Answer:
The dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.
Step-by-step explanation:
Given : The function [tex]h=-16t^2+26t[/tex]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: [tex]h=-16t^2+26t[/tex]
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, [tex]5=-16t^2+26t[/tex]
[tex]16t^2-26t+5=0[/tex]
[tex]16t^2-26t+5=0[/tex] ---1
Using quadratic formula : [tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
General quadratic equation: [tex]ax^2+bx+c=0[/tex] ---A
On Comparing equation 1 with A
a = 16
b = -26
c=5
Substitute the values in the quadratic formula.
[tex]x = \frac{-(-26)\pm\sqrt{(-26)^2-4(16)(5)}}{2(16)}[/tex]
[tex]x = \frac{26\pm 18.86796}{32}[/tex]
[tex]x = \frac{26+18.86796}{32},\frac{26-18.86796}{32}[/tex]
[tex]x = 1.4021,0.2228[/tex]
Thus the dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.
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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