A huge ice glacier in the Himalayas initially covered an area of 45 square kilometers. Because of changing weather patterns, this glacier begins to melt, and the area it covers begins to decrease exponentially. The relationship between A, the area of the glacier in square kilometers, and t, the number of years the glacier has been melting, is modeled by the following equation.


How many years will it take for the area of the glacier to decrease to 15 square kilometers?

Give an exact answer expressed as a natural logarithm.

Which must be true in order for the relationship △zyv ~ △xwv to be correct? zy ∥ wx ∠z ≅ ∠y and ∠w ≅ ∠x zv ≅ vy and wv ≅ vx ∠z ≅ ∠x and ∠w ≅ ∠y

The graph is supposed to show f(x) = 3 sin (x/4+1) - 1/2. which of the following are correctly represented in the graph? select two of the following that apply.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)