Answer:
The Acceleration of bike after 3 minutes of ride is 14 meter² per minutes
Step-by-step explanation:
Given as :
The displacement of bike is the function of time
i.e s(t) = t³ - 2 t² + 3 meters
The Time of bike acceleration = t = 3 minutes
Let The Acceleration of bike = a meter² per minutes
Now, According to question
∵ <u>Acceleration is define as the rate of change of velocity</u>
i.e acceleration = ![\dfrac{\textrm velocity}{\textrm time}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20velocity%7D%7B%5Ctextrm%20time%7D)
or, a = ![\dfrac{\textrm v}{\textrm t}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20v%7D%7B%5Ctextrm%20t%7D)
And
<u>Velocity is define as rate of change of displacement</u>
i.e velocity = ![\dfrac{\textrm displacement}{\textrm time}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20displacement%7D%7B%5Ctextrm%20time%7D)
Or, v = ![\dfrac{\textrm s}{\textrm t}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20s%7D%7B%5Ctextrm%20t%7D)
Since here displacement is function of time
So , v = ![\frac{\partial s(t)}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20s%28t%29%7D%7B%5Cpartial%20t%7D)
Or, v = ![\frac{\partial (t³ - 2 t² + 3)}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20%28t%C2%B3%20-%202%20t%C2%B2%20%2B%203%29%7D%7B%5Cpartial%20t%7D)
Or, v = 3 t² - 4 t + 3
So, velocity is the function of time = v = 3 t² - 4 t + 3 meter per minutes
Now, Again
Acceleration = a = ![\frac{\partial v}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20v%7D%7B%5Cpartial%20t%7D)
Or, a = ![\frac{\partial (3 t² - 4 t + 3)}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20%283%20t%C2%B2%20-%204%20t%20%2B%203%29%7D%7B%5Cpartial%20t%7D)
Or, a = 6 t - 4
∴ Acceleration is the function of time = a = 6 t - 4
Now, Acceleration of bike after 3 minutes
So, at t = 3 min
i.e a = 6 t - 4
Or, a = 6 × 3 - 4
Or, a = 18 - 4
∴ a = 14 meter² per minutes
Hence, The Acceleration of bike after 3 minutes of ride is 14 meter² per minutes . Answer
Step-by-step explanation:
(x= -1)(x=6)
![{x}^{1} = - 1. {x}^{2} = 6](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B1%7D%20%20%3D%20%20-%201.%20%7Bx%7D%5E%7B2%7D%20%20%3D%206)
brainiest pls
Ok log properties
![log_ax+log_ay=log_a(xy)](https://tex.z-dn.net/?f=log_ax%2Blog_ay%3Dlog_a%28xy%29)
and
![\frac{log_ax}{log_ay} log_a(x-y)](https://tex.z-dn.net/?f=%20%5Cfrac%7Blog_ax%7D%7Blog_ay%7D%20log_a%28x-y%29)
and
![nlog_ax=log_ax^n](https://tex.z-dn.net/?f=nlog_ax%3Dlog_ax%5En)
so
pemdas
first make like fractions so we can combine
![\frac{2log_bx}{3} + \frac{3log_by}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2log_bx%7D%7B3%7D%20%2B%20%5Cfrac%7B3log_by%7D%7B4%7D%20)
times first fraction by 4/4 and second by 3/3
![\frac{8log_bx}{12} + \frac{9log_by}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8log_bx%7D%7B12%7D%20%2B%20%5Cfrac%7B9log_by%7D%7B12%7D%20)
combine fractions
![\frac{8log_bx+9log_by}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8log_bx%2B9log_by%7D%7B12%7D%20)
now move fractions up
![\frac{log_b(x^8y^9)}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7Blog_b%28x%5E8y%5E9%29%7D%7B12%7D%20)
now the other part
![\frac{log_b(x^8y^9)}{12}-5log_bz](https://tex.z-dn.net/?f=%5Cfrac%7Blog_b%28x%5E8y%5E9%29%7D%7B12%7D-5log_bz)
we need to combine that
![5log_bz](https://tex.z-dn.net/?f=5log_bz)
with that
![\frac{log_b(x^8y^9)}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Blog_b%28x%5E8y%5E9%29%7D%7B12%7D)
by make it als a fraction of common denomenator of 12
multiply
![5log_bz](https://tex.z-dn.net/?f=5log_bz)
by 12/12
![\frac{60log_bz}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B60log_bz%7D%7B12%7D%20)
move the coefient to expoment
![\frac{log_bz^{60}}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7Blog_bz%5E%7B60%7D%7D%7B12%7D%20)
now conbine fractions
![\frac{log_b(x^8y^9)}{12} - \frac{log_b(z^{60})}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Blog_b%28x%5E8y%5E9%29%7D%7B12%7D%20-%20%20%5Cfrac%7Blog_b%28z%5E%7B60%7D%29%7D%7B12%7D%20)
![\frac{log_b(x^8y^9)-log_b(z^{60})}{12}}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Blog_b%28x%5E8y%5E9%29-log_b%28z%5E%7B60%7D%29%7D%7B12%7D%7D%7B12%7D%20)
apply log property
88.50-75=tip=13.5
13.5/75=0.18=18%
18% tip
Answer:
2560xy^7
Step-by-step explanation:
256x10y^7=16²x10y^7 = 2560xy^7