#2- for the curve given by 4x2+y2=48+2xy show that
dy/dx=y-4x/y-x

#3- for the curve given by 4x2+y2=48+2xy, find the positive y coordinate given that the xcoordinate is 2.

#4- for the curve given by 4x2+y2=48+2xy, show that there is a point p with x-coordinate 2 at which the line tangent to the curve at p is horizontal.

Step-by-step explanation:

A. The given curve is:

Hence proved.

B. The given curve is:

Put x=2, we get

Thus, y=-4,8

C. The given curve is:

To show point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal, consider

⇒

⇒

At y=8,

⇒8=4x

⇒x=2

The equation of the tangent is:

y-8=0(x-2)

⇒y=8.

Thus, at (2,80, therefore with  x-coordinate 2 the line tangent to the curve at P is horizontal.

the answer is a

step-by-step explanation:

because if you put 1 in to the square root of x it equals 300.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: