Answer:
1.58
Step-by-step explanation:
Okay. We're solving for t because we need to know how many seconds. From the problem, we know the height (10), but we don't know when that height happens.
[tex]10 = -16tx^{2} -7t+61[/tex]
We can factor by multiplying -16 by 61 first to get -976 and see what multiplies to get -976 AND adds to get -7 at the same time. But we can also use the quadratic formula because, let's be honest, factoring can be a lot of extra work.
[tex]10 = -16t^{2} -7t+61\\\\0 = -16t^{2} -7t+51\\\\t=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a} \\=\frac{-(-7)\pm \sqrt{(-7)^{2}-4(-16)(51) } }{2(-16)} \\=\frac{7\pm \sqrt{49+64(51) } }{-32} \\=\frac{7\pm \sqrt{3313} }{-32}[/tex]
Plug both the plus and the minus versions into your calculator and...
[tex]t\approx -2.02, 1.58[/tex]
There's no such thing as negative time, so -2.02 is automatically disqualified, leaving 1.58 as the answer.
Hope this helps, let me know if I missed anything!
