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Karolina [17]
4 years ago
7

Determine whether the vector field is conservative. f(x, y) = yi + xj

Mathematics
1 answer:
liubo4ka [24]4 years ago
3 0
<span>If F is a conservative vector fields, then the function f, is called a potential function for F. Example the vector field F(x, y) = y i+x j is a conservative vector field with a potential function of f(x, y) = xy because â‡f =<y,x></span>
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Novay_Z [31]

Answer:

4

Step-by-step explanation:

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5 0
3 years ago
Read 2 more answers
1 Point
I am Lyosha [343]

Option C

The ratio for the volumes of two similar cylinders is 8 : 27

<h3><u>Solution:</u></h3>

Let there are two cylinder of heights "h" and "H"

Also radius to be "r" and "R"

\text { Volume of a cylinder }=\pi r^{2} h

Where π = 3.14 , r is the radius and h is the height

Now the ratio of their heights and radii is 2:3 .i.e  

\frac{\mathrm{r}}{R}=\frac{\mathrm{h}}{H}=\frac{2}{3}

<em><u>Ratio for the volumes of two cylinders</u></em>

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{\pi r^{2} h}{\pi R^{2} H}

Cancelling the common terms, we get

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\left(\frac{\mathrm{r}}{R}\right)^{2} \times\left(\frac{\mathrm{h}}{\mathrm{H}}\right)

Substituting we get,

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\left(\frac{2}{3}\right)^{2} \times\left(\frac{2}{3}\right)

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{2 \times 2 \times 2}{3 \times 3 \times 3}

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{8}{27}

Hence, the ratio of volume of two cylinders is 8 : 27

7 0
3 years ago
I need to know the answer to the question with the circle
KATRIN_1 [288]
___________________________

◆ AREA RELATED TO CIRCLES ◆ ___________________________

As shown in the figure ,

Radius of circle = 5 cm

Side of square = 2 × (Radius of inscribed circle)

Side of square = 2 × 5 cm

Side of square = 10 cm = a

___________________________

Now ,
Area of shaded region = (Area of square) - ( Area of inscribed circle )

Area of shaded region =
{a}^{2} - \pi {r}^{2}

Area of shaded region =
{10}^{2} - \frac{22}{7} \times {5}^{2}

Area of shaded region = 100 - 78.571

= 21.428 \: ans.

7 0
4 years ago
You multiply a number by 3 subtract 6 then add 2 the results is 20 what's the number
e-lub [12.9K]

You multiply a number by 3 subtract 6 then add 2 the results is 20

what's the number​ ?

Let the number = x

multiply a number by 3

so, it becomes 3x

subtract 6 , so, 3x - 6

then add 2

so, 3x - 6 + 2

The result will be 20

So,

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3x - 4 = 20

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3x = 24

Divide both sides by 3

3x/3 = 24/3

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x = 8

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