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3 years ago

Tan [x-pi/4] = tanx - 1

1 answer:

8 0

Solve for x:
-tan(π/4 - x) = tan(x) - 1
Subtract tan(x) - 1 from both sides:
1 - tan(π/4 - x) - tan(x) = 0
Simplify and substitute y = -tan(x).
1 - tan(π/4 - x) - tan(x) = (-tan(x) (1 - tan(x)))/(-tan(x) - 1)
= (y (y + 1))/(y - 1):
(y (y + 1))/(y - 1) = 0
Multiply both sides by y - 1:
y (y + 1) = 0
Split into two equations:
y = 0 or y + 1 = 0
Substitute back for y = -tan(x):
-tan(x) = 0 or y + 1 = 0
Multiply both sides by -1:
tan(x) = 0 or y + 1 = 0
Take the inverse tangent of both sides:
x = π n_1 for n_1 element Z
or y + 1 = 0
Subtract 1 from both sides:
x = π n_1 for n_1 element Z
or y = -1

Substitute back for y = -tan(x):
x = π n_1 for n_1 element Z
or -tan(x) = -1
Multiply both sides by -1:
x = π n_1 for n_1 element Z
or tan(x) = 1
Take the inverse tangent of both sides:
Answer: x = π n_1 for n_1 element Z or x = π n_2 + π/4 for n_2 element Z

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Answer:

$P(r n L) = 0.12$

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Step-by-step explanation:

The chance that it will rain is $P(r ) = 0.30$

The chance that it does not rain is $P(\= r ) = 1 - P(r )$

$P(\= r ) = 1 -0.30$

$P(\= r ) = 0.70$

The probability that the bus run late if it rains is $P(L | r) = 0.4$

The probability that the bus run late if it does not rain is $P(L | \= r) = 0.15$

Generally the probability that it will rain and the bus will be late is mathematically represented as

$P(r n L) = P(L | r) * P(r)$

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=> $P(r n L) = 0.12$

Generally the probability that the bus will be late is mathematically represented as

$P(L) = P(r) * P(L|r) + P(L | \= r) * P(\= r)$

=> $P(L) = 0.30 * 0.4 +0.15*0.70$

=> $P(L) = 0.225$

Generally given that the bus ran late, the probability that the bus it was not raining is mathematically represented as

$P(\= r | L) = 1- P(r | L )$

Here $P(r | L ) = \frac{P(r n L)}{P(L)}$

=> $P(r | L ) = \frac{0.12}{0.225}$

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3 years ago

Which is the correct label of parallel lines?

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Answer: Parallel lines are marked with "feathers". Notice how they appear assets: the lines with one feather are parallels, and the lines with two feathers are parallel. A "box" at the point of intersection indicates the lines are perpendicular.

I found this on the web, maybe it will help you. Sorry if you still don't understand.

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3 years ago

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Consider these dimensions for a cylindrical aquarium.

vagabundo [1.1K]

The amount of water that will fill the tank is 11100 cu.ft to the nearest hundredth.

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A cylinder is a three dimensional figure with two identical circular faces at each end , and a curved surface.

It does not have an edges or vertices.

It is given in the question that

A cylinder with height 14 feet and radius 25 feet.

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2 years ago

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Answer:

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