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ExtremeBDS [4]
3 years ago
5

How many solution does 3=5

Mathematics
1 answer:
swat323 years ago
3 0

Answer:

None.

Step-by-step explanation:

The equation 3=5 is false, therefore, there are no solutions.

3≠5

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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
Simplify to create a equivalent expression.
Ratling [72]

Answer:

\boxed{\bold{66k+9}}

Explanation:

Expand \bold{5\left(10k+1\right): \ 50k+5}

= \bold{50k+5+2\left(2+8k\right)}

Expand \bold{2\left(2+8k\right): \ 4+16k}

= \bold{50k+5+4+16k}

Simplify \bold{50k+5+4+16k: \ 66k+9}

= \bold{66k+9}

Mordancy.

7 0
3 years ago
Read 2 more answers
In the polynomial below, what number should replace the question mark to produce a difference of squares? x2 + ?x - 49
shutvik [7]
We are asked to find unknown or the missing number to complete the polynomial given in the problem which is x² + ?x -49. First, let us equate the number to be equal to zero such as it would become x² + ?x - 49 = 0. Next, we need to find the factors such that it would produce a difference of squares and these two factors are a = +7 and b = -7. Hence, the complete solution is shown below:
(x + 7) (x-7) = 0
perform distribution and multiplication of terms such as shown below:
x² + 7x - 7x - 49 = 0
Combine the same term such as we can either add or subtract +7x to -7x and the result will be equal to 0x.
 x² + 0x - 49 = 0

Therefore, the missing number is 0. The answer is 0 which will result to x² +0x - 49.
4 0
3 years ago
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How do I do this??
Pachacha [2.7K]

Step-by-step explanation:

please mark me as brainlest

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Zachary's soccer camp started at 11:35 A.M. They spent 55 minutes practicing defense and 2 hours and 25 minutes shooting. What t
UNO [17]

camp ended at 2:55pm


4 0
3 years ago
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