Quad. 4.
x is positive & y is negative.
Answer:
Domain = {x : x ≠ 4 , -4} or (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)
Step-by-step explanation:
<u>TO FIND :-</u>
- Domain of

<u>SOLUTION :-</u>
Domain of a function is a value for which the function is valid.
The function
is valid until the denominator is 0.
So make sure that the denominator must not be 0.

Find the values of x for which the denominator becomes 0. To find it , you'll have to solve the above inequality.




We can say that <u>4 & -4 can't be domains</u> because these values will make the function undefined.
Now try putting values of x such that -4 < x < 4. You'll observe that the function will be valid for all those values of x between -4 & 4.
<u>CONCLUSION :-</u>
The function will be valid for any value of 'x' except 4 & -4. So in :-
Interval notation , it can be written as → (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)
Set builder notation , it can be written as → {x : x ≠ 4 , -4}
Answer:

Step-by-step explanation:
<u>The Volume of a Sphere
</u>
The volume of a sphere of radius r is given by:

A. )
If the diameter of the sphere is d, the radius is r=d/2. Substituting:

Operating

Simplifying

B.)
The diameter of the sphere is 2/3 cm, thus the volume is:

Operating:



Step-by-step explanation:
x³ + x² − 14x − 24
x³ + x² − 20x + 6x − 24
x (x² + x − 20) + 6 (x − 4)
x (x + 5) (x − 4) + 6 (x − 4)
(x (x + 5) + 6) (x − 4)
(x² + 5x + 6) (x − 4)
(x + 2) (x + 3) (x − 4)
The other two factors are x + 2 and x + 3.