Answer:
= 
Step-by-step explanation:
To find - Find the average value fave of the function f on the given interval. f(x) = 5 sec²(x/6), [0, 3
/2]
Proof -
We know that,
Average value of f in the interval [a, b] is -
= 
Now,
Here a = 0, b = 
, f(x) = 
Now,
= 
= 
= 
= ![{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) }|^{\frac{3\pi }{2} }_0 \, ]](https://tex.z-dn.net/?f=%7B%5Cfrac%7B10%20%7D%7B3%5Cpi%20%7D%7D%5B%5C%20%7Btan%28%7B%5Cfrac%7Bx%7D%7B6%7D%20%7D%29%20%7D%7C%5E%7B%5Cfrac%7B3%5Cpi%20%7D%7B2%7D%20%7D_0%20%5C%2C%20%5D)
= ![{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) - tan({0) } \, ]](https://tex.z-dn.net/?f=%7B%5Cfrac%7B10%20%7D%7B3%5Cpi%20%7D%7D%5B%5C%20%7Btan%28%7B%5Cfrac%7Bx%7D%7B6%7D%20%7D%29%20-%20tan%28%7B0%29%20%7D%20%5C%2C%20%5D)
= ![{\frac{10 }{3\pi }}[ {1 - 0 } ]](https://tex.z-dn.net/?f=%7B%5Cfrac%7B10%20%7D%7B3%5Cpi%20%7D%7D%5B%20%7B1%20-%200%20%7D%20%20%5D)
=
⇒ =
Answer:x=-2
Step-by-step explanation:
You want to set up the equal to zero
Then add six to both sides
Then divide by -3x
Answer:
243cm^3
Step-by-step explanation:
By Pythagoras' Theorem,
height of the prism ^2 + 5.4^2 = 7.8^2
height of the prism = ±√(7.8^2 -5.4^2) = ±5.6285cm (5s.f.) (rej. - 5.6285 since height > 0cm)
volume of the prism = 1/2 x 5.4 x 5.6285 x 16 = 243cm^3 (3s.f.)
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Answer:
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Step-by-step explanation:
Answer:that hard
Step-by-step explanation:
