Farmer John has goats and chickens on his farm. The total number of 4 legged goats and 2 legged chickens is 18. His son, Joseph counted 56 animal legs on the farm. Represent this situation with a system of linear equations and find the number of goats and chickens on the farm.

There are 10(4-legged) goats and 8(2-legged) chickens.

Step-by-step explanation:

The total number of 4 legged goats and 2 legged chickens is 18.

Therefore: x+y=18

His son, Joseph counted 56 animal legs on the farm.

Therefore: 4x+2y=56

Solving the two equations simultaneously

x+y=18

4x+2y=56

From the first equation, x=18-y

Substitute x=18-y into the second equation

4x+2y=56

4(18-y)+2y=56

72-4y+2y=56

72-56=4y-2y

16=2y

y=8

Recall: x=18-y

           x=18-8=10

x=10, y=8

There are 10(4-legged) goats and 8(2-legged) chickens.

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)