Answer:
16/3 or 5 1/3
Step-by-step explanation:
Because 2/3 * 8 = 16/3.
16/3 simplified is 5 1/3
The period of the function is that distance where the function becomes equal again.
We have then:
Part 1:
The period of the function is:
T = 3
Part 2:
The period of the function is:
T = 4
Answer:
The period of functions 1 and 2 respectively are:
T = 3
T = 4
The solution for l4 is mathematically given as
L_{4}=0.5431
<h3>What is the solution for l4?</h3>
![&\text { Given } f(x)=a \cos ^{2}(x) \quad\left[\frac{\pi}{8}, \frac{\pi}{2}\right] \text { \& } n=4\\\\&\Delta a=\frac{b-a}{n}=\frac{\pi / 2-\pi / 8}{9}=\frac{3 \pi}{32}\\\\&x_{0}=\pi / 8, x_{1}=\frac{\pi}{8}+\frac{3 \pi}{32}=\frac{7 \pi}{32}\\\\&x_{2}=\frac{5 \pi}{16}, \quad x_{3}=\frac{13 \pi}{32}, x_{4}=\pi / 2\\\\&f\left(x_{0}\right)=f(1 / 8)=0.8535\\](https://tex.z-dn.net/?f=%26%5Ctext%20%7B%20Given%20%7D%20f%28x%29%3Da%20%5Ccos%20%5E%7B2%7D%28x%29%20%5Cquad%5Cleft%5B%5Cfrac%7B%5Cpi%7D%7B8%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cright%5D%20%5Ctext%20%7B%20%5C%26%20%7D%20n%3D4%5C%5C%5C%5C%26%5CDelta%20a%3D%5Cfrac%7Bb-a%7D%7Bn%7D%3D%5Cfrac%7B%5Cpi%20%2F%202-%5Cpi%20%2F%208%7D%7B9%7D%3D%5Cfrac%7B3%20%5Cpi%7D%7B32%7D%5C%5C%5C%5C%26x_%7B0%7D%3D%5Cpi%20%2F%208%2C%20x_%7B1%7D%3D%5Cfrac%7B%5Cpi%7D%7B8%7D%2B%5Cfrac%7B3%20%5Cpi%7D%7B32%7D%3D%5Cfrac%7B7%20%5Cpi%7D%7B32%7D%5C%5C%5C%5C%26x_%7B2%7D%3D%5Cfrac%7B5%20%5Cpi%7D%7B16%7D%2C%20%5Cquad%20x_%7B3%7D%3D%5Cfrac%7B13%20%5Cpi%7D%7B32%7D%2C%20x_%7B4%7D%3D%5Cpi%20%2F%202%5C%5C%5C%5C%26f%5Cleft%28x_%7B0%7D%5Cright%29%3Df%281%20%2F%208%29%3D0.8535%5C%5C)
![&f\left(x_{1}\right)=f\left(\frac{7 \pi}{32}\right)=0.5975\\\\\&f\left(x_{2}\right)=f\left(\frac{5 \pi}{16}\right)=0.3086\\\\\&f\left(a_{3}\right)=f\left(\frac{13 \pi}{32}\right)=0.0842\\\\\&L_{4}=\sum_{k_{0}^{=0}}^{3} f\left(x_{k}\right) \Delta x\\\\&=\Delta \\\\x\left[f\left(x_{0}\right)+f\left(x_{1}\right)+f\left(x_{2}\right)+f\left(x_{3}\right)\right]\\\\\&=\frac{3 \pi}{32}[0.8535+0.5975+0.3056+0.0842]\\\\&L_{4}=0.5431](https://tex.z-dn.net/?f=%26f%5Cleft%28x_%7B1%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B7%20%5Cpi%7D%7B32%7D%5Cright%29%3D0.5975%5C%5C%5C%5C%5C%26f%5Cleft%28x_%7B2%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B5%20%5Cpi%7D%7B16%7D%5Cright%29%3D0.3086%5C%5C%5C%5C%5C%26f%5Cleft%28a_%7B3%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B13%20%5Cpi%7D%7B32%7D%5Cright%29%3D0.0842%5C%5C%5C%5C%5C%26L_%7B4%7D%3D%5Csum_%7Bk_%7B0%7D%5E%7B%3D0%7D%7D%5E%7B3%7D%20f%5Cleft%28x_%7Bk%7D%5Cright%29%20%5CDelta%20x%5C%5C%5C%5C%26%3D%5CDelta%20%5C%5C%5C%5Cx%5Cleft%5Bf%5Cleft%28x_%7B0%7D%5Cright%29%2Bf%5Cleft%28x_%7B1%7D%5Cright%29%2Bf%5Cleft%28x_%7B2%7D%5Cright%29%2Bf%5Cleft%28x_%7B3%7D%5Cright%29%5Cright%5D%5C%5C%5C%5C%5C%26%3D%5Cfrac%7B3%20%5Cpi%7D%7B32%7D%5B0.8535%2B0.5975%2B0.3056%2B0.0842%5D%5C%5C%5C%5C%26L_%7B4%7D%3D0.5431)
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The complete Question is attached below
Answer:
MN = 7 cm
Step-by-step explanation:
Well the volume we can separate into pieces
first the ABCDEFGH (? you know this cuboid)
which has a volume of

if you ask where does the 4 come from
it comes from LP = KB = YC and JY + YC =JC
so

this is because JY = MX
the other volume is of BCNPKLXY (hope you understand which one)
and the volume is

and the last one is KYXLMJ (the top "triangle")
the volume is

so now add them up
and has to equal 444

and finally we know that MN = MX + XN = 3+4 = 7
so here is our answer MN = 7 cm
a couple of notes

3. the units don't matter due to the fact that everything is in cm
4. see the picture below to get a better idea of which prism I am talking of
5. tell me if you have questions :D
Answer:
Required equation is
.
Step-by-step explanation:
Given,
Height of the tree=5x+6
Distance from feet of the tree=2x-4
To find straight distance from feet of Madeline to top of the tree.
Let the tree as y-axis and distance from base along x-axis. Then the distence of straight line from foot of Madeline to top is become the hypotenuse of the triangle. Thus if we let,
Distance from feet of Madeline to top of tree= p, then, according to law of finding third side of a triangle we get,


Hence the result.