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Mathematics

2 answers:

Len [333]3 years ago

7 0

Slope is 1/6 and y- intercept is (0,6)

kiruha [24]3 years ago

3 0

Answer:

slope is - 1/6 and y-intercept is (0,6)

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Complete the square x^2+4-12=0

Tatiana [17]

Answer:

x = -6

x = 2

Step-by-step explanation:

x² + 4 - 12 = 0

= (x + 6)(x - 2)

x + 6 = 0

x = -6

x - 2 = 0

x = 2

5 0

3 years ago

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

Gennadij [26K]

(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:

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

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

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

2/3 is the slope

____________

(c)

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

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

3 years ago

How do you determine the value of isosceles triangles?

amid [387]

There's really no such thing as the value of a triangle.

Every triangle has three sides, three angles, a base, a height, and an area,
and there could be problems that ask us to find any one of those.

Whatever we need to find, the process is always the same:

-- Take the information that's given.

-- Gather up everything you can remember that talks about a relationship
between what you're given and what you need to find.

-- Use them together to find the missing value.

6 0

3 years ago

Which phrase describes another way to write the expression?

zhuklara [117]

0.75r+0.75(3.20)=0.75(r+3.20)

So the answer is A. The product of 0.75 with the sum of r and 3.20

4 0

3 years ago

Read 2 more answers

9р - Зр equivalent expression

Vesnalui [34]

Answer:

Step-by-step explanation: