used for one of its products by enlarging the radius of the cylinder. The height must be 20 centimeters. The new volume of the cylinder is given by the equation V(x)=20π(5+x)2. where x is the additional length of the radius in centimeters. Which of the following equivalent expressions displays the current volume of the cylinder as a constant or coefficient?(A) π(20x2+200x+500)(B) 20π(x2+10x+10)+300π(C) 20π(x2+10x+25)(D) 20πx2+200πx+500π
Q. used for one of its products by enlarging the radius of the cylinder. The height must be 20 centimeters. The new volume of the cylinder is given by the equation V(x)=20π(5+x)2. where x is the additional length of the radius in centimeters. Which of the following equivalent expressions displays the current volume of the cylinder as a constant or coefficient?(A) π(20x2+200x+500)(B) 20π(x2+10x+10)+300π(C) 20π(x2+10x+25)(D) 20πx2+200πx+500π
Expand Expression: Step 1: Given V(x)=20π(5+x)2. Expand the expression.
Multiply by 20π: Step 3: Multiply the expanded form by 20π. V(x)=20π(25+10x+x2)
Distribute 20extextpi: Step 4: Distribute 20extextpi to each term inside the parentheses. V(x)=20extextpiimes25+20extextpiimes10x+20extextpiimesx2V(x)=500extextpi+200extextpix+20extextpix2
Compare with Choices: Step 5: Compare the expanded form with the given choices. (A) π(20x2+200x+500) (B) 20π(x2+10x+10)+300π (C) 20π(x2+10x+25) (D) 20πx2+200πx+500π
Identify Correct Choice: Step 6: Identify the correct choice that matches 500extπ+200extπx+20extπx2. The correct choice is (D) 20extπx2+200extπx+500extπ.
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