You are flying from Joint Base Lewis-McChord JBLM to an undisclosed location 24km south and 212km east. Mt. Rainier is located approximately 56km east and 40km south of JBLM. If you are flying at a constant speed of 800km/hr, how long after you depart JBLM will you be closest to Mt. Rainier?

A tug of war has teachers and the principal challenging the students! In the first round 3 teachers and 5 students came to a draw. In the second round the principal joined the students. The principal and 10 students came to a draw against 8 teachers in the second round. Assuming each teacher has the same strength, and each student has the same strength, who will win the tie breaking round if it is: 15 students and the principal challenging 10 teachers? Show your thinking.

The volume created by revolving the area created from 5x-5, x^.5-1 and x=5 around x=5. Please show both shell and washer method. Answer for shell and washer should be the same.

Determine if the following series converge or diverge. If it converges, find the sum.

a. ∑n=(3^n+1)/(2n) (upper limit of sigma∞, lower limit is n=0)

b.∑n=(cosnπ)/(2) (upper limit of sigma∞ , lower limit is n= 1

c.∑n=(40n)/(2n−1)^2(2n+1)^2 (upper limit of sigma ∞ lower limit is n= 1

d.)∑n = 2/(10)^n (upper limit of sigma ∞ , lower limit of sigma n= 10)

0. Let?:?2(R)⟶?1(R)bedefinedby?(?+?x+?x²)=(?+?)+(?−?)x,where ?, ?, ? are arbitrary constants.
   a. DeterminethetransformationmatrixforT.(6pts)
   b. Find the basis and the dimension of the Kernel of T. (10pts)

   c. Find the basis and the dimension of the Range of T. (10pts) d. Determine if T is one-to-one. (7pts)
   e. DetermineifTisonto.(7pts)

(a) Show that the lines
r 1 (t) = (2,1,−4) + t(−1,1,−1) and r 2 (s) = (1,0,0) + s(0,1,−2)
are skew.
(b) The two lines in (a) lie in parallel planes. Find equations for these two planes. Express your
answer in the form ax+by+cz +d = 0. [Hint: The two planes will share a normal vector n. How would one find n?]
would one find n?]

In an effort to replace the destruction of trees, five regions of the US have been tracking the annual rate of trees being planted (per thousand) in each region and the annual rate of trees being destroyed (per thousand). Additionally, the tree population (in thousands) by region has been recorded for five different years. The data is given in the tables below. Determine the number of trees planted and the number destroyed in each of the years listed.

Illustrate with a picture showing that the following are simply not true in Hyperbolic Geometry

a). The area of a triangle can be made arbitrarily large

b). The angle sum of all triangles is a constant.

Find Cartesian equation of a plane through the point a and parallel to the given vectors p and q.

a = (1, - 1, 3) , p= ‹2, -1, 0›, q= ‹2, 0, 6›.

(1 point) Let F=−3yi+4xjF=−3yi+4xj. Use the tangential vector form of Green's Theorem to compute the circulation integral ∫CF⋅dr∫CF⋅dr where C is the positively oriented circle x2+y2=25x2+y2=25.

ty'''+4y''=t^2cost

Can somebody explain to me Derivative of Hyperbolic Functions? May I know its importance and applications in real life? I need it for my essay. Thank you.

PS. I can't find it on the internet.