Evaluate the line integral ∫CF⋅dr, where F(x, y,z)=−5xi−4yj−3zk and C is given by the vector function r(t)=⟨sint, cost, t⟩, 0≤t≤3π/2.

How many triangles can be drawn with side lengths 4 centimeters, 4.5 centimeters, and 9 centimeters? explain

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)