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2 years ago

How to determine if vectors are parallel?

1 answer:

3 0

One could use the relation

$\mathbf a\cdot\mathbf b=\|\mathbf a\|\|\mathbf b\|\cos\theta$

where $\mathbf a,\mathbf b$ are two vectors, $\|\mathbf a\|$ denotes the norm of that vector, and $\theta$ is the angle between the two vectors.

Then the two vectors will be parallel if $\theta=0$ or $\pi$ .

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If sin ⁡x=725, and 0 ∠ x ∠ pi/2, what is the tan (x - pi/4)

krok68 [10]

$Tan(x-\frac{\pi }{4}) = \frac{-17}{31}$

<u>Step-by-step explanation:</u>

Here we have , sin ⁡x=7/25( given sin x = 725 which is not possible ) , $0$ . Let's find tan (x - pi/4):

⇒ $Tanx = \frac{sinx}{cosx}$

⇒ $Tanx = \frac{sinx}{\sqrt{1-(sinx)^{2}}}$

⇒ $Tanx = \frac{\frac{7}{25}}{\sqrt{1-(\frac{7}{25})^{2}}}$

⇒ $Tanx = {\frac{7}{25}}{\sqrt{(\frac{625}{625-49})^{}}}$

⇒ $Tanx = {\frac{7}{25}}(\frac{25}{24} )$

⇒ $Tanx = {\frac{7}{24}}$

Now , $Tan(x-\frac{\pi }{4}) = \frac{Tanx - Tan(\frac{\pi }{4} )}{1+ Tanx(Tan(\frac{\pi }{4} )}$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{Tanx -1}{1+ Tanx(1)}$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{\frac{7}{24} -1}{1+\frac{7}{24} }$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{\frac{7-24}{24} }{\frac{7+24}{24} }$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{-17}{24} (\frac{24}{31} )$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{-17}{31}$

7 0

3 years ago

Please explain how you got this answer.

Tema [17]

150 times

out of the first 5 cards, there is a 3/5 chance of drawing a yellow.
if you replace the card and draw again, you still have a 3/5 chance of drawing a yellow card.
keep doing this process for 250 draws, each draw will always have 3/5 chance of drawing a yellow card.

so 3/5 +3/5 +3/5 +... (250 times) = 250 x 3/5 = 150

3 0

3 years ago

Work out the height of a triangle with base b= 7.7mm and area a=164.78mm2

solong [7]

Answer:

21.4 mm

Step-by-step explanation:

area ÷ base = height

164.78 mm^2 ÷ 7.7 mm

21.4 mm

Check:

base • height = area