Answer:
3125*k^9 + y^3 is an integer my closure property.
but 5^(1/3) is not an integer, which forces z to be irrational.
Note that there is no way an integer value can rationalize 5^(1/3)
Step-by-step explanation:
x^3 = 25z^3 - 5y^3
x^3 = 5 ( 5z^3 - y^3)
x = (5 ( 5z^3 - y^3) )^(1/3) must be an integer
= 5^(1/3) * (5z^3 - y^3)^(1/3)
Then (5z^3 - y^3)^(1/3) = 25*k^3 for some integer k
5z^3 - y^3 = 15625*k^9
5z^3 = 15625*k^9 + y^3
z^3 = 3125*k^9 + (1/5)*y^3
z = ( 3125*k^9 + (1/5)*y^3 )^ ( 1/3)
B) obtuse triangle
Hope this helps!
Answer:
A ≈ 183 cm²
Step-by-step explanation:
Step 1: Find the area of the 2 circles
A = πr²
r = 6/2 = 3
A = π(3)²
A = 9π
Since there are <em>2</em> circles, 9π(2) = 18π
Step 2: Find area of <em>entire </em>rectangle
A = lw
A = 12(20)
A = 240
Step 3: Subtract the area of the circles from the area of the entire rectangle
240 - 18π
Shaded area = 183.451 cm²
And we have our answer!
Answer:
Maximum value of f(x,y) at (10,13)=74
Minimum value of f(x,y) at (10,0)=-56
Step-by-step explanation:
We are given that
Vertices are (0,0),(10,0) and (10,13)
Substitute x=0 and y=0
Substitute x=10 and y=0
Substitute x=10 and y=13
Maximum value of f(x,y) at (10,13)=74
Minimum value of f(x,y) at (10,0)=-56
