CPhill

what is 52 squared 35

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Do you mean this???.......

$${{\mathtt{52}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{35}} = {\mathtt{94\,640}}$$  

$${\mathtt{1\,256\,789}}{\mathtt{\,\small\textbf+\,}}{\mathtt{876\,543\,211}} = {\mathtt{877\,800\,000}}$$

I'm assuming that you want to know about the arc length??

Remember, in the arc length "formula," we need to convert the degrees to radians....so we have....

40 * (pi) / 180   =  2/9 pi

So we have

s = r * Θ

s = (9cm) * (2/9 * pi)       And using 3.14 for pi, we have

s = (2 * 3.14)cm ≈ 6.28cm

what is a when 2+1/4a = 7/4

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Subtract 2 from each side

(1/4)a = 7/4 - 2

(1/4)a = 7/4 - 8/4

(1/4)a = -(1/4)     Multiply by 4 on each side

a = -1

2^3*2^-4/2^-3

I think you might mean this.....???

2³ 2^-4 / 2^-3        So, by a property of exponents, a^m * aⁿ = a ^(m+n)

And so the numerator becomes 2^-1

And we have

2^-1/ 2^-3    And when we have a negative exponent in a fraction, we can "bring it to the other side" and make it a positive. So we have

2³ / 2¹  =

8 / 2 =

4

And that's it......

Note that we can write any odd number as 2n + 1.

So the first one is 2n + 1  - the least

The next is 2n + 3

The third is 2n + 5  - the greatest

So we have (2n + 1) + (2n + 5) = 4n + 6

4n + 6 = 110     Subtract 6 from both sides

4n = 104     Divide by 4 on both sides

n = 26

So 2(26) + 1 = 53

And 2(26) + 5 = 57

And 53 + 57 = 110

Let me add a little to Alan's answer.....Specifically....how do we arrive at those numbers??

Note we can write 2310 as

231 * 10  =

231 * 5 * 2       And there's a number theory property that says that if we can add the digits of a number, and that sum is divisible by three, then the number is divisible by three. So 231 = 2 + 3 + 1 = 6, and that's divisible by three. So, 231 is divisible by three. So we have

77 * 3 * 5 * 2 =

11 * 7 *3 * 5 * 2

Some answerers on here would also include "1" as a factor, but since "1" is a factor of any number, I usually don't include it.  But, if you want to throw it into the mix, be my guest. To be "technically" correct, I suppose it should be included!!

what is the area of the drumhead, that has a diameter of 14 in

So the radius = 7 in

And, since we have 'circular" drumhead, it's area is given by

pi * (7)²          And using 3.14 for pi, we have

$${\mathtt{3.14}}{\mathtt{\,\times\,}}{\mathtt{49}} = {\frac{{\mathtt{7\,693}}}{{\mathtt{50}}}} = {\mathtt{153.86}}$$ 

And that answer is in sq in.

I'm not sure if this is what you meant, or not

$${\frac{{\mathtt{2.925}}}{{\mathtt{1}}}}{\mathtt{\,-\,}}{\mathtt{1.003\: \!75}}{\mathtt{\,-\,}}{\mathtt{24}} = -{\mathtt{22.078\: \!75}}$$

????

So we have

(7^-3)^-7 (7^-2 7⁴)⁵

Simplifying the expression inside the second parentheses by using the exponential property,  a^m * aⁿ = a^(m+n),  we have

(7^-3)^-7 (7²)⁵  

Remember, by another property of exponents,  (a^m)ⁿ = a ^(m*n)

So we have

(7)²¹ (7)¹⁰

And by the first property we have

7³¹  ........which is a REALLY "big" number !!