Alan

Expand the terms in parentheses;

x³ - 3x² + 3x -1 - x³ + 4x² -4x = 1 - 2x

Collect like terms

x² + x - 2 = 0

This factors nicely:

(x - 1)(x + 2) = 0

so x = 1 and x = -2 are the solutions

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What's the question?!!!

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As all prime numbers except the number 2 are odd, any two (excluding the number 2) must sum to an even number.  Therefore to have two prime numbers sum to an odd number, one of them must be 2.  This would mean that the other number would be 287.  However, 287 is not a prime number, so no two prime numbers add up to 289.

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You're welcome!

Here f(x-at) = e^{-(x-t)^2} and g(s) = -2s*e^{-s^2} so:

I'll leave you to sketch the solutions.

(Note: for f use u(x,0), and for g use u_t(x,0)) 

Assuming the given number is in radians then multiply by 180/pi to turn it into degrees.

$${\frac{{\mathtt{0.488}}{\mathtt{\,\times\,}}{\mathtt{180}}}{{\mathtt{\pi}}}} = {\mathtt{27.960\: \!340\: \!402\: \!384\: \!172\: \!6}}$$

or 28° to the nearest degree

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Well done Melody!  You got it so you don't need to worry about my generalisation!

Press = (or the Enter key) twice.  The second time you will get the result displayed in scientific notation.

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A couple more:

If two adjacent sides of a rectangle are (5x2 + 25xy + 4y2) and (2x2 – 2xy + 3y2), find its area

Area of a rectangle is just the product of its adjacent sides:

Area = (5x² + 25xy + 4y²)(2x² - 2xy + 3y²)

=  5x² *(2x² - 2xy + 3y²) + 25xy*(2x² - 2xy + 3y²) + 4y²*(2x² - 2xy + 3y²)

= 10x⁴ - 10x³y +15x²y²   +  50x³y -50 x²y² +75xy³   + 8x²y² - 8 xy³ + 12y⁴

I'll leave you to simplify this by collecting like terms together.

A two digit number is three times the sum of its digits. If 45 is added to the number; its digits are reversed. Find the number

 A two digit number can be represented as 10a + b  where a and b are single digits (a>0).

So:  10a + b = 3(a + b)         ...(1)

       10a + b + 45 = 10b + a  ...(2)

 From (1):  10a + b = 3a + 3b  or  7a - 2b = 0      ...(3)

From (2):    9a  - 9b = -45       or     a - b = -5       ...(4)

From (4) we have a = b - 5  ...(5) 

Use (5) in (3): 7(b-5) - 2b = 0  or 7b - 35 - 2b = 0 or 5b = 35  so b = 7.

Put this back into (5): a = 7 - 5  or a = 2.

So the original 2-digit number was 27

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