From an external point E, tangents and are drawn to . If m

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What will be an ideal response?

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102°

Mathematics

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the velocity vector.r(t) = (cot t)i + (csc t)j

A. v = (-csc2 t)i - (cot t csc t)j B. v = (csc2 t)i + (cot t csc t)j C. v = (sec2 t)i + (tan t sec t)j D. v = (-sec2 t)i - (tan t sec t)j

A balloon is leaking air, and the rate of change in volume is proportional to the volume.  Let V denote the volume, in liters, of air in the balloon after t seconds, and take -0.03 to be the constant of proportionality.

? A: Write an equation of change satisfied by . ? B: If there are initially 8 liters of air in the balloon, find a formula that gives V as a function of t. Write your answer using the alternative form for an exponential function. ? C: How long will it take for 10% of the initial volume of air to leak from the balloon? Round your answer to two decimal places. What will be an ideal response?

Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form.(4(cos 45° + i sin 45°))5

A. -724.077 - 724.077i B. -2.828 - 2.828i C. -724.077 + 724.077i D. -2.828 + 2.828i

Solve the problem.Suppose that a school of fish in a pond grows according to the exponential law  and suppose that the size of the colony triples in 24 days. If the initial size of the school was 50, when will the school contain 200 fish? Enter your answer exactly in the form  

Fill in the blank(s) with the appropriate word(s).