati(809)   on 2011-04-29 15:05:29 (Show Source): You can put this solution on YOUR website!Since the terminal side passes through (1, 2), the legs of the right triangle are 1 and 2 and its hypotenuse is .If angel Q=x we get: ; ; ; ; and .
 Radicals/442422: 4 sq rt 6/sq rt30 simplfy by rationalizing the denominator1 solutions Answer 305192 by Gogonati(809)   on 2011-04-29 14:51:34 (Show Source):
 Travel_Word_Problems/442438: How long would it take for a one mile long frieght train going 15 m.ph. to go through a one mile tunnel?1 solutions Answer 305191 by Gogonati(809)   on 2011-04-29 14:44:24 (Show Source): You can put this solution on YOUR website!Since the train and the tunnel are respectively one mile long, the train must travel two miles to pass the tunnel. Since its speed is 15 mph to travel 2 miles need 2/15 h or 8 minutes.
 Inequalities/442469: -6< 1/4 (3-x)<12 1 solutions Answer 305185 by Gogonati(809)   on 2011-04-29 14:30:01 (Show Source): You can put this solution on YOUR website!Multiply the double inequality by 4:, adding -3 we get: , multiplying by -1 and reversing the signs of inequalities we get the solution:.
 Numeric_Fractions/442467: What is the sum of the 7 over 8 and 1 over 4?1 solutions Answer 305180 by Gogonati(809)   on 2011-04-29 14:19:29 (Show Source): You can put this solution on YOUR website!Add the fractions: The sum is an improper fraction .
 Graphs/442454: How do you graph y is greater than x AND y is less than -x I have the answer, but I don't get it.1 solutions Answer 305176 by Gogonati(809)   on 2011-04-29 14:15:06 (Show Source): You can put this solution on YOUR website!y>x is an inequality, and its boundary line is y=x, which is the bisector of first and third quadrant. y<-x is also an inequality, and its boundary line is y=-x, which is the bisector of the second and fourth quadrant. The solution set of y>x is the region above the line y=x, and the solution set of y<-x is the region below the line y=-x.