I am new to wyzant and I need actual help very quickly please

Question

1.) The voltage V across a capacitor at time t seconds is given by

Identify the voltage across the capacitor at 8 seconds to the nearest hundredth.

A.) 5.49 V

B.) 4.39 V

C.) 6.20 V

D.) 6.69 V

2.) Identify all of the real eighth roots of −256.

A.) −2

B.) −2, 2

C.) 2

D.) no real eighth roots

Answer 1

The first one is simple. Just plug in 8 for t, simplify it a bit and plug it into your calculator:

V = 146.3(1/2.72)^{0.41 * 8} = 146.3(1/2.72)^3.28≈ 5.49 V

The second one is bit tricky. Here's how to go about it. If we have x²ⁿ (to any even power, where x is real), where n is any positive integer, it will always be positive. The reason for this is it is equivalent to x^2*n, which if you remember your exponent rules is equivalent to: (x²)ⁿ. Since x² is always greater than or equal to zero, if we raise that to any whole number power that will always be positive, so x²ⁿ is always positive. Since we are essentially asking if (-256)^1/8 has any real roots (eighth root means to the 1/8 power), an equivalent question is: Is there a real x such that x⁸ = -256? The answer is no, since we just said x^{even number} has to always be positive.

In short, the answer is d) there are no real eighth roots.

Answer 2

V = 146.3(1/2.72)^0.41t

V = 146.3(1/2.72)^3.28

V = 146.3(0.03755)

V = 5.4936

-256 does not have any even numbered roots.