A cup of coffee at 85 degrees Celsius is placed in a room at 25 degrees Celsius. Suppose that the coffee cools at a rate of 5 degrees Celsius per minute when the temperature of the coffee is 70 degrees. The differential equation describing this has the form dT/dt = k (T-A)

A= 25

k=?

Either from drawing the direction field (try Maple or by hand) or other intuitive means, the limiting value of T should be = 25

y=x+9

?

step-by-step explanation:

answer: apothems is your answer

step-by-step explanation: hope u get it right

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)