Answer:
2.013 to 3 DP's.
Step-by-step explanation:
f(4.04) will be very close to the tangent line.
Equation of tangent line
is y - 4 = m(x - 10)
m = (4-2) / (10-4) = 1/3
y - 4 = 1/3(x - 10)
y = 1/3x - 10/3 + 4
y = 1/3x + 2/3
So the require estimate of f(4.04)
= 1/3(4.04) + 2/3
= 2.013333
Answer:
-11, -17
Step-by-step explanation:
Since we are told it is an arithmetic sequence, we find the common difference. To find the common difference, subtract a term from the next term.
1 - 7 = -6
The common difference is -6.
1st term: 7 (We knew this.)
2nd term: 7 + (-6) = 1 (We knew this.)
3rd term: 1 + (-6) = -5 (We knew this.)
4th term: -5 + (-6) = -11
5th term: -11 + (-6) = -17
Answer: -11, -17
Answer with Step-by-step explanation:
We are given that
Height of ball after t seconds is given by
![s(t)=-4t^2+20t+2](https://tex.z-dn.net/?f=s%28t%29%3D-4t%5E2%2B20t%2B2)
a.Substitute the value of t=1
![s(1)=-4(1)+20(1)+2=-4+20+2=18 ft](https://tex.z-dn.net/?f=s%281%29%3D-4%281%29%2B20%281%29%2B2%3D-4%2B20%2B2%3D18%20ft)
b.Differentiate w.r.t x
![s'(t)=-8t+20](https://tex.z-dn.net/?f=s%27%28t%29%3D-8t%2B20)
![s'(t)=0](https://tex.z-dn.net/?f=s%27%28t%29%3D0)
![-8t+20=0](https://tex.z-dn.net/?f=-8t%2B20%3D0)
![8t=20](https://tex.z-dn.net/?f=8t%3D20)
![t=\frac{20}{8}=2.5](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B20%7D%7B8%7D%3D2.5)
Again differentiate w.r.t t
![s''(t)=-8](https://tex.z-dn.net/?f=s%27%27%28t%29%3D-8%3C0)
Hence, the height is maximum at t=2.5 s
![s(2.5)=-4(2.5)^2+20(2.5)+2=27](https://tex.z-dn.net/?f=s%282.5%29%3D-4%282.5%29%5E2%2B20%282.5%29%2B2%3D27)
Maximum height of the baseball=27 ft
A=bh {A} stands for the area, {b} stands for the length of your parallelogram, and {h} stands for the height of your parallelogram.