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goblinko [34]
4 years ago
13

Find the sum of the first 5 terms of the sequence 4,2,0

Mathematics
2 answers:
lora16 [44]4 years ago
7 0

Answer:

27/4=6 3/4

Step-by-step explanation:

2^2,2^1,2^0  so the next will  be   2^(-1),2^(-2)

the sum will be 4+2+0+1/2+1/4=16/4+8/4+2/4+1/4=27/4

Free_Kalibri [48]4 years ago
6 0
4,2,0,-2,-4,-6,-8,-10 because you subtract 2 each time
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Solve the following differential equation: (2x+5y)dx+(5x−4y)dy=0 *Hint: they are exact<br><br> C=.
Tpy6a [65]

Answer with Step-by-step explanation:

The given differential equation is

(2x+5y)dx+(5x-4y)dy=0

Now the above differential equation can be re-written as

P(x,y)dx+Q(x,y)dy=0

Checking for exactness we should have

\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}

\frac{\partial P}{\partial y}=\frac{\partial (2x+5y)}{\partial y}=5

\frac{\partial Q}{\partial x}=\frac{\partial (5x-4y)}{\partial x}=5

As we see that the 2 values are equal thus we conclude that the given differential equation is exact

The solution of exact differential equation is given by

u(x,y)=\int P(x,y)dx+\phi(y)\\\\u(x,y)=\int (2x+5y)dx+\phi (y)\\\\u(x,y)=x^2+5xy+\phi (y)

The value of \phi (y) can be obtained by differentiating u(x,y) partially with respect to 'y' and equating the result with P(x,y)

\frac{\partial u}{\partial y}=\frac{\partial (x^2+5xy+\phi (y)))}{\partial y}=Q(x,y))\\\\5y+\phi '(y)=(5x-4y)\\\\\phi '(y)=5x-9y\\\\\int\phi '(y)\partial y=\int (5x-9y)\partial y\\\\\phi (y)=5xy-\frac{9y^2}{2}\\\\\therefore u(x,y)=x^2+10xy-\frac{9y^2}{2}+c

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Vitek1552 [10]
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The hourly rate is 60, so multiply 60 by the number of hours (h) and add the fee:

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