Product is to multiplications as quotient is to

Evaluate the line integral, where C is the given curve. (x + 6y) dx + x2 dy, C C consists of line segments from (0, 0) to (6, 1)

Dima020 [189]

Split $C$ into two component segments, $C_1$ and $C_2$ , parameterized by

$\mathbf r_1(t)=(1-t)(0,0)+t(6,1)=(6t,t)$

$\mathbf r_2(t)=(1-t)(6,1)+t(7,0)=(6+t,1-t)$

respectively, with $0\le t\le1$ , where $\mathbf r_i(t)=(x(t),y(t))$ .

We have

$\mathrm d\mathbf r_1=(6,1)\,\mathrm dt$

$\mathrm d\mathbf r_2=(1,-1)\,\mathrm dt$

where $\mathrm d\mathbf r_i=\left(\dfrac{\mathrm dx}{\mathrm dt},\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt$

so the line integral becomes

$\displaystyle\int_C(x+6y)\,\mathrm dx+x^2\,\mathrm dy=\left\{\int_{C_1}+\int_{C_2}\right\}(x+6y,x^2)\cdot(\mathrm dx,\mathrm dy)$

$=\displaystyle\int_0^1(6t+6t,(6t)^2)\cdot(6,1)\,\mathrm dt+\int_0^1((6+t)+6(1-t),(6+t)^2)\cdot(1,-1)\,\mathrm dt$

$=\displaystyle\int_0^1(35t^2+55t-24)\,\mathrm dt=\frac{91}6$

6 0

3 years ago

Part C

mel-nik [20]

Answer:

Tamara needs to cover a total of 476 square feet.
Tamara will have enough material to cover all four walls.

Step-by-step explanation:

If the room dimensions are 8 1/3 feet by 11 1/2 feet, the perimeter length is ...

P = 2(L+W) = 2(8 1/3 +11 1/2) = 2(19 5/6) = 39 2/3 feet

The area of the walls is the product of this perimeter length and the height of the wall. If that height is 12 feet, then the wall area is ...

A = PH = (39 2/3 ft)(12 ft) = 476 ft²

Tamara needs to cover a total of 476 square feet.

__

If Tamara orders 480 square feet of material, ...

Tamara will have enough to cover all four walls.

6 0

3 years ago

6) -5x - 7y= 11 x - 2y=-9

sladkih [1.3K]

Answer:

Please check the attachment.

HOPE U UNDERSTOOD

COMMENT IF ANY DOUBTS

THANK YOU.

3 0

3 years ago

For each function below, determine whether or not the function is injective and whether or not the function is surjective. (You

Harlamova29_29 [7]

Answer: First, injective means that for every y, there is only one x such f(x) = y, and surjective means that if f is a function that goes from the set {x} to the set {y}, for every element y in the codomain there is at least one element x in the domain such f(x) = y

(a) f:R----> + R given by f(x) = x2 (i guess you written $x^{2}$ )

The function is not injective, because f(-2) = f(2), and is surjective, because the codomain is +R, and $x^{2}$ is always a positive real number.

(b) f:N----> + N given by f(n) = n2 (i guess you written $n^{2}$ )

As the naturals have no negative numbers, in this case the function is injective, but isn't surjective, because there is no number that when squared is equal to 5, for example.

(c) f: Zx Z → Z given by f(n, k) = n +k:

here the domain is of the form (n,k) and the function is n +k, so the numbers (z,w) and (w,z) return the same value when evaluated in f, then f is not injective. And is easy to see that f is surjective, because in the sum you can reach al the integers on the codomain.

3 0

3 years ago

What is the average of -2.6, 1.8, -3.3, -2.7, 2.2 ? I dont understand this.

olya-2409 [2.1K]

Average = Mean

To find the mean, add up the numbers and divide it by how many numbers there are.

So, $-2.6+1.8+(-3.3)+(-2.7)+2.2=-4.6$

There are 5 numbers in total.

$-4.6 \div 5=-0.92$

To do these types of division, ignore the decimal and add a 0 at the end.

So we can do:
$-460\div5=-92$

And put back the decimal.
Hope this helps :)

4 0

3 years ago

Product is to multiplications as quotient is to​

Product is to multiplications as quotient is to