What is the value of $2 t^2+6$ when $t=5$?
Answer (2)
When we substitute t = 5 into the expression 2 t 2 + 6 , we find the value is 56. This is calculated by first finding 5 2 , then multiplying by 2, and finally adding 6. Thus, the final answer is 56.
;
Substitute t = 5 into the expression 2 t 2 + 6 .
Calculate 5 2 = 25 .
Multiply the result by 2: 2 × 25 = 50 .
Add 6 to the result: 50 + 6 = 56 . The final answer is 56 .
Explanation
Understanding the problem We are given the expression 2 t 2 + 6 and we need to find its value when t = 5 .
Substituting the value of t To find the value of the expression, we substitute t = 5 into the expression 2 t 2 + 6 . This gives us 2 ( 5 ) 2 + 6 .
Simplifying the expression Now, we simplify the expression:
First, we calculate 5 2 , which is 5 × 5 = 25 .
Next, we multiply this result by 2: 2 × 25 = 50 .
Finally, we add 6 to the result: 50 + 6 = 56 .
Final Answer Therefore, the value of the expression 2 t 2 + 6 when t = 5 is 56.
Examples
Imagine you are calculating the total cost of producing a certain item. The cost includes a fixed setup cost and a variable cost that depends on the number of items produced. If the fixed cost is 6 dollars and the variable cost is 2 t 2 where t is the number of items, then when you produce 5 items, the total cost will be 2 ( 5 ) 2 + 6 = 56 dollars. This kind of calculation is useful in business and economics for cost analysis and production planning.
