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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.
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
According to one survey in India, 75% of Instagram users love REELS. Suppose that 25
Instagram users (randomly selected) have been approached in the university located in vile
parle. They have been asked about their status of like/ dislike the Instagram- REELS.
a) What is the probability that Exactly 15 of them would agree with the claim (or said they
love Insta-REELS)?
b) What is the probability that Exactly 20 of them would agree with the claim (or said they
love Insta-REELS)?
What is the probability that the 36 tires will have an
average of less than 16,000 miles until the tires begin
to wear out
A new machine is being considered to replace the old machine being used. This new machine was tested for 10 consecutive hours with the following output: 119, 122, 118, 122, 120, 124, 126, 125, 125, and 124. If the average output per hour using the old machine is 120 units, is the management justified in stating that the output per hour can be increased with the new machine? Use a 0.01 level of significance
: Let 𝑓(𝑥, 𝑦) = 𝑥^2 + 𝑦^3 . Find the slope of the line tangent to this surface at the point (-1, 1) and lying in the plane x = -1
