Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y = 3, x = 4−(y−1)^2; about the x-axis.

Simplify 6sin θsec θ. choices a) 6 tan θ b) 6 cos θ c) 6 cot θ d) 6

Ascientist has 50 grams of a radioactive element. the amount of radioactive element remaining after t days can be determined using the equation (1) after two days the scientist receives a second shipment of 50 grams of the same element. the equation used to represent the amount of shipment 2 remaining after t days is 10) - 50 which of the following is an equivalent form of the expression for the amount remaining in shipment 2? what’s the answer?

Triangles abc and dfg are given. find the lengths of all other sides of these triangles if: b ∠a≅∠d, ab·dg=ac·df, ac=7 cm, bc=15 cm, fg=20 cm, and df-ab=3 cm.