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Snezhnost [94]
2 years ago
11

Express the prime number 19 as the difference of two squares? 19 =​

Mathematics
2 answers:
Lemur [1.5K]2 years ago
6 0

Step-by-step explanation:

Hey there!

<em>Let's take out the square of 1st ten natural numbers to find out the exact answer.</em>

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

Now; You can take any of these numbers and subtract from their squares.

<em>So, let's check 6² and 5²</em>

36-25 = 11 which is not equal to 19

<em>Again check for 10²-9²</em>

100 - 81 = 19 (True value)

Therefore, 19 can be expressed as the difference of square of 10 and 9.

<u>Hope</u><u> it</u><u> helps</u><u>!</u>

o-na [289]2 years ago
5 0

Answer:

The two squares are 81 and 100, and their difference is 19

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Dy/dx = 2xy^2 and y(-1) = 2 find y(2)
Anarel [89]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2887301

—————

Solve the initial value problem:

   dy
———  =  2xy²,      y = 2,  when x = – 1.
   dx


Separate the variables in the equation above:

\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\&#10;\mathsf{y^{-2}\,dy=2x\,dx}


Integrate both sides:

\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\&#10;\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\&#10;\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{y}=x^2+C_1}

\mathsf{\dfrac{1}{y}=-(x^2+C_1)}


Take the reciprocal of both sides, and then you have

\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}


In order to find the value of  C₁  , just plug in the equation above those known values for  x  and  y, then solve it for  C₁:

y = 2,  when  x = – 1. So,

\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\&#10;\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}

\mathsf{C_1=-\,\dfrac{3}{2}}


Substitute that for  C₁  into (i), and you have

\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\&#10;\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\&#10;\mathsf{y=-\,\dfrac{2}{2x^2-3}}


So  y(– 2)  is

\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}


I hope this helps. =)


Tags:  <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

7 0
3 years ago
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Answer:

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Step-by-step explanation:

Simplifying

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Solving

-1ab + ac = d

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Combine like terms: d + -1d = 0

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The solution to this equation could not be determined.

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Step-by-step explanation:

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B)  so 5 x 4 is 20 and there is 8 left over and if you do 2 x 4 you get 8

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