Find two numbers such that their product, sum and difference are in the ratio 5:4:1'

3 1/3 and 2

Step-by-step explanation:

Let the numbers be x and y  and let z be the constant of proportion. Then

xy = 5z  (1)

x + y = 4z (2)

x - y = z (3)     Adding (2) and (3)

2x = 5z

x = 5z/2   (4)

Substituting for x in equation 1:

5z/2 *  y = 5z

y = (5z * 2) / 5z = 2.

Substituting for  y in equations (2) and (3):

x + 2 = 4z

x - 2 = z            Subtracting:

4 = 3z

z = 4/3.

Substituting for z in equation (4)

x =  5(4/3) /2

x = 20/6 = 10/3 = 3 1/3.

So the 2 numbers are  3 1/3 and 2.

Checking the results:

xy = 2 * 10/3 = 20/3 = 5 * 4/3 = 5z

x + y = 10/3 + 2 = 16/3 = 4 * 4/3 = 4z.

x - y = 10/3 - 2 = 4/3 = z.

cosine

step-by-step explanation:

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.