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2 years ago

Write each proof as a two column proof

Mathematics

1 answer:

Karo-lina-s [1.5K]2 years ago

8 0

Answer:

Step-by-step explanation:

What can be used as a statement in a two column proof?

A two-column proof consists of a list of statements, and the reasons why those statements are true. The statements are in the left column and the reasons are in the right column. The statements consists of steps toward solving the problem.

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Red is the favorite color of 7 students. Yellow is the favorite color of 6 students. How many more students like red than yellow

trasher [3.6K]

Well I know you said dont answer with subtraction and adding but thats how you do it... 1 more student likes read more than yellow

7-6.. is 1

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Dont know how else to tell ya

4 0

2 years ago

Read 2 more answers

Anyone help me with this?

den301095 [7]

h = 4(x+3y) + 2

4×x = 4x

4×3y= 12y

4x+12y+2

x= $\frac{12y+2}{4} \\\$

tell me if im wrong

ignore the last bit, x=$

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2 years ago

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.