Please help! Given: 4

Mathematics

1 answer:

andrey2020 [161]3 years ago

4 0

Answer:

help with what? where is the question

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Let f be a function of two variables that has continuous partial derivatives and consider the points a(7, 3), b(12, 3), c(7, 7),

luda_lava [24]

The directional derivative of a function $f(x,y)$ in the direction of $\mathbf v$ is given by

$\nabla f(x,y)\cdot\mathbf v$

We have $\vec{ab}=\mathbf b-\mathbf a=(12-7,3-3)=(5,0)$ , so that $\|\vec{ab}\|=5$ , at which point we're given

$\nabla f(7,3)\cdot\dfrac{(5,0)}5=5\implies1\cdot\dfrac{\partial f}{\partial x}(7,3)+0\cdot\dfrac{\partial f}{\partial y}(7,3)=5$

$\implies\dfrac{\partial f}{\partial x}(7,3)=5$

We're also given that, in the direction of $\vec{ac}=\mathbf c-\mathbf a=(7-7,7-3)=(0,4)$ with $\|\vec{ac}\|=4$ , we have

$\nabla f(7,3)\cdot\dfrac{(0,4)}4=4\implies0\cdot\dfrac{\partial f}{\partial x}(7,3)+1\cdot\dfrac{\partial f}{\partial y}(7,3)=4$

$\implies\dfrac{\partial f}{\partial y}(7,3)=4$

So in the direction of $\vec{ad}=\mathbf d-\mathbf a=(15-7,9-3)=(8,6)$ , with $\|\vec{ad}\|=10$ , we have

$\nabla f(7,3)\cdot\dfrac{(8,6)}{10}=\dfrac1{10}(4,4)\cdot(8,6)=9.60$

5 0

3 years ago

Im not the best at math so pls help

sergejj [24]

Answer:

4/5 is the answer

Step-by-step explanation:

2/5 equals 4/10 plus the other 4/10 equals 8/10 simplified 4/5

7 0

4 years ago

Which of these numbers are divisible by 9 a) 6966 b) 8366 c) 39 015

lakkis [162]