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Nezavi [6.7K]
2 years ago
6

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 5 hours of burning, a candle has a height of 26 centimeters. After 24 hours of burning, its height is 14.6 centimeters. What is the height of the candle after 18 hours?
Mathematics
1 answer:
wel2 years ago
5 0

Answer:Let Y = height

Let X = time

Height is a linear function of time, so Y = mX + b, where m is the slope and b is the y-intercept.  

We can calculate the slope from the given values (8,20.4) and (19,18.2)

Slope = (y2 - y1) / (x2 - x1) = (18.2 - 20.4) / (19 - 8) = -2.2 / 11 = -0.2

This means that the height of the candle is going down by 0.2 cm per hour

Since 16 hours is 8 hours after the first data point of (8,20.4), the height will go down by 8 * (-0.2) = -1.6 cm in the 8 hours between hour 8 and hour 16.  

So the height of the candle after 16 hours = 20.4 - 1.6 = 18.8 centimeters

Step-by-step explanation:

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Keith_Richards [23]

Answer:

a)22

b)7

c)8

Step-by-step explanation: its really complicated so ill try my best.

so the say 11 like both coffee and tea so that means that they also added 11 to

the other two sections. so if we take 11 away from 18 we get 7, and that's how many people like coffee and not tea. to get answer c) we need to also subtract 11 from 15, which gets us 4. so we have 11 plus 4 plus 7. and that gets us 22.  so 30 subtract 22 gets us 8 so 8 people don't like tea or coffee. 22 is also the answer to a). did you get that? i hope so

3 0
3 years ago
The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.
Sladkaya [172]

Answer:

4, 10

Step-by-step explanation:

The value for the third side of the triangle is given by

b-a < n < b+a where a and b are the two other sides of the triangle and b>a

7-4 < n < 7+4

3 < n < 11

Since n is an integer

4 would be the smallest value and 10 would be the largest

8 0
3 years ago
Read 2 more answers
PLEASE HELP PLEASE PLEASE
sp2606 [1]

Answer:

14.8

Step-by-step explanation:

By the Pythagorean theorem, ...

... x² = 7² + 13² = 218

... x = √218 ≈ 14.7648 ≈ 14.8

4 0
3 years ago
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A long paper strip with a width of 5 cm is folded, as shown in the picture. Find the smallest possible area of the gray triangle
Stolb23 [73]

By using some logic and the formula of the triangle's area, we will find that the smallest possible area is 12.5 cm²

How to start thinking about the problem.

First of all, for the configuration of this paper strip, we can see that the base of the triangle will <u>always be equal of the width of the paper</u>. Thus, the smallest area will be only dependent of the height of the triangle.

Now, we need to analyze the picture to figure out how we can get the smallest height possible for that triangle.

What is the smallest height possible.

Doing this, we shall see that the smallest height possible is actually when the height equals the width itself, as it's shown in the attached image.

How to calculate the smallest area possible.

Thus, to calculate the smallest area, we just have to use the formula of the area of the triangle, which is   \frac{b\times h}{2}<em>, where </em><u><em>b is the base</em></u><em> and </em><u><em>h is the height</em></u><em>.</em>

As we previously found, for this question, the

<em>base = height = width of the paper = 5cm</em>

Now, we just have to calculate it with the formula

Area = \frac{base \times height}{2} \\\\&#10;\\&#10;Area = \frac{5 \times 5}{2} \\&#10;\\&#10;Area = \frac{25}{2}\\&#10; \\&#10;Area = 12.5 cm^{2}

learn more about the area of the triangle here: brainly.com/question/15442893

3 0
2 years ago
Find the remainder when f(x) is divided by (x - k).<br><br> f(x) = 4x3 - 6x2 + 3x + 1; k= -2
laila [671]
\frac{f(x)}{(x-k)}
\frac{4x^3-6x^2+3x+1}{(x+2)}
Using Long Division, pic below
Your remainder is -61

8 0
3 years ago
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