Question

the area of a circle is A = (px² + 6xp + 9p)m². find the radius of the circle. [ hint: (a²+2ab+b²) = (a+b)²]​

Answer 1

Answer:

x+3

Step-by-step explanation:

Step-by-step explanation:$p {x}^{2} + 6xp + 9 {p} \\ ={( \sqrt{p} \times x)}^{2} + 2 \times( 3 \times \sqrt{p} ) \times \sqrt{p} + (3 \times \sqrt{p} )^{2} \\ = (\sqrt{p} x + 3 \sqrt{p} )^{2}$

Step-by-step explanation:$p {x}^{2} + 6xp + 9 {p} \\ ={( \sqrt{p} \times x)}^{2} + 2 \times( 3 \times \sqrt{p} ) \times \sqrt{p} + (3 \times \sqrt{p} )^{2} \\ = (\sqrt{p} x + 3 \sqrt{p} )^{2}$$r = \sqrt{ \frac{area}{\pi} } = \sqrt{ \frac{ {( \sqrt{p} x + 3 \sqrt{p} ) }^{2} }{\pi} } \\ = \frac{ \sqrt{p} x + 3 \sqrt{p} }{ \sqrt{\pi} } = \frac{ \sqrt{p} (x + 3)}{ \sqrt{\pi} } = (x + 3) \times \sqrt{ \frac{p}{\pi} }$

Step-by-step explanation:$p {x}^{2} + 6xp + 9 {p} \\ ={( \sqrt{p} \times x)}^{2} + 2 \times( 3 \times \sqrt{p} ) \times \sqrt{p} + (3 \times \sqrt{p} )^{2} \\ = (\sqrt{p} x + 3 \sqrt{p} )^{2}$$r = \sqrt{ \frac{area}{\pi} } = \sqrt{ \frac{ {( \sqrt{p} x + 3 \sqrt{p} ) }^{2} }{\pi} } \\ = \frac{ \sqrt{p} x + 3 \sqrt{p} }{ \sqrt{\pi} } = \frac{ \sqrt{p} (x + 3)}{ \sqrt{\pi} } = (x + 3) \times \sqrt{ \frac{p}{\pi} }$well this is the final answer if p is a random variable. but if you wanted to refer to pi by p the the answer is simply x+3

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