The Height of a Hill (In Feet) Is Given By h

question 40

Multiple Choice

The height of a hill (in feet) is given by
$$h ( x , y ) = 30 \left( 14 - 5 x ^ { 2 } - 2 y ^ { 2 } + 3 x y + 30 x - 18 y \right)$$
where $x$ is the distance (in miles) east and $y$ is the distance (in miles) north of your cabin. If you are at a point on the hill 1 mile north and 1 mile east of your cabin, what is the rate of change of the height of the hill (a) in a northerly direction and (b) in an easterly direction?

• A) (a) \(570 \mathrm { ft } / \mathrm { mi }\), (b) \(690 \mathrm { ft } / \mathrm { mi }\)
• B) (a) \(- 570 \mathrm { ft } / \mathrm { mi }\), (b) \(690 \mathrm { ft } / \mathrm { mi }\)
• C) (a) \(690 \mathrm { ft } / \mathrm { mi }\), (b) \(570 \mathrm { ft } / \mathrm { mi }\)
• D) (a) \(690 \mathrm { ft } / \mathrm { mi }\), (b) \(- 570 \mathrm { ft } / \mathrm { mi }\)

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Definitions:

Macrosystems

The broadest context in ecological systems theory, encompassing societal norms, values, and laws that influence an individual's development.

Nuclear Families

Families consisting of parents (including single parents) and their children.

Extended Families

Families in which not only parents and their children but other kin—grandparents, cousins, nieces and nephews, or more distant family relations—share a household.

Allocaregiving

Child care and protection provided by group members other than the parents, usually other relatives.