Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations. z = xy, z = 0, y = x, x =1, first octant.

1/8

Step-by-step explanation:

Given:

z = xy

z = 0

y = x

x =1

To find:

volume of the solid bounded by the graphs of the equations

Solution:

Compute integral of volume in the first octant:

= x y²/2 |ˣ₀  dx

= 1/2   x y² |ˣ₀  dx

= 1/2   x (x²-0²) dx

= 1/2   x³dx

=   |¹₀

= (1/2) (x⁴/4) |¹₀

= 1/8 x⁴ |¹₀

= 1/8 (1⁴ - 0⁴)

= 1/8 (1)

V = 1/8

c. 16 units

step-by-step explanation:

mark brainliest and have a great day!

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500