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3 years ago

What’s the answer to this question below. A b c or d

Mathematics

2 answers:

forsale [732]3 years ago

4 0

Answer:

x = 4

Step-by-step explanation:

You have to remember the "Quotient Rule" for exponent having same base.

The quotient rule tells us that we can divide two powers with the same base by subtracting the exponents.

Here,

base = 3

exponents = 2x + 1 , x + 5

3^(2x + 1) = 3^( x + 5)

3^(2x + 1) / 3^(x + 5) = 1

3^((2x + 1) - (x + 5) )= 1

3^(2x + 1 - x - 5) = 1

3^(2x - x +1 - 5) = 1

3^(x - 4) = 1

log 3^(x - 4) = log(1)

(x - 4) (log (3)) = 0

log(3) = 0 rejected

x - 4 = 0 accepted

x = 0 + 4

x = 4

kati45 [8]3 years ago

3 0

Answer:

Choice C is the answer.

Step-by-step explanation:

We have given a equation.

$3^{2x+1} = 3^{x+5}$

We have to find the value of x.

Since, we know that same bases have equal powers.

2x+1 = x+5

Adding -x-5 to both sides of above equation, we have

2x+1-x-5 = x+5-x-5

x-4 = 0

x = 4 which is the answer.

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Convert,the complex number into polar form: 4+4i

kow [346]

Z = a + bi
z = 4 + 4i

r² = a² + b²
r² = (4)² + (4)²
r² = 16 + 16
r² = 32
r = 4√(2)
r = 4(1.414)
r = 5.656

$cos\theta = \frac{a}{r}$
$cos\theta = \frac{4}{4\sqrt{2}}$
$cos\theta = \frac{4}{4\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}$
$cos\theta = \frac{4\sqrt{2}}{4\sqrt{4}}$
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$cos\theta = \frac{4\sqrt{2}}{8}$
$cos\theta = \frac{\sqrt{2}}{2}$
$2(cos\theta) = 2(\frac{\sqrt{2}}{2})$
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$sin\theta = \frac{b}{r}$
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$sin\theta = \frac{4\sqrt{2}}{8}$
$sin\theta = \frac{\sqrt{2}}{2}$
$2(sin\theta) = 2(\frac{\sqrt{2}}{2})$
$2sin\theta = \sqrt{2}$
$2sin\theta = 1.414$

z = a + bi
z = rcosθ + (rsinθ)i
z = r(cosθ + i sinθ)

z = 4 + 4i
z = 5.656cosθ + (5.656sinθ)i
z = 5.656(cosθ + i sinθ)
z = 5.656(cos45 + i sin45)

$\theta = tan^{-1}\frac{b}{a}$
$\theta = tan^{-1}\frac{4}{4}$
$\theta = tan^{-1}(1)$
$\theta = 45$

The polar form of 4 + 4i is approximately equal to 5.656(cos45 + i sin45).

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