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belka [17]
3 years ago
14

Pls pls help!! there's 3 images. I WILL MARK YOU BRAINLIEST IF U GET IT RIGHT

Mathematics
1 answer:
Damm [24]3 years ago
6 0

Answer:

im not sure about the 1st one but sec one is 162 i think and im  i dont know the last eaither srry  

Step-by-step explanation:

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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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3 years ago
If you double a number and then add 32, the result is 80. what is the number?
maw [93]
80-32 ÷ 2= 24
( you just do it sdrawkcab)









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Which statement compares the two numbers correctly?
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Answer:

A

Step-by-step explanation:

Six hundred seventy-two thousandths = 0.672

0.672 < 0.8

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1/4 + 1/8 divided by 2

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The correct answer is A. 120 ft squared because you must multiply the height times the width which comes to 120.
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