2 years ago

Express the radical using the imaginary unit i

Mathematics

1 answer:

diamong [38]2 years ago

6 0

Answer:

$i$ $\sqrt{30}$

Step-by-step explanation:

$\sqrt{-30}$

= $\sqrt{30 * -1}$

= $\sqrt{30} * \sqrt{-1}$ Separate the two numbers into 2 radicals.

= $i\sqrt{30}$ Simplify, knowing that $i = \sqrt{-1}$ .

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Answer:

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Step-by-step explanation:

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3 years ago

What is the area of the sector with a central angle of 49° and a radius of 11 cm? Use 3.14 for pi and round your final answer to

olga_2 [115]

Answer:

$\boxed{\text{51.71 cm}^{2}}$

Step-by-step explanation:

If the angle θ is in radians, the formula for the area (A) of a sector of a circle is

A = ½r²θ

If θ is in degrees

$A = \dfrac{1}{2}r^{2}\theta \times \dfrac{\pi \text{ rad}}{180^{\circ}}= \pi r^{2}\times\dfrac{\theta }{360}$

Data:

θ = 49°

r = 11 cm

Calculation:

$\begin{array}{rcl}A& = &3.14\times 11^{2}\times\dfrac{49}{360}\\\\ & = &3.14 \times 121 \times 0.1361\\ & = & \mathbf{51.71}\\\end{array}\\\text{The area of the sector is }\boxed{\textbf{51.71 cm}^{2}}$

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