Find cot x if sin x cot x csc x = √2.

The answer is (b) ⇒ cotx = √2

Step-by-step explanation:

∵ (sinx) (cotx) (cscx) = √2

∵ cotx = cosx/sinx

∵ cscx = 1/sinx

∴ (sinx)(cosx/sinx)(1/sinx) = √2

∴ cosx/sinx = √2

∴ cotx = √2

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: