Find an equation for the level curve of the function f (x, y) that passes through the given point. f (x, y) = 64 - 4x2 - 4y2, (3 underroot 2, 3 underroot 2)  

the level curve of the function that passes through the point is x² - y² = - 36

Step-by-step explanation:

Given that;

the function is;

f(x, y) = 64 - 4x² - 4y²

At the point P = ( 3√2, 3√2)

so we have

f( 3√2, 3√2) = 64 - 4(3√2)² - 4(3√2)²

= 64 - 72 - 72 = -80

so the level curve containing the point P = ( 3√2, 3√2) is the curve,

f(x,y) = -80

64 - 4x² - 4y² = -80

divide through by 4

4x² - 4y² = -80 - 64

4x² - 4y² = 144

divide through by 4

x² - y² = - 36

therefore, the level curve of the function that passes through the point is,

x² - y² = - 36

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720

the distance between the school and her home is 3.6km.

12 mins = 0.2 hours = 1/5 hour

54 ÷ 3 = 18km per hour

1/5 of 18 = 3.6km per 12 mins