Alan

Like so:

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I don't have any great insights to offer!  I agree the total number of 3s is 12*10^11.  

There is a distinction to be made between number of individual digits that are 3s and number of integers that contain 3s. For example there are 20 individual digits that are 3s between 1 and 100, but only 19 different integers that contain 3s (because 33 counts two towards individual digits, but just one towards individual integers). The figure of 12*10^11 refers to individual digits, not individual integers.

I assume the 10 in the denominator is in seconds. The numerator is the distance travelled in 10 seconds, so if we divide this by 10 seconds we get the average speed (in ft/sec) over the first 10 seconds.    

Note that for h(10) you have: -16*10^2 + 294.4*10 + 15  and for h(0), just 15

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Nicely done Melody!  Here's a similar, but step by step version.  Again, X and Y values are plotted as coordinates within a square box:

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"What is the frequency of a 0.85-kg block bouncing on the end of a 3.8 Newton meter spring?"

Frequency is \(\omega=\sqrt{\frac{k}{m}} \text{ radians/sec or: }f=2\pi \sqrt{\frac{k}{m}}\text{ cycles/sec}\)

(m is mass, k is spring constant)

I'll leave you to fill in the numbers!

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Excel has a non-standard hierarchy rule for unary negation, which it places higher than exponentiation.

For example, most sensible pieces of calculational software calculate -3^2 as -9 because exponentiation has higher priority than negation.  However, Excel will return -3^2 as +9 because it gives unary negation a higher priority.  It doesn't give the binary operator the same priority though, so, in Excel 0 - 3^2 results in -9.  That is, in Excel,  -3^2 is different from 0 - 3^2.

(The macro language VBA, which comes with Excel does not exhibit this peculiarity.  It uses the standard priorities, so it returnes -9 for both -3^2 and 0 - 3^2.)

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So, if your calculation included a unary minus, then it isn't surprising that you got a different answer from the calculator here.  If this isn't the explanation for your problem then specify the calculation here and we'll look at it in more detail.

If you have a right-angled triangle and the opposite side length (= b, say) and the length of the hypotenuse (= h, say)

then the angle ( = B) is given by 2nd asin (b/h) enter

If you have the adjacent side length (= a, say) and the hypotenuse 

then B is given by 2nd acos (a/h) enter

If you have the opposite and adjacent side lengths

then B is given by 2nd atan (b/a) enter

"sinh" is what is known as a hyperbolic function.  It is defined as follows:

sinh(x) = (e^x - e^-x)/2

We also have cosh(x) = (e^x + e^-x)/2

and tanh(x) = sinh(x)/cosh(x)

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Click on the "Draw Graph" command at the bottom right of the calculator.  Enter your function in one of the input lines and press enter.  You may well have to alter the ymin, ymax, xmin and xmax values below the graph to get a good view (press enter after each one).

e.g.

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"I am trying to work out standard deviations and have to square numbers I am getting two different answers if I use the X2 square function it comes out as a negative if I just times the number by itself it comes out positive which one is right"

-2² = -4  because exponentiation takes priority over negation

(-2)² = +4  because parentheses take highest priority

So -2 x -2 = +4  because -2 x -2 is the same as (-2)²

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With Poisson distribution, P(x) = e^-mumu^x/x!

Here:  mu = 1.3, x = 4, so P(4) ≈ 0.032

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