4 years ago

Solve for y in the circle below.

Mathematics

1 answer:

mart [117]4 years ago

8 0

Answer:

y = 40.

Step-by-step explanation:

The opposite sides of a cyclic quadrilateral sum to 180, so:

3y + 2y - 20 = 180

5y = 180 + 20 = 200

y = 40.

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inessss [21]

One thing you could try is to set $x=\sqrt y$ . This makes $y=x^2$ , so that $\mathrm dy=2x\,\mathrm dx$ , and $y^2=x^4$ . So the integral is

$\displaystyle\int\frac x{x^4+1}\,\mathrm dx=\frac12\int\frac{\mathrm dy}{y^2+1}=\frac12\arctan y+C=\frac12\arctan(x^2)+C$

A "trickier" way to do it is to write

$x^4+1=(x^2+\sqrt2x+1)(x^2-\sqrt2x+1)$

so you could decompose the integrand into partial fractions. But that's more work than needed.

4 0

4 years ago

Please help! I would also like an explanation on how you find the answer if possible.

pentagon [3]

check the picture below.