What is the equation of the circle with center (0, 0) that passes through the point (–4, –6)?

Mathematics

1 answer:

Vadim26 [7]2 years ago

4 0

If the center is in point P(a,b) and has a radius r then circle equation is:

(x-a)²+(y-b)²=r².

In your task we've got P(0,0) so the circle equation is x²+y²=r².

We have to find r. Radius start at (0,0) and end at (-4,-6) therefore

r=√((-4)²+(-6)²) and

r²=(-4)²+(-6)²=16+36=52.

So answer is x²+y²=52.

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If f(x) =5x-6 what is the inverse of f(x)

Akimi4 [234]

Replace f(x) with y:

y = 5x-6

Swith the variables:

x = 5y -6

Now solve for y:

add 6 to each side:

x +6 = 5y

Divide both sides by 5:

y = (x+6)/5

Now replace y with the inverse function f^-1 (x):

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From a hot-air balloon, Brody measures a 39° angle of depression to a landmark

EleoNora [17]

The balloon's vertical distance above the ground is 430 feet.

<h3>What is the angle of depression?</h3>

You look straight parallel to the ground. But when you have to watch something down, then you take your sight down by moving your head up.

The angle from horizontal to the point where you stopped your head is called the angle of depression.

From a hot-air balloon, Brody measures a 39° angle of depression to a landmark that's 532 feet away, measuring horizontally.

The angle of depression = 39°

The base = 532

We need to find the vertical distance consider perpendicular.

$\rm Tan \theta = \dfrac{perpendicular}{base } \\\\\rm Tan 39 = \dfrac{perpendicular}{532} \\\\\rm Tan 39 \times 532 =perpendicular\\\\0.80 \times 532\\\\P = 430.80$