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2 years ago

Evaluate. PICTRE BELOW.

Mathematics

1 answer:

ololo11 [35]2 years ago

4 0

Answer:

d ko makita yung pic sorry

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Find the distance d(A,B) between points A and B.

Misha Larkins [42]

Answer:

A(4,-5) ; B(4,3)

distance d(A,B) = $\sqrt{( 4 - 4)^{2} + (3 -(-5))^{2} }$ = 8

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2 years ago

Is 2 to the power of 3 equal to 3 to the power of 2

Mama L [17]

Answer:

Step-by-step explanation:

$2^{3}$ =2•2•2=8

${3}^2$ =3•3=9

8≠9

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2 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

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

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3 years ago

Determine the value of y, if x is 5. y = x2-7

lions [1.4K]

Answer:

Y = 3

Step-by-step explanation:

5 times 2 is 10 minus 7 is 3.

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3 years ago

Read 2 more answers

two linear functions have the same slope,same x-intercept, and same y-intercept. Must these functions be identical? Explain your

Leviafan [203]

Yes, because only one line can go through two set points and because they have the same slope and the same x and y-intercepts they have two set points that they must both go through making them identical.

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2 years ago