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3 years ago

Rewrite the formula for the circumference of a circle C=2xpix r in terms of its diameter d. Show your work.

2 answers:

ozzi3 years ago

7 0

Hi there!

The answer is
$circumference \: = d\pi$
In this formula d represents the diameter.

We know that 2 times the radius equals the diameter, hence
$2r = d$

Therefore we can replace the 2r in the original formula by d, and then we get the following:
$circumference = 2\pi \: r = 2r\pi = d\pi$

Keith_Richards [23]3 years ago

3 0

Diameter = 2·radius

С = 2·π·r ⇒ С = π·d

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Find the trigonometric form of the number 3 + √3i.

sattari [20]

Any complex number $z$ can be written in trigonometric form as

$z = |z| e^{i\arg(z)} = |z| \left(\cos(\arg(z)) + i \sin(\arg(z))\right)$

where $|z|$ is the modulus of $z$ and $\arg(z)$ is its argument, i.e. the angle $z$ makes with the positive real axis in the complex plane.

We have

$|z| = \sqrt{3^2 + \left(\sqrt3\right)^2} = \sqrt{12} = 2\sqrt3$

and

$\arg(z) = \tan^{-1}\left(\dfrac{\sqrt3}3\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6$

Then

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1 year ago

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3 years ago

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liubo4ka [24]

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2 years ago

a bird flies 25 miles Due West then turns due south and flies for another 15 miles and lands how far is the bird from its starti

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3 years ago

a water balloon is tossed into the air with an upward velocity of 25 ft/s its height h(t) in ft after t seconds is given by the

Montano1993 [528]

When the height is 0 that is when it hits the ground
solve
0=-16t²+25x+3
cant factor so use quadratic formula

for
0=ax²+bx+c
$x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}$

so for
0=-16t²+25t+3
a=-16
b=25
c=3
so

$x=\frac{-25+/-\sqrt{25^2-4(-16)(3)}}{2(-16)}$
$x=\frac{-25+/-\frac{625+192}}{-32}$
$x=\frac{-25+/-\frac{817}}{-32}$
it has to be a positive time

so it will hit the ground after $\frac{25+\sqrt{817}}{32}$ seconds

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2 years ago