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2 years ago

12

Parallel to 7x+5y=3, through (9,-9)

1 answer:

love history [14]2 years ago

3 0

The answer should be -5x + 7y = -108

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Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.

This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

3 0

2 years ago

Cindy took her five grandchildren to the movies, where she offered to buy all of them popcorn and candy. A popcorn bag costs $4.

Svetradugi [14.3K]

Answer:

She buys 5 boxes of popcorn and 6 boxes of candy

Step-by-step explanation:

this is because 5 times 4.00 is 20$ and 2.50 times 6 is 15$

15 + 20 is 35

so your answer is 5 boxes of popcorn and 6 boxes of candy

hope this helped :D

6 0

2 years ago

Simplify the expression:<br> 10s+–2s

likoan [24]

Answer:

8s

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Algebra I</u>

Terms

Step-by-step explanation:

<u>Step 1: Define</u>

10s + -2s

<u>Step 2: Simplify</u>

Rewrite: 10s - 2s
Combine like terms: 8s

3 0

2 years ago

Read 2 more answers

Easy problem nice about of points

bezimeni [28]

Answer:

1

Step-by-step explanation: i am not sure

6 0

2 years ago

TJ earns a 20% commission on all sales plus a base salary of $40,000. His total income last year was more than $70,000. Which in

sukhopar [10]

Answer:

40,000 + 0.2x ≥ 70,000

3 0

2 years ago