Algebra problem 001
Solve for when the radius of a cone equals , the height equals and the slant height equals .
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1 solution
We can put this problem into the 2nd dimension and solve for x :
Using the Pythagorean Theorem, we can set up an equation: x 2 + ( x − 7 ) 2 = ( x + 1 ) 2 And simplify into a trinomial that equals 0: x 2 − 1 6 x + 4 8 = 0 Then, we can factor the trinomial into 2 binomials to solve for x : ( x − 1 2 ) ( x − 4 ) = 0 If one of the factors is 0, then the entire equation is true. Therefore, we can set each of the binomials equal to zero: x − 1 2 = 0 ; x − 4 = 0 Solving for both equations, we get 2 positive solutions of 1 2 and 4 .
Note : 4, in the real world, would not be a valid solution. This is because you would have a height of -3, which is impossible.