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3 years ago

Which equation represents the

Mathematics

1 answer:

pickupchik [31]3 years ago

8 0

Answer:

theta = 180 -(A +B)

Step-by-step explanation:

The sum of the angles of a triangle is 180

theta + A + B = 180

solve for theta

Subtract ( A + B) from each side

theta +A+B -(A +B) = 180 -(A +B)

theta = 180 -(A +B)

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Step-by-step explanation:

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3 years ago

Find all points on the circle (x^2) + (y^2) = 676 where the slope is 5/12

borishaifa [10]

Implicit defferentation

remember that dy/dx y= dy/dx

so
take derivitive of both sides
$2x+2y \space\ \frac{dy}{dx}=0$
solve for $\frac{dy}{dx}$
minus 2x both sides
$2y \space\ \frac{dy}{dx}=-2x$
divide both sides by 2y
$\frac{dy}{dx}=\frac{-2x}{2y}$
$\frac{dy}{dx}=\frac{-x}{y}$

when is the slope equal to $\frac{5}{12}$
solve for $\frac{dy}{dx}=\frac{5}{12}$
$\frac{dy}{dx}=\frac{5}{12}$
$\frac{5}{12}=\frac{-x}{y}$
$5y=-12x$
$y=\frac{-12}{5}x$
find where the circle and this line intersects

substitute $\frac{-12}{5}x$ for y
$x^2+(\frac{-12}{5}x)^2=676$
$x^2+\frac{144}{25}x^2=676$
$\frac{25}{25}x^2+\frac{144}{25}x^2=676$
$\frac{169}{25}x^2=676$
times both sides by $\frac{25}{169}$
$x^2=100$
sqrt both sides, take positive and negative roots
x=+/-10

sub back

$y=\frac{-12}{5}x$
$y=(\frac{-12}{5})(10) \space\ or \space\ (\frac{-12}{5})(-10)$
$y=\frac{-120}{5} \space\ or \space\ \frac{120}{5}$
$y=-24 \space\ or \space\ 24$

the points are (10,-24) and (-10,24)

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3 years ago