Answer:
V=5.333cubit unit
Step-by-step explanation:
this problem question, we are required to evaluate the volume of the region bounded by the paraboloid z = f(x, y) = 3x² + y² and the square r: -1≤ x ≤ 1, -1 ≤ y ≤ 1
The question can be interpreted as z = f(x, y) = 3x² + y² and the square r: -1≤ x ≤ 1, -1 ≤ y ≤ 1 and we are told to evaluate the volume of the region bounded by the given paraboloid z
The volume V of integral evaluated along the limits of x and y for the 2-D figure, can be evaluated using the expression below
V = ∫∫ f(x, y) dx dy then we can now substitute and integrate accordingly.
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLATION:
4 - 1/x (16)-1/x 2
4x-18/x
In solving equations, each must have vales of x and y. X is any number and Y is the output of any number. If you substitute x for a number, you can solve the equation for y.
Answer:
y ≤-7
Step-by-step explanation:
-8y ≥56
Divide each side by -8. Remember to flip the inequality
-8y/-8 ≤56/-8
y ≤-7
Answer:
(a) yes
(b) no; see below
Step-by-step explanation:
(a) Integer roots of the quartic will be integer divisors of 6. One of the divisors of 6 is 3, so 3 is a possible root.
(b) In order for 3 to be a double root, it would have to be a double factor of 6. The only integer factors of 6 are 1, 2, 3, 6. (3² = 9 is not one.)
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The quartic can be written as ...
k(x -a)(x -b)(x -c)(x -d) . . . . . where a, b, c, d, k are integers
The constant term will be kabcd, of which each of the roots is a factor. If the constant is 6 and one root is d=3, then we must have
kabcd = 3kabc = 6
kabc = 6/3 = 2
Among these four integer factors, there must be an even number of minus signs, and one that has the value ±2. Another root whose value is 3 will not satisfy the requirements.
