264 is the correct replacement for the question mark
Answer:
Area = 32/3
Step-by-step explanation:
x = u
²
y = uv
z = 12v
²
0 ≤ u ≤ 2
0 ≤ v ≤ 1
Since ru = <2u, v, 0> and rv = <0, u, 24v>, we have
Where ru is the differentiation of x, y, z with respect to u and rv is the differentiation of x, y, z wit respect to v.
we find the cross product of ru and rv
ru × rv = 24v²i - 48uv²j + 2u²k
absolute value of ru × rv = 2u² + 24v²
We can now find the area
∫₀² du ∫₀¹ dv (2u² + 24v²) = ∫₀² du [2u²v + 8v³]₀¹ = 32/3
Detailed description can be found in the attachment
You have to distribute the minus sign to the second parenthesis, changing the sign of every term:
X = 25 dollar items and y = 15 dollar items
x + y = 72....x = 72 - y
25x + 15y = 1380
25(72 - y) + 15y = 1380
1800 - 25y + 15y = 1380
-25y + 15y = 1380 - 1800
-10y = - 420
y = -420/-10
y = 42
x + y = 72
x + 42 = 72
x = 72 - 42
x = 30
so they sold 30 twenty five dollar items (x) and 42 fifteen dollar items (y)
A circumscribed circle is a circle which passes through all the points of a triangle or polygons in general. The center of this circle is called the circumcenter.
so b) circumcenter