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## Philip P.'s Resources

The general equation of circle is:   (x-h)2 + (y-k)2 = r2   Where: (h.k) = the location of the circle's center r = the circle's radius   Your equation is:   (x+5)2 + (y+7)2 = 81   (x-(-5))2 + (y-(-7))2...

Let h = the height of the taller building:   14 m          h --------  =  ------- 16 m        24 m   Solve for h.   ------------   Geometrically, you can...

Givens: Radius of the orbit = 8000 km Period of the orbit = 2 hours   Angular Velocity = 2pi/period = 2pi/2 = pi radians per hour.   Linear Velocity = angular velocity*radius = 8000*pi km/h ≅ 25,133 km/h

PEMDAS: P = operations within Parentheses E = Exponents (including radicals) M = Multiplications D = Divisions A = Additions S = Subtractions   20/2(5+5)   The confusion here is whether the problem is:   20*(5+5)               ...

1.  √a + √a = 2a 2√a = 2a Divide both sides by 2: √a = a square both sides: a = a2 0 = a2-a 0 = a(a-1)   a = 0 and 1     The expression is true for a = 0 and 1, but not for any other values of a.   2.  You...

sin(0.75 radians) = (opposite side)/(hypotenuse)   sin(0.75 radians)*(hypotenuse) = opposite side   Plug in the length of the hypotenuse and use your calculator to determine the sin(0.75 radians).

Arc Length = 2*pi*radius*(θ/360o)  where θ is the central angle of the sector   Area = pi*radius2*(θ/360o) = (1/2)*(Arc Length)*radius   So Radius = 2*Area/(Arc Length)   Area = 10.72 m2 Arc Length = 5.36 m   Radius = 2*(10.72)/(5.36)...

The double angle identity is: sin(x+y) = sinx cosy + cosx siny   Let x = 50o and y = 10o:   sin(50o)cos(10o)+cos(50o)sin(10o) = sin(50o+10o) = sin(60o) = (√3)/2

Use the double angle identity:  sin(u±v) - sinu cosv ± cosu sinv   sin(x+y)-sin(x-y)   = sinx cosy + cosx siny - [sinx cosy - cosx siny]   = 2 cosx siny

A = pi*r2   To evaluate dA/dt, use the chain rule: dA/dt = (dA/dr)*(dr/dt)   dA/dt = pi*2*r*dr/dt   Since dr/dt = 3:   dA/dt = 6*pi*r   When r = 1:   dA/dt = 6*pi

You need to compute the surface area of the can, which is a cylinder with a top and bottom   Area of cylinder = 2*pi*radius*height   Area of top and bottom = 2*pi*radius2   Plug in the values for height (13.2 cm), radius (=diameter*1/2 = 4.1 cm), and pi (3...

FG = x+5 GH = 3x-9 FH = 2x-2   Because the triangle is equilateral, all sides are the same length.  Thus we can set any two sides equal and solve for x:   FG = GH x + 5 = 3x - 9 14 = 2x   7 = x   The lengths of the...

momentum = mass*velocity = (6 kg)*(10 m/s) = 60 Newton-seconds   Just make sure all of the terms are in the same measurement system (in this case, the m-k-s system)

Volume = Length*Width*Height   144x3 + 216x2 + 81x = 9x(16x2 + 24x + 9) = 9x(4x+3)2   The 3 sides could be: Length = 9x Width = 4x+3 Height = 4x+3   The perimeter of a square face would one that has (4x+3)...

Interest = Principle*Rate*Time   Where: Principle = \$40,000 Rate = 11.5% = 0.115 (must use the decimal form) Time = 2 years   Plug the numbers into the formula to get the answer.

18x3 - 2x2 + 27x - 3   (18x3 - 2x2) + (27x - 3)   2x2(9x-1) + 3(9x-1)   (2x2+3)(9x-1)

a. The Earth exerts a force of gravity on the astronaut equal to:   Fg = GMm/(1.5R)2   Where: G = the Gravitational Constant = -6.673*10−11 N·(m/kg)2 M = the Mass of the Earth = 5.9736*1024 kg m = the mass of the astronaut = 80 kg R = the Earth's radius...

The  total wages for the 11 employees is:   \$782*11 = \$8602   Now add in the 12th employee's wages:   \$8602 + \$1261 = \$9863   Now divide by 12:   \$9863/12 = \$821.92   ----   You can also do a weighted...

£17.40 = £4.80 + £1.80(x-1)   £17.40 = £4.80 + £1.80x - £1.80   £17.40 = £3.00 + £1.80x   Solve for x.

z2 + 2z + 2 = 0   Use the quadratic formula:   -(2/2) ± (1/2)√(22-4*2*1)   -1 ± (1/2)√(-4)   -1 ± (1/2)√4√(-1)   -1 ± i