If;
A = Adjacent
O = Opposite
H = Hypotenuse
Then,
Sin Ф = O/H
Cos Ф = A/H
Therefore,
(Sin Ф)/Cos Ф) = (O/H)/(A/H) = (O/H)*(H/A) = O/A
Now,
tan Ф = O/A ----
Therefore, it is true that
tan Ф = SinФ/CosФ
Answer:
16π square units.
Step-by-step explanation:
Please refer to the graph below.
So, if we draw a representative rectangle, the width of the rectangle will be (x), and the height of the rectangle at each (x) will be given by f(x) - g(x).
By the shell method:
![\displaystyle V=2\pi\int_a^bp(x)h(x)\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D2%5Cpi%5Cint_a%5Ebp%28x%29h%28x%29%5C%2Cdx)
We are integrating from x = 0 to x = 2. p(x) is x and h(x) is f(x) - g(x):
![\displaystyle V=2\pi\int_0^2(x)((8-x^2)-(x^2))\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D2%5Cpi%5Cint_0%5E2%28x%29%28%288-x%5E2%29-%28x%5E2%29%29%5C%2Cdx)
Evaluate. Simplify:
![\displaystyle V=2\pi \int_0^2(8x-2x^3)\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D2%5Cpi%20%5Cint_0%5E2%288x-2x%5E3%29%5C%2Cdx)
Hence:
![\displaystyle V=2\pi\Big(4x^2-\frac{1}{2}x^4\Big|_{0}^{2}\Big)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D2%5Cpi%5CBig%284x%5E2-%5Cfrac%7B1%7D%7B2%7Dx%5E4%5CBig%7C_%7B0%7D%5E%7B2%7D%5CBig%29)
Evaluate:
![\displaystyle \begin{aligned} V &= 2 \pi \Big[(4(2)^2-\frac{1}{2}(2)^4)-(4(0)^2-\frac{1}{2}(0)^4)\Big]\\ &=2\pi(8) \\&=16\pi\text{ square units} \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20V%20%26%3D%202%20%5Cpi%20%5CBig%5B%284%282%29%5E2-%5Cfrac%7B1%7D%7B2%7D%282%29%5E4%29-%284%280%29%5E2-%5Cfrac%7B1%7D%7B2%7D%280%29%5E4%29%5CBig%5D%5C%5C%20%26%3D2%5Cpi%288%29%20%5C%5C%26%3D16%5Cpi%5Ctext%7B%20square%20units%7D%20%5Cend%7Baligned%7D)
Since it is asking you to graph heres what it should look like. Since -4/3 is the slope it should be a negative line (going down) and the 8 is the y-intercept (where the line hits the y axis) And I didnt draw the numbers because it's going by 1's. Hope this helps!
Answer:
4k - 8
Step-by-step explanation:
Lucy is k years old so we know k is an important part of this problem.
Sister 1 is 3 years younger, so she is k - 3 years old.
Sister 2 is 5 years less than twice Lucy's age therefore, she is 2k (twice Lucy's age) - 5 years old.
Now we have: k + (k - 3) + (2k - 5)
We can simplify like terms with the k's and get 4k. then we add (-3) and (-5) to get 4k - 8.
Hope this helps!
9514 1404 393
Answer:
a) 16
b) any value. For example, 2, or 29.
Step-by-step explanation:
a) The sum of the 23 given values is 389. For the mean of 24 values to be 16.875, the total must be 405. Adding the value 16 to the list will make the total be 405
The value that makes the mean 16.875 is 16.
__
b) The median of the given data is 17, it is the middle of 3 instances of 17 in the data set. If a lower number is added to the data set, the median will be the average of the first two 17s. If a higher number is added, the median will be the average of the last two 17s. In other words, there is no number that can be added that will change the median from 17.
Any value can be added without changing the median.