Prove that if x is a rational number and y is an irrational number,then x+y is an irrational number. If in addition, x≠0, then show that xy is an irrational number.
Define a relation T on R as follows: for all x and y in R, x T y if and only if x2=y2.
Then T is an equivalence relation on R.
(a) Prove that T is an equivalence relation on R.
(b) Find the distinct equivalence classes of T.
Find a vector function F whose graph is the curve of intersection of the hemisphere z=√4-x^2-y^2 and the curve y=x^2.
For what value of c, is the function continuous on (−∞, ∞)
f(x)={𝑐𝑥^2+2𝑥 𝑖𝑓 𝑥<2
𝑥^3−𝑐𝑥 𝑖𝑓 𝑥 ≥2
Consider a category five hurricane that has a maximum wind speed of 160 mph at the eye wall, 10 miles from the center of the hurricane. If the flow in the hurricane outside of the hurricane’s eye is approximated as a free vortex, determine the wind speeds at locations 20 mi, and 40 mi from the center of the storm.
Point R is on line segment QR. Given QR=3x-8, QS=3x, and RS=2x, determine the numerical lenght of RS.