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ValentinkaMS [17]

2 years ago

7

Sandra scores 12 out of 30 in her maths test. Write this as a fraction in its simplest form.

1 answer:

Andrew [12]2 years ago

8 0

Step-by-step explanation:

12/30

find highest common factor; 6

divide both sides by 6

(12/6) (30/6)

2/5

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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

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2 years ago

Increase £140 by 5%. <br> Thank you so much

liubo4ka [24]

Answer:

£140 increased by 5% is £147.00

8 0

2 years ago

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Show that 6x^2+17x-39=0

8_murik_8 [283]

I hope this helps you

4 0

2 years ago

PLEASE HELP ! (2/4) - 50 POINTS -

tatuchka [14]

Answer:

The correct answer would be 15.5 or C.

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A cell phone company charges $4 per GB beyond

MArishka [77]

Answer:

25GB was used that month

Step-by-step explanation:

Here, we want to calculate the GB used for the month.

Since we have $59.99 for 20GB, then the extra that brought the bill to $75.99 must have been from the beyond charges.

The extra charges is thus $75.99 - $59.99 = $20

Now, since $4 is charged as extra and we have a total of $20, the number of extra GB is thus 20/4 = 5

So the total GB for that month is 20 + 5 = 25GB

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2 years ago