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finlep [7]
4 years ago
9

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.

After 6 hours of burning, a candle has a height of 17.4 centimeters. After 23 hours of burning, its height is 7.2 centimeters. What is the height of the candle after 11 hours?
Mathematics
1 answer:
Alborosie4 years ago
7 0
Assume that the rule connecting height of the candle to time is a linear one.  If you do, then we have to find the equation of this line, and then use this equation to predict the height of the candle after 11 hours.

Two points on this line are (6,17.4) and (23, 7.2).  The slope is thus
         7.2-17.4           -6
m = ---------------  =  -----------  or   -3/5.
           23-6                 10

Find the equation of the line.  I'm going to use the slope-intercept formula:

y = mx + b  =>   7.2 = (-3/5)(23) + b.  Solving for b,   b = 21.

Now    we know that y = (-3/5)x + 21

Let x=11 to predict the height of the candle at that time.

y = (-3/5)(11) + 21 = 14.4 inches  (answer)
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The <em>twelfth</em> element of the <em>geometric</em> sequence is equal to 4,096. (Correct choice: D)

<h3>How to find a determined element of a geometric sequence by exponential formulae</h3>

Sequences are series of elements generated according to at least one condition, usually equations. <em>geometric</em> sequences are generated according to a <em>exponential</em> formulas, whose form and characteristics are described below:

f(n) = a · bⁿ ⁻ ¹    (1)

Where:

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If we know that a = 4, b = 2 and n = 12, then the twelfth element of the geometric sequence from the statement is:

f(12) = 4 · 2¹² ⁻ ¹

f(12) = 4 · 2¹¹

f(12) = 4 · 2,048

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The <em>twelfth</em> element of the <em>geometric</em> sequence is equal to 4,096. (Correct choice: D)

To learn more on geometric sequences: brainly.com/question/4617980

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6 0
2 years ago
Can someone actually answer this question pls its my 3rd time posting it and ill ive gotten was wrong or answers that make no se
andre [41]

Answer:

(-2+-5) equals -7.

Because the signs are the same, we dont change it.

(3+5) equals 8. Same like the other equation, the signs are the same so we do not change it.

Now we do (-7+8) The answer will be 1. Lets use a little graph since its hard to explain.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Mark -7 anyway you want. (Circle it, draw a line under it, what ever you want.)

Now Move the line 8 times.

When you do that your line will stop at 1.

And thats how you do it.

Step-by-step explanation:

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