Use the method of lagrange multipliers to find a. the minimum value of x + y, subject to the constraints xy=64, x> 0, y> 0

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ab=9, and ac=12, find hc.

An appliance store sells a washer-dryer combination for $1800. if the washer costs $300 more than the dryer, find the cost for each appliance.

The random variable x has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 show that k = 2/9 find 2 e(x), 3 the mode of x, 4 the cumulative distribution function f(x) for all x. 5 evaluate p(x ≤ 2.5). 6 deduce the value of the median and comment on the shape of the distribution.