Find the volume of the given solid. Enclosed by the paraboloidz = 7x2 + 4y2and the planesx = 0, y = 2, y = x, z = 0

The volume of the solid is:

Step-by-step explanation:

Consider the given paraboloid and the planes:

z = 7x² + 4y², x = 0, y = 2, y = x , z = 0

The region of  type -II can be expressed as:

D = {(x,y)| 0 ≤ x ≤ y, 0 ≤ y ≤ 2}

Suppose f(x,y) is continous  on type-I region D such that:

D = {(x,y) | a ≤ y  ≤ b, g₁(y)  ≤ x  ≤ g₂ (y) }

Then, we can compute the double integral as follows:

Thus, the volume of the solid is:

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17