Respuesta :
Answer:
[tex]T_w = \frac{11 + w}{4}[/tex]
Step-by-step explanation:
Given
[tex]Starts = 3 miles[/tex]
[tex]Difference = \frac{1}{4}\ mile[/tex]
Required
Determine the distance for w weeks
This will be calculated using the following Arithmetic progression formula
[tex]T_n = a +(n -1) d[/tex]
Where
[tex]a =3[/tex]
[tex]n = w[/tex]
[tex]d = \frac{1}{4}[/tex]
Substitute these values
[tex]T_w = 3 + (w - 1)* \frac{1}{4}[/tex]
Open Bracket
[tex]T_w = 3 + \frac{1}{4}w - \frac{1}{4}[/tex]
Collect Like Terms
[tex]T_w = 3 - \frac{1}{4} + \frac{1}{4}w[/tex]
[tex]T_w = \frac{11}{4} + \frac{1}{4}w[/tex]
Take LCM
[tex]T_w = \frac{11 + w}{4}[/tex]
The expression that shows the distance Kane runs in a training session after w weeks is [tex]\rm T_w = \dfrac{11+w}{4}[/tex] and this can be determined by using the arithmetic progression.
Given :
- Kane starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile.
- w be the number of weeks.
Expression to show the distance Kane runs in a training session after w weeks can be determined by using the arithmetic progression.
The formula for the nth term in arithmetic operation is given by:
[tex]\rm T_n = a + (n-1)d[/tex]
where a is the first term that is 3, d is the difference between two consecutive terms that is [tex]1\div 4[/tex], [tex]\rm T_n[/tex] is the last term and n is the total number of terms that is w.
[tex]\rm T_w = 3+(w-1)\times \dfrac{1}{4}[/tex]
[tex]\rm T_w = \dfrac{11}{4}+\dfrac{w}{4}[/tex]
[tex]\rm T_w = \dfrac{11+w}{4}[/tex]
The expression that shows the distance Kane runs in a training session after w weeks is [tex]\rm T_w = \dfrac{11+w}{4}[/tex].
For more information, refer to the link given below:
https://brainly.com/question/16764034
