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kifflom [539]
3 years ago
8

The equation 9 x 2 − 12 x + 4 = 0 9 x 2 − 12 x + 4 = 0 has how many different solutions?

Mathematics
1 answer:
Hatshy [7]3 years ago
5 0

We have the equation:

9x^2-12x+4=0

so:

a=9\qquad b=-12\qquad c=4

and:

\Delta=b^2-4ac=(-12)^2-4\cdot9\cdot4=144-144=\boxed{0}

This equation has one solution.

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The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π
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(a)

\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta

or, via symmetry

\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta

____________

(b)

By the chain rule:

\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}

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Differentiating with respect to theta

\begin{aligned}&#10;\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\&#10;&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\&#10;\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}&#10;&= 2/3&#10;\end{aligned}

2/3 is the slope

____________

(c)

"</span><span>distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time

</span><span />\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}
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3 years ago
Write an equation of the line containing the given point and perpendicular to the given line. express your answer in the form y=
katovenus [111]
The given line
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The slope of the given line is -4

Find the slope of perpendicular line
m₁ × m₂ = -1
-4 × m₂ = -1
m₂ = -1/-4
m₂ = 1/4

Find the equation of perpendicular line
y - y₁ = m(x - x₁)
y - 9 = 1/4(x - 8)
y - 9 = (1/4) x - 2
y = (1/4)x - 2 + 9
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PLZ help<br> solve for x
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Answer:

X = - 6                                                                                                                                

Step-by-step explanation:

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You order plant seeds from a catalog. Each packet cost 0.90 each. The shipping charge is 2.50. If you have 18.50 to spend, how m
kramer
<h2>Answer:</h2>

17

<h2>Step-by-step explanation:</h2>

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Rearrange the formula to find b

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You can't have 0.7 of a packet so you have to round down to 17.

Now if you put it into the original formula:

0.90 * 17 + 2.50 = 17.80

And 17.80 is less than 18.50.

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the answer will be triangular/

Hope I helped. Mark as brainliest

4 0
4 years ago
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