Answer:
99 ounces
Step-by-step explanation:
ok for this you'll need to convert the 6 pounds to ounces first.
there are 16 ounces in 1 pound (16oz=1 lb)
use a conversion factor:
6 pounds * (16oz/1 lb)=96 oz
dont forget to add the three original ounces::
96+3=99 ounces total
Answer:
x ≥ 89
Step-by-step explanation:
Since Jonathan needs at least an 89, his score must be greater than or equal to an 89.
Answer:
B
Step-by-step explanation:
I'm not that smart, but. I have a gut feeling this is right.
Answer:
It would roll in this direction.
![\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})](https://tex.z-dn.net/?f=%5Cnu%20%20%3D%20%20%28-a%2F%5Csqrt%7Ba%5E2%2Bb%5E2%7D%2C-b%2F%5Csqrt%7Ba%5E2%2Bb%5E2%7D%29)
Step-by-step explanation:
It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.
Since
![z = ax^2 + by^2](https://tex.z-dn.net/?f=z%20%3D%20%20ax%5E2%20%20%2B%20by%5E2)
For this case, the gradient of your function would be
![\nabla z = (2ax , 2by)](https://tex.z-dn.net/?f=%5Cnabla%20z%20%20%3D%20%282ax%20%2C%202by%29)
And -1 times the gradient of your function would be
![-\nabla z = (-2ax , -2by)\\](https://tex.z-dn.net/?f=-%5Cnabla%20z%20%20%3D%20%28-2ax%20%2C%20-2by%29%5C%5C)
Then, at
![(1,1,a+b),\\x = 1 \\y = 1](https://tex.z-dn.net/?f=%281%2C1%2Ca%2Bb%29%2C%5C%5Cx%20%3D%201%20%5C%5Cy%20%3D%201)
So it would go towards
![v = (-2a,-2b)](https://tex.z-dn.net/?f=v%20%3D%20%28-2a%2C-2b%29)
The magnitud of that vector is
![|v| = 2\sqrt{a^2+b^2}](https://tex.z-dn.net/?f=%7Cv%7C%20%3D%20%202%5Csqrt%7Ba%5E2%2Bb%5E2%7D)
and to conclude it would roll in this direction.
![\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})](https://tex.z-dn.net/?f=%5Cnu%20%20%3D%20%20%28-a%2F%5Csqrt%7Ba%5E2%2Bb%5E2%7D%2C-b%2F%5Csqrt%7Ba%5E2%2Bb%5E2%7D%29)
Answer:
the distributive property. or distribution
hope this helps! :)