An arrow is shot upward. its height h, in feet, is given b the equation h=-16t^2+32+5, where t is the time in seconds. how many seconds does it take until the arrow hits the ground?

The time taken to reach the ground is t=2.146 approx 2 seconds.

Step-by-step explanation:

Given : An arrow is shot upward. Its height h, in feet, is given by the equation , where t is the time in seconds.

To find : How many seconds does it take until the arrow hits the ground?

Solution :

We have given the equation,

where, h is the height in feet and t is the time in seconds.

We have to find in how many seconds does it take until the arrow hits the ground i.e. height became zero or h(t)=0

Substituting in the equation,

Solve by quadratic formula,

Solution of equation is

On comparing, a=-16 , b=32 , c=5

Solution is

We reject t=-0.146.

So, The time taken to reach the ground is t=2.146 approx 2 seconds.

a

step-by-step explanation:

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the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places