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irina [24]
2 years ago
11

4x^2-21x-18=0 Find the discriminate

Mathematics
2 answers:
SpyIntel [72]2 years ago
6 0

a = 4, b = -21, c = -18

to keep from getting "mixed up", evaluate the discriminant first ...

b<sup>2</sup> - 4ac = (-21)<sup>2</sup> - 4(4)(-18) = 729

sqrt(729) = 27

x = (21 +/- 27)/8

x = -3/4, x = 6

since the discriminant is a perfect square, the original quadratic will factor ...

4x<sup>2</sup> - 21x - 18 = 0

(4x + 3)(x - 6) = 0

x = -3/4, x = 6

GaryK [48]2 years ago
5 0

Answer:729

Step-by-step explanation: Use the values of a, b and c to find the discriminant. Which is 729

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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
I also need help with 1,000,000 in exponential form , 10x10 , and 10,000 x10 please
xxMikexx [17]

Answer:

1,000,000= 10^6

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7 0
3 years ago
12. 4x2 - 4y2 + 1622 - 16xz​
Snezhnost [94]

Answer:

8(203-2xz)

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have a great day :)

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sashaice [31]
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7 0
3 years ago
Using quadratic form 6x^2-8x+3=0
LenaWriter [7]

x=8+sqrt-8/12, x=8-sqrt-8/12

I think...

5 0
3 years ago
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