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The total cost of producing x items of product A and y items of product B is
"TC=22x^2+8y^2-5xy"
If the firm is committed to producing 20 items in total, write down the constraint connecting x and y. Hence find the number of each type that should be produced to minimise costs.
Find the maximum value of z=6x−3x2 +2y
subject to the constraint
y − x2 = 2
Consider a particle moving along the x-axis where x(t) is the position of the
particle at time t, x′(t) is its velocity, and x
′′(t) is its acceleration.
If x(t) = t3
− 6t2 + 9t − 2, 0 ≤ t ≤ 5
(a) Find the velocity and acceleration of the particle. (b) Find the open
t-
intervals on which the particle is moving to the right. (c) Find the velocity of
the particle when the acceleration is 0
Find the angle of the largest right circular cone which can be inscribed in a sphere of
radius 9 inches.
At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the
greatest angle.
For a 95% confidence level, what are the critical values for a one-tailed test?
the base of a right prism is an equilateral triangle whose edges is 10cm each and its lateral edge is 80 cm. Determine the total surface area of the prism in cm2
Find all combinations of truth values for p, q and r for which the statement ¬p ↔ (q ∧ ¬(p → r)) is true.
Find the general solution of the DE(y^2-2xy+6x)dx-(x^2-2xy+2)dy=0
2. A researcher intends to estimate the effect of a drug on the scores of human subjects
performing a task of psychomotor coordination. The members of a random sample of 9
subjects were given the drug prior to testing. The mean score in this group was 9.78, and
the sample variance was 17.64. An independent random sample of 10 subjects was used as
a control group and given a placebo prior to testing. The mean score in this control group
was 15.10, and the sample variance was 27.01. Assuming that the population distributions
are normal with equal variances, find a 90% confidence interval for the difference between
the population mean scores.
