Verify the identity.tan x(csc x - sin x) = cos x

What will be an ideal response?


tan x(csc x - sin x) = tan x ? csc x - tan x ? sin x =  ?  -  ? sin x =  -  =  =  = cos x

Mathematics

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Solve the problem.The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use Simpson's Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon.

A. 7,733 gal B. 8,850 gal C. 7,050 gal D. 7,725 gal

Mathematics

For the curve r(t), find an equation for the indicated plane at the given value of t.r(t) = (t - 4)i + (ln(sec t) - 1)j + 4k, -?/2 < t < ?/2; normal plane at t = 6?.

A. x = 4 - 6? B. x = 6? + 4 C. x = -6? - 4 D. x = 6? - 4

Mathematics

Suppose the total cost in maunufacturing x units of a certain product is C (x) dollars.

a. What does C'(x) measure? Give units. b. What can you say about the sign of C'? c. Given that C'(3000)=11, estimate the additional cost in producing the 3001st unit of the product.

Mathematics

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible.6a + 10a

A. -4a B. 30a C. 4a D. 16a

Mathematics