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Construct a relation on the set {a, b, c, d} that is
a. reflexive, symmetric, but not transitive.
b. irreflexive, symmetric, and transitive.
c. irreflexive, antisymmetric, and not transitive.
d. reflexive, neither symmetric nor antisymmetric, and transitive.
The price of lumber is typically a nonlinear distribution. Here are the current prices at a popular home improvement store for 2"*4" lumber in different lengths.
The edge of a cube was found to be 30 cm with a possible error in measurement of .1 cm. Use differentials to estimate the percentage error (to the nearest hundredth) in computing (a) the volume of the cube and (b) the surface area of the cube.
which of the following statements are true? justify your answers i) the contrapositive of "not a ⇒ not b' is "a&b', where a and b are two statements. ii) any set can be represented by the listing method
An open box is to be made out of a 8-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.
A rectangular billboard 5 feet in height stands in a field so that its bottom is 6 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x
x
feet from the billboard. Express θ
θ
, the vertical angle subtended by the billboard at her eye, in terms of x
x
. Then find the distance x
x
the cow must stand from the billboard to maximize θ
θ
.
P(3,-3) lies on the terminal arm of an angle in standard position.
a. Draw a sketch of the principal angle (θ) in standard position. Label θ AND the related acute
angle, RA. [2 marks]
b. Determine the exact primary trig ratios for θ. Show ALL your work. You do not need to
rationalize the denominator, but you must simplify your radical and your ratios. [5 marks]
c. Determine the values of the principal angle and related acute angle to the nearest degree.
Solve g(y)= 1/y over the interval (1,4)
The finite region bounded by the planes z = x, x + z = 8, z = y, y = 8, and z = 0 sketch the region in R3 write the 6 order of integration. No need to evaluate. clear writing please
Given the initial value problem x 0 1 − 2x1 − 3x2 = 0 x 0 2 + x1 + x2 = 0 x1(0) = √ 3, x2(0) = 0 , find x2(t). (a) x2(t) = e t 2 sin √ 3 2 t (b) x2(t) = e t cos 1 2 t + sin 1 2 t (c) x2(t) = −2e t 2 sin √ 3 2 t (d) x2(t) = 2e t 2 cos √ 3 2 t + sin √ 3 2 t ! (e) x2(t) = 2e t 2 sin √ 3 2 t
