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2 years ago

Write the equation of the line parallel to 4x-5y=2 and passing through point (0,0)

Mathematics

1 answer:

kotykmax [81]2 years ago

8 0

$k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2$

We have:

$4x-5y=2\ \ \ \ |-4x\\\\-5y=-4x+2\ \ \ \ |:(-5)\\\\y=\dfrac{4}{5}x-\dfrac{2}{5}\to m_1=\dfrac{4}{5}\\\\l:y=m_2x+b\\\\k\ \prep\ l\Rightarrow\dfrac{4}{5}m_2=-1\ \ \ \ |\cdot\dfrac{5}{4}\\\\m_2=-\dfrac{5}{4}$

$l:y=-\dfrac{5}{4}x+b$

The line l is passing through point (0, 0). Substitute the coordinates of the point to the equation of a line l:

$0=-\dfrac{5}{4}\cdot0+b\to b=0$

$y=-\dfrac{5}{4}x\ \ \ \ |\cdot4\\\\4y=-5x\ \ \ \ |+5x\\\\5x+4y=0$

<h2>Answer: 5x + 4y = 0</h2>

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Dafna11 [192]

Answer:

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2 years ago

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere. Wh

viktelen [127]

Answer:

Radius of sphere is 3 units.

Step-by-step explanation:

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Given that

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assuming r as the radius.

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2 years ago

The dot product of u with itself is 12. What is the magnitude of u?

Brilliant_brown [7]

Dot product is
a*b = |a|*|b|*cosα.
In our case
u*u =|u|*|u|*cos 0
u*u =|u|*|u|
12=|u|²
|u|=√12=√(4*3)=2√3
Answer: <span>D. 2√3</span>

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3 years ago