For all values of x, x² + 6x - 2 = (x+p)² + q Find the value of p and the value of q.

Mathematics

1 answer:

Vlad [161]2 years ago

3 0

Step-by-step explanation:

${x}^{2} + 6x - 2 = {x}^{2} + 2px + {p}^{2} + q$

$2p = 6$

${p}^{2} + q = - 2$

$p = 3$

${3}^{2} + q = - 2$

$q = - 11$

p=3, q=-11

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Step-by-step explanation:

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The area of the sector formed by the 110 degree central angle is 50 units squared. What is the circumference of the circle

Mama L [17]

Answer:

The circumference of the circle is $C=45.346 \:units$ .

Step-by-step explanation:

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The formula used to calculate the area of a sector of a circle is:

$A_{sector}=\frac{central \:angle}{360} \cdot {Area \:of \:whole \:circle}\\\\A_{sector}=\frac{\theta}{360} \cdot \pi r^2$

The circumference of a circle is the distance around the outside of the circle and its given by

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We know the central angle $\theta$ = 110º and the area of the sector 50 units squared.

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$50=\frac{110}{360} \cdot \pi r^2\\\\\frac{110}{360}\pi r^2=50\\\\\frac{11\pi }{36}r^2=50\\\\11\pi r^2=1800\\\\r^2=\frac{1800}{11\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{1800}{11\pi }},\:r=-\sqrt{\frac{1800}{11\pi }}$