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3 years ago

Log(10) u = 3/2 log(10) 4

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

3 0

u = 8

Step-by-step explanation:

log(10) u = log(10) 4^(3/2)

u = 4^(3/2)

= [sqrt(4)]^3

= (2)^3

= 8

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there are 32 female performers in a dance recital. The ratio of men to women are 3:8. how many men are in the recital?

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This table represents a quadratic function with a vertex at (1, 1). What is the

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The average rate of change on the interval (5, 6) is 9. So the correct option is D.

<h3>How to find the average rate of change on the interval?</h3>

Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).

This is just:

$r = \frac{f(6) - f(5)}{6 - 5}$

$f(x) = a*x^2 + b*x + c$

I we look at the table we see that:

$f(1) = 1 = a + b + c$

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From that we take two relations:

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Now we can replace these two in the last equations so we get:

$5 = 9a + 3b + c\\\\5 = 9a + 3*(1 - 3a) + 2a\\\\5 = 9a + 3 - 9a + 2a\\\\5 = 3 + 2a\\\\5 - 3 = 2a\\\\2 = 2a\\\\a = 1$

Now that we know the value of a:

$c = 2a = 2*1 = 2\\\\b = 1 - 3a = 1 - 3 = -2$

The quadratic equation is:

$f(x) = x^2 - 2x + 2$

Evaluating this in x = 6 we get:

$f(6) = 6^2 - 2*6 + 2 = 26$

And from the table we know that f(5) = 17, then the average rate of change is:

$r = \frac{f(6) - f(5)}{6 - 5} = \frac{26-17}{1} = 9$

The correct option is D.

If you want to learn more about average rates of change:

brainly.com/question/8728504

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2 years ago

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$\\ \rm\longmapsto 5+(-7)$

$\\ \rm\longmapsto 5-7$

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Note:-

(-)(-)=(+)
(+)(-)=(-)
(-)(+)=(-)
(+)(+)=(-)

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