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2 years ago

What is one true mathematical statement involving exponents I could make out of 5, 25, and 2?

Mathematics

1 answer:

pentagon [3]2 years ago

8 0

Answer:

5^2 x 2^0 = 25 or 5^2 = 25

Step-by-step explanation:

5^2 = 25

2^0 = 1 (Anything raised to the zero power equals one no matter what the number is)

25 x 1 = 25

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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)

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

5 0

3 years ago

four times a number minus twice another number is -16 the sum of the two numbers is -1 find the numbers

lianna [129]

Answer: The numbers are -3 and 2

Step-by-step explanation: Let x be the first number and y be the second number

then according to given statements the linear equations will be:

"Four times a number minus twice another number is -16"

"The sum of the two numbers is -1"

From equation 2:

Putting y = -x-1 in equation 1

Subtracting 2 from both sides

Dividing both sides by 6

Putting x = -3 in equation 2:

Hence,

The numbers are -3 and 2

6 0

2 years ago

GUYS PLEASE HELP ILL GIVE YOU A BRAINLIEST ( the measure of arc XY is:)

Svetlanka [38]

Answer:

what

Step-by-step explanation:

3 0

2 years ago

What is the Answer to -14.5 + (-1.24)

Bingel [31]

The answer would be -15.74

4 0

2 years ago

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Which of the a-values satisfy the following inequality?<br> 7 + a < 11

Zolol [24]

Answer:

a < 4

Step-by-step explanation:

7 + a < 11

Subtract 7 from each side

7+a-7 <11-7

a < 4

7 0

3 years ago

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