Answer:
a) 5![cm^{3}](https://tex.z-dn.net/?f=cm%5E%7B3%7D)
Step-by-step explanation:
Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.
When raising to 3, these dimensions are included and therefore 5
is a measure of volume.
The Taylor series is defined by:
![f(x) = \sum \frac{f^n (a)}{n!} (x-a)^n](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csum%20%5Cfrac%7Bf%5En%20%28a%29%7D%7Bn%21%7D%20%28x-a%29%5En)
Let a = 0.
Then its just a matter of finding derivatives and determining how many terms is needed for the series.
Derivatives can be found using product rule:
![f^n (x) = e^x g^{n-1} (x) + e^x g^n (x) \\ g^0 (x) = sin x](https://tex.z-dn.net/?f=f%5En%20%28x%29%20%3D%20e%5Ex%20g%5E%7Bn-1%7D%20%28x%29%20%2B%20e%5Ex%20g%5En%20%28x%29%20%20%5C%5C%20g%5E0%20%28x%29%20%3D%20sin%20x)
Do this successively to n = 6.
![f^1 (x) = e^x (sinx +cos x) \\ f^2 (x) = e^x (2cos x) \\ f^3 (x) = e^x(2cos x - 2sin x) \\ f^4 (x) = e^x (-4 sin x) \\ f^5 (x) = e^x(-4sinx -4cos x) \\ f^6(x) = e^x(-8cos x)](https://tex.z-dn.net/?f=f%5E1%20%28x%29%20%3D%20e%5Ex%20%28sinx%20%2Bcos%20x%29%20%5C%5C%20f%5E2%20%28x%29%20%3D%20e%5Ex%20%282cos%20x%29%20%20%5C%5C%20f%5E3%20%28x%29%20%3D%20e%5Ex%282cos%20x%20-%202sin%20x%29%20%20%5C%5C%20f%5E4%20%28x%29%20%3D%20e%5Ex%20%28-4%20sin%20x%29%20%20%5C%5C%20f%5E5%20%28x%29%20%3D%20e%5Ex%28-4sinx%20-4cos%20x%29%20%5C%5C%20f%5E6%28x%29%20%3D%20e%5Ex%28-8cos%20x%29)
Plug in x=0 and sub into taylor series:
![e^x sin x = x+x^2 +\frac{x^3}{3} -\frac{x^5}{30}-\frac{x^6}{90}...](https://tex.z-dn.net/?f=e%5Ex%20%20sin%20x%20%3D%20x%2Bx%5E2%20%2B%5Cfrac%7Bx%5E3%7D%7B3%7D%20-%5Cfrac%7Bx%5E5%7D%7B30%7D-%5Cfrac%7Bx%5E6%7D%7B90%7D...)
If more terms are needed simply continue the recursive derivative formula and add to taylor series.
Coral reef = 0.15x
0.15(11) = 1.65
1 meter = 100 cm
1.65 * 100 = 165
Solution: 165 cm
1. H=4
W=8
2. L=27
W=21
1. 160÷5=32
1/2 of 8 is 4
8×4=32
I am default dancing right now
2. 2×6=12
96-12=84
84÷4=21
21+6=27 (the length)
21= (the Width)
I think 6) is 17/25, 82%, 8,5, 8/5