How to find the value of k ?

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Answer 1 · 2017-08-29T11:58:25

# k=10.#

The Volume of the tank#"=length"xx"breadth"xx"height,"#

#=2x(k-x)=2kx-2x^2, (k, a const.)# which is a fun. of #x,# so,

let us write, #V(x)=2kx-2x^2.#

We are given that, #V_max=50.#

But, for #V_max, V'(x)=0, and, V''(x) < 0.#

# V'(x)=0 rArr 2k-4x=0 rArr x=(2k)/4=k/2.#

# V'(x)=2k-4x rArr V''(x)=-4 < 0,# meaning that,

#x=k/2" gives "V_max.#

#:. V_max=V(k/2)=2(k/2)(k-k/2)=k^2/2.#

But, #V_max=50. :. k^2/2=50, or, k^2=100," giving, "k=+10.#

[#k=-10,# is not admissible, as it being the height of the tank.]