Triple Button Line

Angle of first line is θ = tan −1 ⎜ ⎟ = 42°. Angle of second line is 42° + 30° = 72°. ⎝ 210 − 10 ⎠ Therefore X = 10 + 250 cos 72° = 87 , Y = 20 + 250 sin 72° = 258 for a final point of (87,258). (b) The computer screen now looks something like Figure 1.77. The length of the bottom line is 258 − 200 ⎞ 2 2 ( 210 − 87 ) + ( 200 − 258) = 136 and its direction is tan −1 ⎛ ⎜ ⎟ = 25° below straight left. ⎝ 210 − 87 ⎠ EVALUATE: Figure 1.77 is a vector addition diagram. The vector first line plus…

Angle of first line is θ = tan −1 ⎜ ⎟ = 42°. Angle of second line is 42° + 30° = 72°. ⎝ 210 − 10 ⎠ Therefore X = 10 + 250 cos 72° = 87 , Y = 20 + 250 sin 72° = 258 for a final point of (87,258). (b) The computer screen now looks something like Figure 1.77. The length of the bottom line is 258 − 200 ⎞ 2 2 ( 210 − 87 ) + ( 200 − 258) = 136 and its direction is tan −1 ⎛ ⎜ ⎟ = 25° below straight left. ⎝ 210 − 87 ⎠ EVALUATE: Figure 1.77 is a vector addition diagram. The vector first line plus…

of first line is θ = tan −1 ⎜ ⎟ = 42°. Angle of second line is 42° + 30° = 72°. ⎝ 210 − 10 ⎠ Therefore X = 10 + 250 cos 72° = 87 , Y = 20 + 250 sin 72° = 258 for a final point of (87,258). (b) The computer screen now looks something like Figure 1.77. The length of the bottom line is 258 − 200 ⎞ 2 2 ( 210 − 87 ) + ( 200 − 258) = 136 and its direction is tan −1 ⎛⎜ ⎟ = 25° below straight left. ⎝ 210 − 87 ⎠ EVALUATE: Figure 1.77 is a vector addition diagram. The vector first line plus the

Linear Equations 368 Homogeneous Linear Systems with Constant Coefficients 373 Complex Eigenvalues 384 Fundamental Matrices 393 Repeated Eigenvalues 401 Nonhomogeneous Linear Systems 411 Numerical Methods 419 8.1 8.2 The Euler or Tangent Line Method 419 Improvements on the Euler Method 430 xvi Contents 8.3 8.4 8.5 8.6 Chapter 9 Nonlinear Differential Equations and Stability 459 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 Chapter 10 The Phase Plane;…

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connecting all the phones together, but with intelligence built in to control how everything works. Telephone networks for voice communication operate very similarly to the Internet for computer communication (in fact, part of the Internet still uses phone lines). In storage communication, the network is made of servers and storage arrays (the devices) connected together via optical cables and switches (the medium) — and the rules for communicating between the devices (the protocol) is…

connecting all the phones together, but with intelligence built in to control how everything works. Telephone networks for voice communication operate very similarly to the Internet for computer communication (in fact, part of the Internet still uses phone lines). In storage communication, the network is made of servers and storage arrays (the devices) connected together via optical cables and switches (the medium) — and the rules for communicating between the devices (the protocol) is…