The total distance traveled by the robot from t=0 to t=9 is 1422 units
Integration is a way in which smaller components are brought together in pieces to form a whole. Integration can be used in finding areas, volumes and so on.
Given that the position s(t) at any time t is given by the function:
s(t)=9t²−90t+4
The total distance traveled by the robot from t=0 to t=9 can be gotten by integrating the position function within the limits 0< t < 9
Therefore:
![Total\ distance = \int\limits^9_0 {s(t) \, dt \\\\Total\ distance = \int\limits^9_0 {(9t^2-90t+4) \, dt\\\\Total\ distance = [3t^3-45t+4t]_0^9\\\\Total\ distance=-1422\ units](https://tex.z-dn.net/?f=Total%5C%20distance%20%3D%20%5Cint%5Climits%5E9_0%20%7Bs%28t%29%20%5C%2C%20dt%20%5C%5C%5C%5CTotal%5C%20distance%20%3D%20%5Cint%5Climits%5E9_0%20%7B%289t%5E2-90t%2B4%29%20%5C%2C%20dt%5C%5C%5C%5CTotal%5C%20distance%20%3D%20%5B3t%5E3-45t%2B4t%5D_0%5E9%5C%5C%5C%5CTotal%5C%20distance%3D-1422%5C%20units)
The total distance is 1422 units
Find out more at: brainly.com/question/22008756
Answer:
603.19
Step-by-step explanation:
v=π
pi is 3.14
Radius= Diameter/2= 4, so r square= 16
Height= Radius*3=12
So volume= 3.14*16*12=603.19
Answer:
11/12 = 3/4
Step-by-step explanation:
sorry that's the only one I know :(
Since in the above case, the beaker has two sections each with different radius and height, we will divide this problem into two parts.
We will calculate the volume of both the beakers separately and then add them up together to get the volume of the beaker.
Given, π = 3.14
Beaker 1:
Radius (r₁) = 2 cm
Height (h₁) = 3 cm
Volume (V₁) = π r₁² h₁ = 3.14 x 2² x 3 = 37.68 cm³
Beaker 2:
Radius (r₂) = 6 cm
Height (h₂) = 4 cm
Volume (V₂) = π r₂² h₂ = 3.14 x 6² x 4 = 452.16 cm³
Volume of beaker = V₁ + V₂ = 37.68 + 452.16 = 489.84 cm³
Answer:
6^2
Step-by-step explanation:
We know a^b / a^c = a^(b-c)
6^5 / 6^3 = 6^(5-3) = 6^2
