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2 years ago

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A city planner wants to build a road perpendicular to D Street. What is the slope of the new road?

2 answers:

Shtirlitz [24]2 years ago

8 0

Answer:

<h2>The slope of the new road is zero.</h2>

Step-by-step explanation:

According to the image attached, D street is represents by a vertical line, which angle of inclination is 90°. In other words, the slope of D street is infinite.

So, if the new road is going to be perpendicular to D street, that means the new road has 0° of inclination, because if they are perpendicular and D street is vertical, that means the new road is horizontal, which have 0° of inclination.

Now, the slope of an horizontal line is zero.

Therefore, the slope of the new road is zero.

Romashka-Z-Leto [24]2 years ago

7 0

Answer:

The slope of the new road is 0.

Step-by-step explanation:

the slope of d street line is tan(90)

[if the angle made by a line with x axis is $\alpha$ then, the slope of that line will be tan( $\alpha$ ) ]

here, the angle made by the d street line with x axis is 90 degrees.

if a road is to be built which is perpendicular to d street , it should make 0 degrees i.e, it should be parallel to x axis .

so, the slope of new road will be tan(0) = 0

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2 years ago

Use the formula for the cosine of the difference of two angles to find the exact value of the following expression.

Zolol [24]

Answer:

Exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

Step-by-step explanation:

Given:

Cos(45° - 60°)

We have to apply the formula of cosine for difference of the two angles.

Formula:

$cos(a-b)=cos(a)\ cos(b)+sin(a)\ sin(b)$

Plugging the values.

⇒ $cos(45-60)=cos(45)\ cos(60) + sin(45)\ sin(60)$

We know that the values :

$sin(45) =cos(45) = \frac{1}{\sqrt{2} }$

$sin(60)=\frac{\sqrt{3} }{2}$ and $cos(60)=\frac{1}{2}$

So,

⇒ $cos(45-60)=(\frac{1}{\sqrt{2} } \times \frac{1}{2} ) + (\frac{1}{\sqrt{2} } \times \frac{\sqrt{3} }{2})$

⇒ $cos(45-60)=(\frac{1}{2\sqrt{2} } + \frac{\sqrt{3} }{2\sqrt{2} })$

⇒ $cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )$

⇒ $cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )\times \frac{2\sqrt{2} }{2\sqrt{2} }$ ...<em>rationalizing </em>

⇒ $cos(45-60)=\frac{2\sqrt{2} +2\sqrt{6} }{ 8}$

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<em>⇒ </em> $cos(45-60)=\frac{(\sqrt{2}+\sqrt{6})}{4}$

To find the exact values we have to put the values of sq-rt .

As<em>, </em> $\sqrt{2}=1.41$ and $\sqrt{6} =2.44$

Then

<em>⇒ </em> $cos(45-60)=\frac{( 1.41+2.44)}{4}$ <em />

<em>⇒ </em> $cos(45-60)=\frac{( 3.85)}{4}$ <em />

⇒ $cos(45-60)=0.96$

So the exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

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swat32

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3 years ago

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andrezito [222]

Answer:

Step-by-step explanation:

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