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Zigmanuir [339]
2 years ago
6

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

7 0
2 years ago
Is 2 to the power of 3 equal to 3 to the power of 2
Mama L [17]

Answer:

No

Step-by-step explanation:

2^{3}=2•2•2=8

{3}^2=3•3=9

8≠9

4 0
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
<span>r = 3 + 2cosθ, it follows that

x = (3 + 2\cos\theta) \cos \theta \\ &#10;y = (3 + 2\cos\theta) \sin \theta

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}
5 0
3 years ago
Determine the value of y, if x is 5.<br> y = x2-7
lions [1.4K]

Answer:

Y = 3

Step-by-step explanation:

5 times 2 is 10 minus 7 is 3.

5 0
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.
4 0
2 years ago
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