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Finger [1]
2 years ago
7

Look at the figure. Which step should be taken next to construct a line through point R that is perpendicular to ST ?

Mathematics
1 answer:
Alika [10]2 years ago
8 0

Answer:

where is the figure without figure how to find out

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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
3 years ago
9) Let<br> X-2, x, x+3 <br> be the first 3 terms of a geometric sequence. FInd the value of x..
Reil [10]
Hello,

Let's r the ration

We suppose x ≠0

x=r*(x-2)==>r=x/(x-2)

x+3=r*x==> (x+3)/x=x/(x-2)==>(x+3)(x-2)=x²
==>x²+3x-2x-6=x² ==>x-6=0==>x=6

x-2=6-4=4
x=6
x+3=6+3=9
6=4*3/2
9=6*3/2

Ration 3/2
First term: 4

7 0
2 years ago
The hypotenuse of a right triangle measures 9 inches, and one of the acute angle measures 36 degrees. What is the area of the tr
Pie
<span>sin(36)(9) = 5.29
cos(36)(9) = 7.28

Area = (1/2)bh
Area = (1/2)(5.29)(7.28)
Area = 19 sq. in.</span>
8 0
3 years ago
Age If you add Natalie's age and Fred's age, the result is 40. If you add Fred's age to 4 times
jolli1 [7]

Answer:

Fred is 28 yrs old. Nathalie is 12yrs old

Step-by-step explanation:

Let Nathalie's age be x

Let Fred's age be a

x+a=40 yrs•••••1

4x+a=76yrs•••••2

a=40-x

Substitute a for 40-x in equation (2)

4x+40-x=76

3x=76-40

3x=36

x=12

a=40-12

a=28

5 0
2 years ago
An 5 in. by 7 in. photo is reduced so that the width (the shorter dimension) is 4 in.
Lemur [1.5K]
I think A which is 4in but not sure
4 0
2 years ago
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