Using geometry, calculate the volume of the solid under z=9−x2−y2‾‾‾‾‾‾‾‾‾‾‾√ and over the circular disk x2+y2≤9.Using geometry,
calculate the volume of the solid under z=9−x2−y2‾‾‾‾‾‾‾‾‾‾‾√ and over the circular disk x2+y2≤9.
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Answer:
Step-by-step explanation:
Given the following expression shown in the picture:
You need to use a process called "Ratinalization".
By definition, using Rationalization you can rewrite the expression in its simplest form so there is not Radicals in its denominator.
Then, in order to simplify the expression, you can follow the following steps:
<em>Step 1</em>. You need to multiply the numerator and the denominator of the fraction by , which is the conjugate of the denominator
.
<em>Step 2</em>. Then you must apply the Distributive property in the numerator.
<em>Step 3</em>. You must apply the following property in the denominator:
Therefore, applying the procedure shown above, you get:
<em>Step 4</em>. You can observe that the expression can be simplified even more. Since:
You get: