Is the answer a or b and why?

B

Step-by-step explanation:

The area between the curves y = d and y = f(x), between the limits x=a and x=b, is:

∫ₐᵇ (d − f(x)) dx

Alternatively, the area between the curves x = f(y) and x = a, between the limits y = c and y = d, is:

∫ᵈ (f(y) − a) dy

Answer A would give you the area between x = f(y) and the y-axis.  It needs to include the − a term to be correct.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47