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3 years ago

1-1 Points Lines and Planes PAP Day 2 Can someone help with answering this full worksheet?

Mathematics

1 answer:

snow_tiger [21]3 years ago

5 0

Answer:

first 3 are Yes on the top. number 4: because they are both coplanar. number 5: Yes. number 6 is no. number 7: Yes. number 8 is plan.

Step-by-step explanation:

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Find the counterclockwise circulation and outward flux of the field Fequals7 xy Bold i plus 2 y squared Bold j around and over t

77julia77 [94]

Answer:

The counterclockwise circulation is $\frac{7}{12}$ and the outward flux is $\frac{11}{15}$

Step-by-step explanation:

We are given the field $F(x,y) = (7xy,2y^2)$ . A picture of the region and the path we are considering is attached. Recalll the following theorems.

Given a field of the form F(x,y)=(f(x,y),g(x,y) with f,g having continous partial derivates, C is a closed path counterclockwise oriented, R is the region enclosed by C and n is the normal vector pointing outwards of the path C. Then

$\oint_C F\cdot dr =\iint_R \frac{\partial f}{dy}- \frac{\partial g}{dx} dA$ (this one calculates the counterclockwise circulation)

$\oint_C F\cdot n ds =\iint_R (\frac{\partial f}{dx}+ \frac{\partial g}{dy} dA$ (This one calculates the outward flux)

Then, recall that in our case f(x,y) = 7xy, g(x,y)=2y^2[/tex]. Then

$\frac{\partial f}{dx} = 7y,\frac{\partial f}{dy} = 7x$

$\frac{\partial g}{dx}=0, \frac{\partial g}{dy} = 4y$ .

Note that we just need to describe our region R. The region R lies between the parabola y=x^2 and the line y=x. Thus, one way to describe the region is as follows $0\leq x \leq 1, x^2\leq y \leq x$ . Then, using the previous results, we get that

$\oint_C F\cdot dr =\int_{0}^{1}\int_{x^2}^{x}7x-0dydx = 7\int_{0}^1x(x-x^2)dx = 7 \left.(\frac{x^3}{3}-\frac{x^4}{4})\right|_{0}^1 = 7(\frac{1}{3}-\frac{1}{4}) = \frac{7}{12}$ (circulation)

$\oint_C F\cdot n ds=\int_{0}^{1}\int_{x^2}^{x}7y+4ydydx = \frac{11}{2}\int_{0}^1\left.y^2\right_{x^2}^{x}dx = \frac{11}{2}\int_{0}^{1}x^2-x^4 dx = \frac{11}{2}\left(\frac{x^3}{3}-\frac{x^5}{5})\right|_{0}^{1}=\frac{11}{2}(\frac{1}{3}-\frac{1}{5})=\frac{11}{15}$ (flux)

5 0

3 years ago

Which is an equation of the line with x-intercept 2 and y-intercept 12?

Troyanec [42]

Answer:

Step-by-step explanation:

it fits correctly to the description

4 0

3 years ago

Read 2 more answers

The sum of two numbers is 436. The larger number is 3 times the smaller number. What are the numbers?

wolverine [178]

The numbers are 109 and 327. Hope it helps!

5 0

3 years ago

During the summer holidays sarah earns pocket money by mowing lawn. She can mow 6 lawns in 1 1/2 and clean the pool in one-sixth

tigry1 [53]

Answer:

It will take Sarah 2 1/2 hours to mow 10 lawns

It will take Sarah 1 2/3 hours to clean 10 pools

Step-by-step explanation:

During the summer holidays, Sarah earns pocket money by mowing the lawn. She can mow 6 lawns in 1 1/2 hour and clean a pool in one-sixth of an hour. How long does Sarah take to clean 10 pools and 10 lawns?

Number of lawns : Time to mow lawns = 6 : 1 1/2

= 6 : 3/2

Number of lawns : Time to mow lawns = 10 : x

6 : 3/2 = 10 : x

6 ÷ 3/2 = 10/x

6 * 2/3 = 10/x

12/3 = 10/x

Cross product

12 * x = 3 * 10

12x = 30

x = 30/12

x = 2 6/12

x = 2 1/2 hours

It will take Sarah 2 1/2 hours to mow 10 lawns

Number of pools cleaned : time taken = 1 : 1/6

Number of pools cleaned : time taken = 10 : x

1 : 1/6 = 10 : x

1 ÷ 1/6 = 10/x

1 * 6/1 = 10/x

6 = 10/x

Cross product

6 * x = 10

6x = 10

x = 10/6

x = 1 4/6

x = 1 2/3 hours

It will take Sarah 1 2/3 hours to clean 10 pools

3 0

3 years ago

Simplify (shown in photo)<br> A: 2^1/6<br> B: 2^2/3<br> C: 2^5/6<br> D: 2^7/6

mihalych1998 [28]

Your answer would be C

(√2)(∛2)

( $\sqrt[6]{2^3}$ )( $\sqrt[6]{2^2}$ )

$\sqrt[6]{2^5}$ = $\sqrt[6]{32}$

If you do 2^5/6

$\sqrt[6]{2^5}$ = $\sqrt[6]{32}$

5 0

4 years ago