The given temperatures of 70 °F, 50 °F, and 35 °F, at the given 3, 3, and
6 days give the following step function;
![\begin{cases}f(x) = 70^{\circ } & \text{ if } 0 \leq x \leq 3 \\f(x) = 50^{\circ} & \text{ if } 3 < x \leq 6 \\ f(x) = 35^{\circ }& \text{ if } 6 < x \leq 12 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Df%28x%29%20%3D%2070%5E%7B%5Ccirc%20%7D%20%20%26%20%5Ctext%7B%20if%20%7D%200%20%5Cleq%20x%20%5Cleq%203%20%5C%5Cf%28x%29%20%3D%2050%5E%7B%5Ccirc%7D%20%26%20%5Ctext%7B%20if%20%7D%203%20%3C%20x%20%5Cleq%206%20%5C%5C%20f%28x%29%20%3D%2035%5E%7B%5Ccirc%20%7D%26%20%5Ctext%7B%20if%20%7D%206%20%3C%20x%20%5Cleq%2012%20%5Cend%7Bcases%7D)
- Please find attached the graph of the step function?
<h3>How can the step function be written?</h3>
The temperature at it is fermented in the first three days = 70 °F
From day 3 to 6 the temperature = 50 °F
From day 6 to day 12, the temperature at which it is kept in the freezer = 35 °F
The step function is therefore;
![\begin{cases}f(x) = 70^{\circ } & \text{ if } 0 \leq x \leq 3 \\f(x) = 50^{\circ} & \text{ if } 3 < x \leq 6 \\ f(x) = 35^{\circ }& \text{ if } 6 < x \leq 12 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Df%28x%29%20%3D%2070%5E%7B%5Ccirc%20%7D%20%20%26%20%5Ctext%7B%20if%20%7D%200%20%5Cleq%20x%20%5Cleq%203%20%5C%5Cf%28x%29%20%3D%2050%5E%7B%5Ccirc%7D%20%26%20%5Ctext%7B%20if%20%7D%203%20%3C%20x%20%5Cleq%206%20%5C%5C%20f%28x%29%20%3D%2035%5E%7B%5Ccirc%20%7D%26%20%5Ctext%7B%20if%20%7D%206%20%3C%20x%20%5Cleq%2012%20%5Cend%7Bcases%7D)
The graph of the above function created with MS Excel is attached
Learn more about step functions here:
brainly.com/question/2509505
Answer:
The sum of the first 37 terms of the arithmetic sequence is 2997.
Step-by-step explanation:
Arithmetic sequence concepts:
The general rule of an arithmetic sequence is the following:
![a_{n+1} = a_{n} + d](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3D%20a_%7Bn%7D%20%2B%20d)
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
![a_{n} = a_{1} + (n-1)*d](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7D%20%2B%20%28n-1%29%2Ad)
The sum of the first n terms of an arithmetic sequence is given by:
![S_{n} = \frac{n(a_{1} + a_{n})}{2}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20%5Cfrac%7Bn%28a_%7B1%7D%20%2B%20a_%7Bn%7D%29%7D%7B2%7D)
In this question:
![a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%20-27%2C%20d%20%3D%20-21%20-%20%28-27%29%20%3D%20-15%20-%20%28-21%29%20%3D%20...%20%3D%206)
We want the sum of the first 37 terms, so we have to find ![a_{37}](https://tex.z-dn.net/?f=a_%7B37%7D)
![a_{n} = a_{1} + (n-1)*d](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7D%20%2B%20%28n-1%29%2Ad)
![a_{37} = a_{1} + (36)*d](https://tex.z-dn.net/?f=a_%7B37%7D%20%3D%20a_%7B1%7D%20%2B%20%2836%29%2Ad)
![a_{37} = -27 + 36*6](https://tex.z-dn.net/?f=a_%7B37%7D%20%3D%20-27%20%2B%2036%2A6)
![a_{37} = 189](https://tex.z-dn.net/?f=a_%7B37%7D%20%3D%20189)
Then
![S_{37} = \frac{37(-27 + 189)}{2} = 2997](https://tex.z-dn.net/?f=S_%7B37%7D%20%3D%20%5Cfrac%7B37%28-27%20%2B%20189%29%7D%7B2%7D%20%3D%202997)
The sum of the first 37 terms of the arithmetic sequence is 2997.
Answer:
x= -10
Step-by-step explanation:.......
<u>Given</u>:
The system of linear equations are
and ![3x-2y=-5](https://tex.z-dn.net/?f=3x-2y%3D-5)
We need to determine the solution to the system of equations using substitution method.
<u>Solution</u>:
The solution can be determined using the substitution method.
Let us substitute
in the equation ![3x-2y=-5](https://tex.z-dn.net/?f=3x-2y%3D-5)
Thus, we have;
![3(4+y)-2y=-5](https://tex.z-dn.net/?f=3%284%2By%29-2y%3D-5)
![12+3y-2y=-5](https://tex.z-dn.net/?f=12%2B3y-2y%3D-5)
![12+y=-5](https://tex.z-dn.net/?f=12%2By%3D-5)
![y=-17](https://tex.z-dn.net/?f=y%3D-17)
Thus, the value of y is -17.
Substituting
in the equation
, we get;
![x+17=4](https://tex.z-dn.net/?f=x%2B17%3D4)
![x=-13](https://tex.z-dn.net/?f=x%3D-13)
Thus, the value of x is -13.
Hence, the solution to the system of equations is (-13,-17)