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:
The total distance is 1422 units
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Answer:
- x-intercept (12.5, 0)
- y-intercept (0, -5)
Step-by-step explanation:
The slope of the line is ...
... (change in y)/(change in x) = (-3 -(-5))/(5 - 0) = 2/5
The y-intercept is given: (0, -5).
The slope-intercept form of the equation can be written from this information as ...
... y = (2/5)x - 5
Solving this for y=0 (to find the x-intercept), we have
... 0 = (2/5)x - 5
... 5 = (2/5)x
... 5·(5/2) = x = 12.5
So, the x-intercept is 12.5, and the y-intercept (given) is -5.
Answer:
Length = 12 inches, height = 3 inches
Step-by-step explanation:
First, you have to set up a proportion. 2/7, x/42.
Then, you cross multiply and get the setup of 84=7x
Finally, you divide 84 by 7 and get 12.
12 is the length, and there is no other answer that has 12 in the height. You could just do the same proportion to get 3, though.
Answer:
$19,201.09
Step-by-step explanation:
The future value of the annuity due can be found using any of a number of apps, calculators, or spreadsheets. It can also be found using the formula ...
A = P(1 +r)((1 +r)^n -1)/r
where P is the annual payment, r is the annual interest rate, and compounding is yearly for n years.
A = 2535(1.1418)(1.1418^5 -1)/0.1418 ≈ 19,201.09
The value will be $19,201.09.