Question

Solve the equation 93=20t−16t²

A) t = -3 or t = 7/4

B) t = 3 or t = -7/4

C) t = -32 or t = 7/4

D) t=3/2 or t=-7/4

Answer 1

The correct solutions for the equation 93=20t−16t² using the quadratic formula are t = 7/4 and t = 3. Neither of these solutions match the options provided in the question.

Step-by-step explanation:

To solve the equation 93=20t−16t², we first need to express it in the standard form by rearranging the terms to get 0 on one side of the equation:

16t² - 20t + 93 = 0

Now, we can use the quadratic formula, −b ± √b² - 4ac / 2a, to find the values of t.

In our equation, a = -16, b = 20, and c = 93. Plugging these values into the quadratic formula we get:

t = −(20) ± √(20)² - 4(-16)(93) / 2(-16)

Simplifying under the radical we have:

t = −(20) ± √400 + 5952 / -32

t = −(20) ± √6352 / -32

t = −(20) ± 79.7 / -32

Now, we find the two possible solutions for t:

t = (−20 + 79.7) / -32 ≈ 7/4

t = (−20 − 79.7) / -32 ≈ 3

So the two solutions are t = 7/4 or t = 3. Option B) t = 3 or t = −7/4 is incorrect because of the minus sign. Hence, the correct answer is not listed in the options provided.