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3 years ago

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Find the equation of the line that passes through point C and is perpendicular to the line that passes through points A and B. G

raph the two lines in GeoGebra finding their point of intersection and verifying the angle between them
A(1,-8); B(3,2); C(9,-7)

1 answer:

Setler79 [48]3 years ago

5 0

Answer:

The equation is y=-0.2x-5.2

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For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?

Bond [772]

Given that $r=\theta$ , then $r'=1$

The slope of a tangent line in the polar coordinate is given by:

$m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}$

Thus, we have:

$m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}$

Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

$\sin\theta+\theta\cos\theta=0 \\ \\ \theta\cos\theta=-\sin\theta \\ \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta$

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

</span><span>θ = 0

</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488

Part B:

For vertical tangent lines, $\frac{1}{m} =0$

Thus, we have:

$\cos\theta-\theta\sin\theta=0 \\ \\ \Rightarrow\theta\sin\theta=\cos\theta \\ \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta$

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

</span>θ = <span>4.91718592528713</span>

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djyliett [7]

Answer:

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Step-by-step explanation:

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True [87]

Quotient would be 8 because 88 divided by 11 is 8.

hope this helped :D

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The work is incorrect.

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ustin wants to use 188 ft of fencing to fence off the greatest possible rectangular area for a garden. What dimensions should he

Tema [17]

Answer:

I would say that it should be 48 ft long and 46 ft wide, the area would be 2208 square feet

Step-by-step explanation:

I will try my best to answer this.

I would start by dividing 188 by 4

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