Function notation is simply replacing y with f(x), g(x), h(x), and so on. f(x) = -0.875x + 11 g(8) = 13 = -0.875(8) + c = -7 + c c = 13 + 7 = 20 Parallel Line: g(x) = -0.875x + 20
Function notation is simply replacing y with f(x), g(x), h(x), and so on. f(x) = -0.875x + 11 g(8) = 13 = -0.875(8) + c = -7 + c c = 13 + 7 = 20 Parallel Line: g(x) = -0.875x + 20
s(2) = 100 + 80(2) - 16(2)2 = 100 + 160 - 64 = 196 ft s(1) = 100 + 80(1) - 16(1)2 = 100 + 80 - 16 = 164 ft Average Velocity = vavg = [s(2) - s(1)]/(2 - 1) = 32 ft/s Power rule: d/dt (tn) = n*tn-1 v(t) = ds/dt = d/dt (100 + 80t - 16t2) = 80*t0 - 2*16*t1 = 80 -...
y = -4x + 1 Slope = m = -4 x = 1, y = 2 y = -4x + b b = y + 4x = 2 + 4(1)
Find the slope: m = (y2 - y1)/(x2 - x1) = (-4 - 2)/(5 - (-1)) = (-6/6) = -1 y = -mx + b = -x + b Plug in values: -4 = -5 + b --> b = -4 + 5 = 1 Check: 2 = -(-1) + 1 = 1 + 1 The line that passes through these points is y = -x + 1 Any line with the...
Skyrie did an excellent job of creating a step by step solution, and she has my vote. Having said that, there is a shortcut. -5x + y = -7 6x - y = 7 Just add the two equations. The y's cancel out. -7 and 7 also cancel out. -5x + y + 6x - y = x x = -7 + 7 = 0 -5(0)...
The equilibrium points are at the values where dy/dt = 0. Simply factor the y out of (ay + by^2) to get y(a + by). ay + by^2 = y(a + by) = 0 a + by = 0 --> a = -by --> y = -a/b y = 0, -a/b
z1 = x1 + i*y1 z2 = x2 + i*y2 z1 + z2 = (x1 + x2) + i*(y1 + y2) = X + iY X = x1 + x2, Y = y1 + y2 i = sqrt(-1), i^2 = -1 |z1 + z2| = |X + iY| = sqrt(X^2 + (i^2)*Y^2) = sqrt(X^2 - Y^2) |z1 + z2|^2 = (sqrt(X^2 - Y^2))^2 =...
Number: n Twice a number: 2n Three Less: subtract 3 from 2n. n = 2n - 3
(4y - 3x)dx + (2x - y)dy = 0 y = vx, dy = xdv + vdx (4y - 3x)/(2x - y) = (4v - 3)/(2 - v) λ = 1/x
It depends on the direction of the bearings. Let's assume that the first course is 65 degrees west of north. 1 knot = 1.151 mph --> 40 knots = 46.04 mph Ms. Jeffrey initially travels 138.12 miles. Now the second bearing is 153 degrees. We assume that Ms. Jeffrey is...
You plug the values into the equation. x + y = 7 3x - y = 9 Add the equations. x + 3x + y - y = 7 + 9 4x = 16 --> x = 4 3(4) - y = 12 - y = 9 --> y = 12 - 9 = 3 x + y = 4 + 3 = 7
The first step is D: solve both equations for x. This can be done by simply adding the equations. The Ys cancel out. (3x + y = 6) + (x - y = 2) --> 3x + x + y - y = 4x = 8 x = 8/4 = 2 Now you plug in x into either equation. x - y = 2 - y = 2 --> y = 2 -...
Foil principle: first, outer, inner, last First: x*x Outer: x*2 Inner: 4*x Last: 4*2 (x+4)(x+2) = x*x + x*2 + 4*x + 4*2 = x^2 + 2x + 4x + 8 = x^2 + 6x + 8
Greetings Ted. Speed is a scalar quantity. So it's essentially positive. cos (pi/3) = 1/2; sin (pi/3) = sqrt(3)/2 Velocity (x-direction) = vx = dx/dt = d/dt (4*t*cos(pi/3) = 4*(1/2) = 2 m/s Since the velocity is positive, the velocity is also the speed. Acceleration...
The first step is to set the equation to zero. 10y^2 + 45y - 25 = 0 Next you extract the common factors. 10y^2 + 45y - 25 = 5(2y^2 + 9y - 5) 2y^2 + 9y - 5 = 0 a = 2, b = 9, c = -5 Discriminant: d = b^2 - 4*a*c = 9^2 - 4*2*(-5) = 81 + 40 = 121 Quadratic...
You simply multiply the two trinomials. You can also treat them as a difference of two squares. (u + v)(u - v) = u^2 - v^2 In this case: u = x^2 + 3; v = x 1. [(x^2 + 3) + x]*[(x^2 + 3) - x] = (x^2 + 3)^2 - x^2 (f + g)^2 = f^2 + 2*f*g + g^2 f...
Purple Eggplants Make Delicious Afternoon Snacks. (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) Exponents precede addition. 9^3 = 9*9*9 = 81*9 = 729 Now add 729 to 5 to simplify.
1. Multiply the denominators 2. Multiply first numerator by second denominator. 3. Multiply second numerator by first denominator. 4. Add the products of Steps 2 and 3 in the numerator 45/67 + 77/89 = (45*89 + 67*77)/(67*89)