The solution to H(t) = g(t) is located in the function between 1 and 2.
<h3>How to illustrate the function?</h3>
H(t) = −16t2 + 64t + 12
g(t) = 10 + 10.4t,
t. H(t) g(t)
0 12. 10
1. 60. 20.4
2. 76. 30.8
The ball that follows function H(t) increase its height, reaches a maximum and, then, decreases its height. The ball that follows function g(t) increases its height all the time. In the beginning, the ball that follows function H(t) increases its height faster than the other ball, but after it reaches its maximum height, its height starts to decrease, giving the opportunity to the other ball to reach it.
Learn more about functions on:
brainly.com/question/16134033
#SPJ1
Answer:
![10^{-p\left(t\right)}=t^{\left(0.5\right)}](https://tex.z-dn.net/?f=10%5E%7B-p%5Cleft%28t%5Cright%29%7D%3Dt%5E%7B%5Cleft%280.5%5Cright%29%7D)
Step-by-step explanation:
Given equation is ![p\left(t\right)=-\log_{10}t^\left(0.5\right)](https://tex.z-dn.net/?f=p%5Cleft%28t%5Cright%29%3D-%5Clog_%7B10%7Dt%5E%5Cleft%280.5%5Cright%29)
Now question says to write that in exponential form.
So we can use the following conversion formula:
![\log_ca=b\ \Rightarrow c^b=a](https://tex.z-dn.net/?f=%5Clog_ca%3Db%5C%20%5CRightarrow%20c%5Eb%3Da)
![p\left(t\right)=-\log_{10}t^\left(0.5\right)](https://tex.z-dn.net/?f=p%5Cleft%28t%5Cright%29%3D-%5Clog_%7B10%7Dt%5E%5Cleft%280.5%5Cright%29)
![-p\left(t\right)=\log_{10}t^\left(0.5\right)](https://tex.z-dn.net/?f=-p%5Cleft%28t%5Cright%29%3D%5Clog_%7B10%7Dt%5E%5Cleft%280.5%5Cright%29)
![\log_{10}t^\left(0.5\right)=-p\left(t\right)](https://tex.z-dn.net/?f=%5Clog_%7B10%7Dt%5E%5Cleft%280.5%5Cright%29%3D-p%5Cleft%28t%5Cright%29)
Apply conversion formula
![p\left(t\right)=-\log_{10}t^\left(0.5\right)\ \Rightarrow 10^{-p\left(t\right)}=t^{\left(0.5\right)}](https://tex.z-dn.net/?f=p%5Cleft%28t%5Cright%29%3D-%5Clog_%7B10%7Dt%5E%5Cleft%280.5%5Cright%29%5C%20%5CRightarrow%2010%5E%7B-p%5Cleft%28t%5Cright%29%7D%3Dt%5E%7B%5Cleft%280.5%5Cright%29%7D)
![10^{-p\left(t\right)}=t^{\left(0.5\right)}](https://tex.z-dn.net/?f=10%5E%7B-p%5Cleft%28t%5Cright%29%7D%3Dt%5E%7B%5Cleft%280.5%5Cright%29%7D)
Answer:
1 : 3.5
Step-by-step explanation:
8 : 28 = 1 : n
n = 28 * 1 : 8
n = 3.5
1 : 3.5
(x-1)(x+6)
⇒ x²+6x-1x-6
⇒ x²+5x-6