Arithmetic sequences have a common difference (addition)
geometric sequences have a common ratio (multiplication)
Answer:
Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations". ... A reflection is called a rigid transformation or isometry because the image is the same size and shape as the pre-image.
Hope it helps!!!
Answer:
Step-by-step explanation:
![x + 2y + 3z = 12](https://tex.z-dn.net/?f=x%20%2B%202y%20%2B%203z%20%3D%2012)
![z=\frac{12-x-2y}{3}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B12-x-2y%7D%7B3%7D)
Volume = ![V=f(x,y) = xy(\frac{12-x-2y}{3} )](https://tex.z-dn.net/?f=V%3Df%28x%2Cy%29%20%3D%20xy%28%5Cfrac%7B12-x-2y%7D%7B3%7D%20%29)
find partial derivatives using product rule
![f_x =\frac{y}{3} (12-2x-2y)\\f_y = \frac{x}{3} (12-x-4y)](https://tex.z-dn.net/?f=f_x%20%3D%5Cfrac%7By%7D%7B3%7D%20%2812-2x-2y%29%5C%5Cf_y%20%3D%20%5Cfrac%7Bx%7D%7B3%7D%20%2812-x-4y%29)
i.e.
Using maximum for partial derivatives, we equate first partial derivative to 0.
y=0 or x+y =6
x=0 or x+4y =12
Simplify to get y =2, x = 4
thus critical points are (4,2) (6,0) (0,3)
Of these D the II derivative test gives
D<0 only for (4,2)
Hence maximum volume is when x=4, y=2, z= 4/3
Max volume is = 4(2)(4/3) = 32/3
Answer:
5 hours
Step-by-step explanation:
If shes going 59mph and the total trip is 295mph
then you would divid 295 by 59 and get 5
Answer:
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