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kow [346]
4 years ago
12

Write the standard form of an equation with p=3 sqrt2, theta= 135°​

Mathematics
1 answer:
Arlecino [84]4 years ago
7 0

Answer:

x - y + 6 = 0

Step-by-step explanation:

In normal form of a straight line, the equation is given by  

x\cos \theta + y\sin \theta = p

where p is the perpendicular distance of the line from the origin and \theta is the angle between the perpendicular line and the positive direction of the x-axis.

Here, in our case p = 3\sqrt{2} and \theta = 135 Degree,

Therefore, the normal form of the straight line equation is  

x \cos 135 + y \sin 135 = 3\sqrt{2}

⇒ x \cos (180 - 45) + y \sin (180 - 45) = 3\sqrt{2}

⇒ - x \cos 45 + y \sin 45 = 3\sqrt{2} {Since, Cos (180 - Ф) = - Cos Ф and Sin (180 - Ф) = Sin Ф}

⇒- \frac{x}{\sqrt{2}} + \frac{y}{\sqrt{2}} = 3\sqrt{2}

⇒ - x + y = 3√2 × √2 = 6

⇒ x - y + 6 = 0  

So, the standard form of the equation is x - y + 6 = 0. (Answer)

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A set of children’s blocks contains three shapes: long, flats, and cubes. There are three times as many longs as cubes and 30 fe
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Answer:

<u>There are 270 longs</u>

Step-by-step explanation:

<u>Equations</u>

We must write the problem into a mathematical model that allows us to apply the properties of basic algebra and solve for the variable which must be adequately set up.

We have three unknowns: the number of long blocks, flats blocks, and cubes. The conditions are given:

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For the equation to be easier solved, let's set the variable as the number of cubes:

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Solving for x

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Answer: there are 270 longs

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Answer:

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Step-by-step explanation:

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