Sec[sin-1 square root of 3 over 2]

√3/2

Step-by-step explanation:

Sin[sin⁻¹ (√3/2)]

sin⁻¹ (√3/2 = 60°

60° is the acute angle, in the first quadrant

Therefore;

Sin[sin⁻¹ (√3/2)] = sin 60° ; since sin⁻¹ (√3/2 = 60°

Sin 60° = √3/2

Therefore, the answer = √3/2

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.