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erma4kov [3.2K]
3 years ago
12

A quantity with an initial value of 390 the keys continuously at a rate of 5% per decade what is the value of the quantity after

51 years to the nearest hundred
Mathematics
1 answer:
Fed [463]3 years ago
3 0

Answer:

4695.90

Step-by-step explanation:

The exponential growth function is given as:

y = a(1 + r)^t

a = Initial value = 390

y = Value after time t = ?

r = Growth rate = 5% = 0.05

t = Time in years =51

Hence

y = 390(1 + 0.05)⁵¹

y = 4695.9002123

Approximately = 4695.90

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Step-by-step explanation:

Given 7 ( 4x + 2 )  + 3 = - 67

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Z^5=-243i, find the solution to the equation whose argument is strictly between 180 degrees and 270 degrees. Round your answer t
11Alexandr11 [23.1K]

Answer:

The solution is z = -2.853 - i 0.927.

Step-by-step explanation:

Complex power is determined by means of the De Moivre's Theorem, whose expression is:

z^{n} = r^{n} \cdot (\cos n\theta + i \sin n\theta)

Where r is the norm of the complex number. In this case, expression can be written as:

-i 243 = 3^{5} \cdot (\cos 5\theta + i \sin 5\theta)

The real component must be equal to zero and complex component must be equal to -1. That is to say:

\cos 5\theta = 0

\sin 5\theta = -1

Possible solutions for each component are, respectively:

Real component

5\theta = \cos^{-1}0

5\theta = \frac{\pi}{2} \pm \pi\cdot j, \forall j \in \mathbb{N}_{O}

\theta = \frac{\pi}{10} \pm \frac{\pi}{5}  \cdot j, \forall j \in \mathbb{N}_{O}

Possible solutions: \frac{11\pi}{10}, \frac{13\pi}{10}, \frac{3\pi}{2}

Complex component

5\theta = \sin^{-1}(-1)

5\theta = \frac{3\pi}{2} \pm 2\pi \cdot j, \forall j \in \mathbb{N}_{O}

\theta = \frac{3\pi}{10} \pm \frac{2\pi}{5}  \cdot j, \forall j \in \mathbb{N}_{O}

Possible solutions: \frac{11\pi}{10}, \frac{3\pi}{2}

There is one solution whose argument is strictly between 180 degrees (\pi) and 270 degrees (1.5\pi).

z = 3 \cdot \left( \cos \frac{11\pi}{10} + i \sin \frac{11\pi}{10} \right)

z = -2.853 - i 0.927

6 0
3 years ago
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Answer:

49 degrees

Step-by-step explanation:

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