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8_murik_8 [283]
3 years ago
6

What is the solution to log2(2x^3-8)-2log2x=log2x?

Mathematics
1 answer:
Alexxandr [17]3 years ago
5 0

Answer:

<h2>x = 2</h2>

Step-by-step explanation:

\\\\\text{Domain:}\\\\2x^3-8>0\ \wedge\ x>0\\2x^2>8\to  x^3>4\to x>\sqrt[3]4\\\\x\in(\sqrt[3]{4},\ \infty)\\\\\log_2(2x^3-8)-2\log_2x=\log_2x\qquad\text{add}\ 2\log_2x\ \text{to both sides}\\\\\log_2(2x^3-8)=3\log_2x\qquad\text{use}\ n\log_ab=\log_ab^n\\\\\log_2(2x^3-8)=\log_2x^3\iff2x^3-8=x^3\qquad\text{subtract}\ 2x^3\ \text{from both sides}\\\\-8=-x^3\qquad\text{change the signs}\\\\8=x^3\to x=\sqrt[3]8\\\\x=2\in D

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Ratling [72]

Answer: point estimate = 3.88

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Step-by-step explanation:

Confidence interval is written in the form,

(Point estimate - margin of error, Point estimate + margin of error)

The sample mean, x is the point estimate for the population mean. Let m represent the margin of error. Since the confidence interval is given as (3.25 , 4.51), it means that

x - m = 3.25

x + m = 4.51

Adding both equations, it becomes

2x = 7.76

x = 7.76/2

x = 3.88

Substituting x = 3.88 into x + m = 4.51, it becomes

3.88 + m = 4.51

m = 4.51 - 3.88

m = 0.63

8 0
3 years ago
Which values of A and B make the following equations true?
Korolek [52]
<span>(5x^7 y^2)(-4x^4 y^5) =-20x^a y^b
</span><span>
solve this:
(5x^7 y^2)(-4x^4 y^5)
= -20 x^(7 + 4) y^(2 + 5)
= -20 x^11 y^7

answer

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5 0
3 years ago
What is the angle, in degrees, if the Area is 180 square miles and the radius is 42,240 feet?
Savatey [412]

Step-by-step explanation:

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the area of a circle segment is just the corresponding fraction of the whole circle.

so the area of a segment of x degrees is

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in our case we know

pi×42240² × x/360 = 180 mi²

we also know that there are 5280 ft in 1 mile.

so, the radius is actually

42240 / 5280 = 8 miles

and therefore our equation resulting in mi² has to use miles and not ft and has to look that way :

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pi×64 × x = 180×360

pi×x = 180×360/64 = 1012.5

x = 1012.5/pi = 322.2887598...°

so, the angle of the segment of a circle with the area of 180 mi² and the radius of 8 mi is 322.2887598...°

5 0
2 years ago
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Likurg_2 [28]
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7 0
3 years ago
The sum of nine-tenths and g is two-thirds solve for g
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Answer:

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Thank me later :D

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3 years ago
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