HOw do you solve this?

Question

Can you show your work or explain it to me?

I always freeze up on questions like this.

7.27= 5t+4.9t^2

Answer 1

First get everything on one side so you can equate it to zero.

4.9t² + 5t - 7.27 = 0

Optionally, multiply everything by 100 to get integer coefficients.
490t² + 500t - 727 = 0

Now use the quadratic equation to solve.

a = 490
b = 500
c = -727

t = (-500 +/- sqrt( 500² - 4(490)(-727) ) ] / 2(490)
t = -500 / 980 +/- sqrt(1674920) / 980
t = -0.510204082 +/- 1.320598

Therefore:
t = 0.8103949 or t = -1.8308030

If you are looking for only a positive answer, it will be at time t = 0.81.

Answer 2

Set it in the proper form, ax^2 + bx +c = 0 and use the quadratic equation. Plug and chug.

Answer 3

7.27=5t+4.9t^2

5t
+
9t^2
--------
14t^2

7.27=4+14t^2
-4 -4
-----------------------
3.27=14^2
---------------------
14 14

.23358714

t=0.167857