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3 years ago

A small metal bar whose temperature is 30 C is dropped into a container of 75 C

Mathematics

1 answer:

Mariulka [41]3 years ago

4 0

It would take about 40 seconds for the temperature to reach 70°C and 44 second to reach 74°C.

<h3>Linear equation</h3>

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the temperature of the metal bar after x seconds, hence:

Since the metal bar has an initial temperature of 30°C, hence:

b = 30, also m = 1°C (increase), The equation becomes:

y = 1(x) + 30 = x + 30

To reach 70°C:

70 = x + 30

x = 40 seconds

To reach 74°C:

74 = x + 30

x = 44 seconds

It would take about 40 seconds for the temperature to reach 70°C and 44 second to reach 74°C.

Find out more on Linear equation at: brainly.com/question/14323743

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15, 11, 7, 3, -1, ... explicit formula and recursive formula

monitta

Recursive formula is: $a_n = a_{n-1} -4$

Explicit formula is: $a_n = 19-4n$

Step-by-step explanation:

Given sequence is:

15,11,7,3,-1

Here

$a_1 = 15\\a_2 = 11\\a_3 = 7$

First of all, we have to find the common difference

Common difference is the difference between consecutive terms of an arithmetic sequence

So,

$d = a_2-a_1 = 11-15 = -4\\d = a_3-a_2 = 7-11 = -4$

<u>Recursive Formula:</u>

A recursive formula is used to find the next term of an arithmetic sequence using previous term and common difference

General form of recursive formula for a given common difference d is:

$a_n = a_{n-1} + d$

Putting the value of d

$a_n = a_{n-1} -4$

<u>Explicit Formula:</u>

The explicit formula is given by:

$a_n = a_1 + (n-1)d$

Putting the first term and common difference

$a_n = 15 + (n-1)(-4)\\a_n = 15 -4n+4\\a_n = 19-4n$

Hence,

Recursive formula is: $a_n = a_{n-1} -4$

Explicit formula is: $a_n = 19-4n$

Keywords: Arithmetic sequence, common difference

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