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Luda [366]
3 years ago
10

Hello!

Mathematics
1 answer:
Gnesinka [82]3 years ago
8 0

Answer:

  • A. 2 < x < 10

Step-by-step explanation:

With two congruent sides the third side is greater against a greater angle.

<u>34 < 36, therefore:</u>

  • 3x - 6 < 24
  • 3x  < 30
  • x < 10

<u>And, the angle should have a positive value:</u>

  • 3x - 6 > 0
  • 3x > 6
  • x > 2

<u>Combined, we get:</u>

  • 2 < x < 10
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Use the fundamental identities and appropriate algebraic operations to simplify the following expression. (18 +tan x) (18-tan x)
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Answer:

a) \left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)+\sec ^2\left(x\right)=325

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Step-by-step explanation:

a) To simplify the expression \left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)+\sec ^2\left(x\right) you must:

Apply Difference of Two Squares Formula: \left(a+b\right)\left(a-b\right)=a^2-b^2

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\left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)=18^2-\tan ^2\left(x\right)=324-\tan ^2\left(x\right)

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Apply the Pythagorean Identity 1+\tan ^2\left(x\right)=\sec ^2\left(x\right)

From the Pythagorean Identity, we know that 1=-\tan ^2\left(x\right)+\sec ^2\left(x\right)

Therefore,

324[-\tan ^2\left(x\right)+\sec ^2\left(x\right))]\\324[+1]\\325

b) According with the below graph, the lowest point of y=\cos \left(x\right), 0\leq x\leq 2\pi is when x = \pi

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