The function h=−16t2+26t models the height h (in feet) of the dolphin after t seconds. after how many seconds is the dolphin at a height of 5 feet? round your answers to the nearest tenth.

The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Let h represent the height of dolphin at t seconds.

Given the function:

For a height of 5 ft.:

5 = −16t² + 26t

16t² - 26t + 5 = 0

t = 0.2 or t = 1.4

The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.

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The dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.

Step-by-step explanation:

Given : The function models the height h (in feet) of the dolphin after t seconds.

To Find: After how many seconds is the dolphin at a height of 5 feet?

Solution:

Function:

h is the height

t is the time

Now we are supposed to find After how many seconds is the dolphin at a height of 5 feet

Substitute h = 5

So,

---1

Using quadratic formula :

General quadratic equation:   ---A

On Comparing equation 1 with A

a = 16

b = -26

c=5

Substitute the values in the quadratic formula.

Thus the dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.