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e-lub [12.9K]
4 years ago
15

What is 0.624 an expanded form

Mathematics
1 answer:
sveta [45]4 years ago
4 0

Answer: 0 + 0.6  + 0.02  + 0.004

A Number in expanded form is written like a sentence.

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Find the length of the radius of the circle whose perimeter is xcm and the area is
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\bf \stackrel{\textit{perimeter}}{\textit{circumference}}\textit{ of a circle}\\\\ C = 2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=x \end{cases}\implies x = 2\pi r\implies \boxed{\cfrac{x}{2\pi }=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=x \end{cases}\implies x = \pi \left( \boxed{\cfrac{x}{2\pi }} \right)^2\implies x = \pi \cdot \cfrac{x^2}{2^2\pi^2}

\bf x = \cfrac{x^2}{4\pi }\implies 4\pi x = x^2\implies \cfrac{4\pi x}{x}=x\implies \blacktriangleright 4\pi = x\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since the radius is}}{r = \cfrac{x}{2\pi }}\implies r =\cfrac{4\pi }{2\pi }\implies \blacktriangleright r = 2\blacktriangleleft

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4 years ago
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An airplane with a speed of 120 knots is headed west while a 30-knot wind is blowing from 120°. Find the ground speed to the nea
SVEN [57.7K]

Answer:

Velocity of the plane relative to the ground

= [(-145.98î) + (15j)] knots

Magnitude = groundspeed = 146.75 knots

Direction = -5.9°

Step-by-step explanation:

This is a relative velocity question.

Let the velocity of the airplane relative to the wind be V(aw)

Velocity of the airplane relative to the ground = Va

The velocity of the wind relative to the ground = Vw

The relative velocity theory enables us o relate these as thus,

V(aw) = Va - Vw

Va = V(aw) + Vw

V(aw) = (-120î) knots (120 west)

For Vw, the wind is said to be blowing from 120°, reading this on a three figure bearing as angle from the north,

This gives the real direction of the wind to be 150° from the positive x-axis as shown in the attached image.

Vw = (30cos 150°)î + (30sin 150°)j

Vw = (-25.98î + 15j) knots

Va = V(aw) + Vw = (-120î) + (-25.98î + 15j)

Va = (-145.98î) + (15j)

Magnitude of Va = √[(-145.98)² + (15)²] = 146.75 knots

Direction = tan⁻¹ (-15/145.98) = -5.9°

Hope this Helps!!!

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