Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11).

Step-by-step explanation:

The standard form of hyperbola centered at origin is given by:

            ....[1]

where,

vertices and foci are and respectively.

As per the statement:

The hyperbola with vertices at (0, ±2) and foci at (0, ±11).

⇒a = 2 and c = 11

⇒ and

To find :

Using the equation:

then;

⇒

Substitute the given values in [1] we have;

Therefore, an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11) is,

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )