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castortr0y [4]
3 years ago
15

What is the value of x?

Mathematics
1 answer:
musickatia [10]3 years ago
3 0

Answer:

The value of x is 88° enjoy

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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>
3 0
3 years ago
The question says~<br><br>Find the number that makes the ratio equivalent to 1:4....<br><br>4: ?​
Anarel [89]

Answer:

ikd

Step-by-step explanation:

k

8 0
3 years ago
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Why did farmer john ask the sumpermark manger where the overralls were
Alexeev081 [22]

Answer:

Because the store claimed to have the best overall prices

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Carina says that to divide by 12, she will need to write 12 as the fraction and then divide. Is she correct? Explain your reason
Alika [10]

Answer:

I do not know

Step-by-step explanation:

I think so

6 0
2 years ago
Simplify 4n5 + 3.5n5 + (-2.1n5).<br><br> 4.4 n5<br> 5.4 n5<br> 20 n5<br> 6.4 n5
ella [17]

Answer:

4 {n}^{5}  + 3.5 {n}^{5}  + ( - 2.1 {n}^{5} )

first create a bracket:

= ( {4n}^{5}  + 3.5 {n}^{5} ) + ( - 2.1 {n}^{5} )

then solve the first bracket:

=  {7.5 {n}^{5} } + ( - 2.1 {n}^{5} )

then open the remaining bracket:

=  {7.5n}^{5}  -  {2.1n}^{5}

carryout the subtraction operation:

= (7.5 - 2.1) {n}^{5}  \\ { \boxed{ =  {5.4n}^{5} }}

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