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...
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