Mathematics, 21.07.2019 21:00 vjackie101ov3kju

Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90∘.

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Convert Ф = 90°, 45°, 0°, -45°, -90° into radans to obtain
Ф = π/2, π/4, 0, -π/4, -π/2 rad.

The given function is
v = 100 cos(ωt + Ф)

Create the following tables.
We shall use
ωt : 0 π/2 π (3/2)π 2π

Ф = π/2
ωt+Ф : π/2 π (3π)/2 2π (5π)/2
v : 0 -100 0 100 0

Ф = π/4
ωt+Ф : π/4 (3/4)π (5/4)π (7/4)π (9/4)π
v : 70.7 -70.7 -70.7 70.7 70.7

Ф = 0
ωt+Ф : 0 π/2 π (3/2)π 2π
v : 100 0 -100 0 100

Ф = -π/4
ωt+Ф : -π/4 π/4 (3/4)π (5/4)π (7/4)π
v : 70.7 70.7 -70.7 -70.7 70.7

Ф = -π/2
ωt+Ф: -π/2 0 π/2 π (3/2)π
v : 0 100 0 -100 0

Sketches of graphs for the different cases are shown below.

Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90

Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90

Answer from: Quest

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Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90...