hectictar

\((-2 + \sqrt{-12}) + (8 +\sqrt{-27})\)

= \(-2+2\sqrt{-3} + 8 + 3\sqrt{-3}\)

Combine like terms.

=\(6+5\sqrt{-3}\)

The square root of negative one equals i, so take that out.

= \(6+5i\sqrt{3}\)

tangent squared

First let's just find the volume of one book.

Volume is length times width times height.

V = (L)(W)(H)

V = (2.85)(2.15)(0.4)

Just multiply these together in a calculator.

V = 2.451 cubic dm

The volume of one book is 2.451 cubic dm.

Since there are 19 books, just multiply that volume by 19.

2.451*19 = 46.569

Total volume = 46.569 cubic dm.

175/x = tan30°

Multiply both sides by x

175 = xtan30°

Divide both sides by tan30°

175/tan30° = x

You can simply plug this into a calculator and get that x ≈ 303.109

You can stop there, but if you want to you can also look at a unit circle to find the exact value of tan30º.

tan30° = sin30°/cos30°

tan30° = \(\frac{1}{2}/\frac{\sqrt{3}}{2}\)

tan30° = \(\frac{1}{2}*\frac{2}{\sqrt{3}}\)

tan30°= \(\frac{2}{2\sqrt{3}}\)

tan30°= \(\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}\)

so

x = \(175/\frac{1}{\sqrt{3}}\)

x = \(175*\frac{\sqrt{3}}{1}\)

x = \(175\sqrt{3}\)

-------------------------------------------------

tan(x) = 1/12

Here, all you need to do is take the arctangent of both sides.

x = arctan(1/12)

Just plug this into a calculator and you get that x ≈ 4.764°

The height of the building over the height of the man equals the length of the building's shadow over the length of the man's shadow.

h/1.8 = 26.4/3

h = 15.84

The height of the building is 15.84 meters.

The tangent of the angle of elevation to the sun is 15.84/26.4

tan a = 15.84/26.4

a = arctan 0.6

The angle of elevation to the sun is approximately 30.964 degrees.

I worked on this some and I think it is impossible to go from the beginning equation to the final equation without writing down an equation with integer roots at least once. At some point the constant, "c", will be exactly one greater than the linear coefficient, "b". When c is one greater than b,  there will be integer roots.

If I understand your question correctly, the two points are:

(M,-44) and (P,[2-1])

That is:

(M,-44) and (P,1)

All you need to do is put this info into the distance formula.

d=\(\sqrt{(M-P)^{2}+(-44-1)^{2}}\)

d=\(\sqrt{(M - P)^{2}+(-45)^{2}}\)

d= \(\sqrt{(M - P)^{2}+2025}\)

4^3 - 5^2

= 64 - 25

= 39

5(1+2)^2-4(3-1)^3-6(2+3)^4

= 5(3)^2 - 4(2)^3 - 6(5)^4

=5(9) - 4(8) - 6(625)

= 45 - 32 - 3750

= -3737

Oh I feel stupid now mine is wrong because the base and height are not both 3t.