Solve the system of equations below. Enter your answer in the boxes.

1 answer:

3 0

Simplifying
8a + 12b = 92

Solving
8a + 12b = 92

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-12b' to each side of the equation.
8a + 12b + -12b = 92 + -12b

Combine like terms: 12b + -12b = 0
8a + 0 = 92 + -12b
8a = 92 + -12b

Divide each side by '8'.
a = 11.5 + -1.5b

Simplifying
a = 11.5 + -1.5b

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The circumference of the ellipse approximate. Which equation is the result of solving the formula of the circumference for b?

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Answer:

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

Step-by-step explanation:

Given - The circumference of the ellipse approximated by $C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }$ where 2a and 2b are the lengths of 2 the axes of the ellipse.

To find - Which equation is the result of solving the formula of the circumference for b ?

Solution -

$C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }\\\frac{C}{2\pi } = \sqrt{\frac{a^{2} + b^{2} }{2} }$

Squaring Both sides, we get

$[\frac{C}{2\pi }]^{2} = [\sqrt{\frac{a^{2} + b^{2} }{2} }]^{2} \\\frac{C^{2} }{(2\pi)^{2} } = {\frac{a^{2} + b^{2} }{2} }\\2\frac{C^{2} }{4(\pi)^{2} } = {{a^{2} + b^{2} }$