p varies directly as (x^2+y^2+z^2). When x=1, y=2, z=3, then p=70. What is the value of p when x=-1, y=1, z=5?

Explanation

Given p = k(x^2+y^2+z^2). Substituting the initial values: 70 = k(1^2+2^2+3^2) \implies 70 = 14k \implies k = 5. For the new values, p = 5((-1)^2+1^2+5^2) = 5(1+1+25) = 5 \times 27 = 135.

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