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Jobisdone [24]
3 years ago
15

Help please someone math

Mathematics
1 answer:
NeX [460]3 years ago
3 0
I think it is c, because the probability is the littlest thing and you add most of it, you are welcome my boy
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1. Let f(x, y) be a differentiable function in the variables x and y. Let r and θ the polar coordinates,and set g(r, θ) = f(r co
Olenka [21]

Answer:

g_{r}(\sqrt{2},\frac{\pi}{4})=\frac{\sqrt{2}}{2}\\

Step-by-step explanation:

First, notice that:

g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}cos(\frac{\pi}{4}),\sqrt{2}sin(\frac{\pi}{4}))\\

g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}(\frac{1}{\sqrt{2}}),\sqrt{2}(\frac{1}{\sqrt{2}}))\\

g(\sqrt{2},\frac{\pi}{4})=f(1,1)\\

We proceed to use the chain rule to find g_{r}(\sqrt{2},\frac{\pi}{4}) using the fact that X(r,\theta)=rcos(\theta)\ and\ Y(r,\theta)=rsin(\theta) to find their derivatives:

g_{r}(r,\theta)=f_{r}(rcos(\theta),rsin(\theta))=f_{x}( rcos(\theta),rsin(\theta))\frac{\delta x}{\delta r}(r,\theta)+f_{y}(rcos(\theta),rsin(\theta))\frac{\delta y}{\delta r}(r,\theta)\\

Because we know X(r,\theta)=rcos(\theta)\ and\ Y(r,\theta)=rsin(\theta) then:

\frac{\delta x}{\delta r}=cos(\theta)\ and\ \frac{\delta y}{\delta r}=sin(\theta)

We substitute in what we had:

g_{r}(r,\theta)=f_{x}( rcos(\theta),rsin(\theta))cos(\theta)+f_{y}(rcos(\theta),rsin(\theta))sin(\theta)

Now we put in the values r=\sqrt{2}\ and\ \theta=\frac{\pi}{4} in the formula:

g_{r}(\sqrt{2},\frac{\pi}{4})=f_{r}(1,1)=f_{x}(1,1)cos(\frac{\pi}{4})+f_{y}(1,1)sin(\frac{\pi}{4})

Because of what we supposed:

g_{r}(\sqrt{2},\frac{\pi}{4})=f_{r}(1,1)=-2cos(\frac{\pi}{4})+3sin(\frac{\pi}{4})

And we operate to discover that:

g_{r}(\sqrt{2},\frac{\pi}{4})=-2\frac{\sqrt{2}}{2}+3\frac{\sqrt{2}}{2}

g_{r}(\sqrt{2},\frac{\pi}{4})=\frac{\sqrt{2}}{2}

and this will be our answer

3 0
3 years ago
Which statement describes how to solve<br> 3x+4 = 3x+4?
Likurg_2 [28]

Answer:

That is a infinite solutions equation, but to solve this you would have to subtract 3x from both sides and you will get 4=4.

Step-by-step explanation:

3x+4=3x+4

<u>-3x    -3x</u>

4=4

5 0
3 years ago
What is 24 kg =_____g
Evgen [1.6K]
1 kg = 1 * 10 ^ 3 g

kilo = 10^3
5 0
3 years ago
Read 2 more answers
John was having a party he knows his bowl can hold 2/3 of a bag of Doritos.if he has 4 bags or Doritos how many bowls does he ne
Verizon [17]

Step-by-step explanation:

2•4 =8

8/3 =2 2/3

answer : 3

7 0
3 years ago
What part of this problem needs to be changed to make it correct? explain how you know. 46 divided by 8 = 6.75
Mnenie [13.5K]
46 \div 8 = 6.75\\47/8 ?= 6.75\\5.75 = 6.75 [no]\\So the equation is False.\\ In order to make it correct it has to equal 6.75
7 0
3 years ago
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