Alan

area = pi*r²  so  r = √(area/pi)

$${\mathtt{r}} = {\sqrt{{\frac{{\mathtt{58}}}{{\mathtt{\pi}}}}}} \Rightarrow {\mathtt{r}} = {\mathtt{4.296\: \!739\: \!856\: \!991\: \!561}}$$  square inches

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Multiply the terms inside the parentheses by x:

9x² + 9x = 270

Divide all terms by 9

x² + x = 30

Subtract 30 from both sides

x² + x - 30 = 0

This factorises

(x + 6)(x - 5) = 0

So x = -6 and x =5 are the two possible solutions

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Yes.  asin = arcsine = sin^-1

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To find the y-intercept set x = 0

y-intercept = -3^(-2) - 3 = -1/3^2 - 3 = -1/9 - 3 = -(3+1/9) ≈ -3.11

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The fraction setting on the calculator is not working at present.

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If n is the number then we can write

n² = 2n + 15

Rearrange:

n² - 2n - 15 = 0

This factorises as

(n - 5)(n + 3) = 0

so the the negative value of n that makes this true is n = -3

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If you are taking about a cylinder than the radius is 25/(2*pi) cm, so the volume is pi*(25/(2*pi))²*8 cm³.  You can use the calculator to evaluate this.

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I think this is asking for 3 ways of writing z = 4/(1+i√3)

1.  Multiply numerator and denominator by 1 - i√3:   4(1 - i√3)/(1+3), so z = 1 - i√3

2. |z| = √(1+3) = 2,  tan^-1(-√3/1) = -pi/3:  z = 2e^-i*pi/3

3. e^iθ = cos(θ) + i*sin(θ), so z = 2cos(pi/3) - 2i*sin(pi/3)

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