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2 years ago

What is the common rule for simplifying a negative exponent with a coefficient? Ex: 3^-1

Mathematics

2 answers:

Sergeeva-Olga [200]2 years ago

4 0

<h2>Answer:</h2>

<u>Negative exponents in the numerator get moved to the denominator and become positive exponents</u>

<h2>Step-by-step explanation:</h2>

In any problem where the exponent is given in negative can be solved by taking negative exponents in the numerator to the denominator and become positive exponents.

For instance the given problem can be solved as writing 3 ^ -1 as 1/3

So the rule is moving the exponent to the denominator and make it positive

rjkz [21]2 years ago

3 0

Anything to a negative power becomes the inverse with the coefficient to a positive power.
For example, 3^-1 becomes 1/3^1 or just 1/3.
3^-2 would be 1/3^2 or 1/9.

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2 years ago

The given series has six terms. what is the sum of the terms of the series? 17 + 25 + 33 + . . . + 57

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2 years ago

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Fantom [35]

Answer:

We have function,

$y = 3 - 6 \sin {}^{} (2x + \frac{\pi}{2} )$

Standard Form of Sinusoid is

$y = - 6 \sin(2x + \frac{\pi}{2} ) + 3$

Which corresponds to

$y = a \sin(b(x + c)) + d$

where a is the amplitude

2pi/b is the period

c is phase shift

d is vertical shift or midline.

In the equation equation, we must factor out 2 so we get

$y = - 6(2(x + \frac{\pi}{4} )) + 3$

Also remeber a and b is always positive

So now let answer the questions.

a. The period is

$\frac{2\pi}{ |b| }$

$\frac{2\pi}{ |2| } = \pi$

So the period is pi radians.

b. Amplitude is

$| - 6| = 6$

Amplitude is 6.

c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.

So using that<em> rule, our range is [6+3, -6+3]= [9,-3] So our range</em> is [-3,9].

D. Plug in 0 for x.

$3 - 6 \sin((2(0) + \frac{\pi}{2} )$