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3 years ago

Which relation is a function?

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

8 0

The answer is B.
Because the domain is not repeating

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What is the probability of not getting a blue on this spinner? Be sure to reduce. [?]

exis [7]

Answer:

5/8

Step-by-step explanation:

The probability of not getting blue can be found by dividing the number of sections that are not blue by the total number of sections.

P(not blue)= not blue / total

There are a total of 8 sections. 3 are blue, which leaves 5 that are not blue (1 yellow, 2 red and 2 green).

not blue= 5

total= 8

P ( not blue)= 5/8

This fraction cannot be reduced, therefore our answer is 5/8

6 0

3 years ago

Sylvia has a total of 16 trading cards: 8 superhero cards, 4 princess cards,2 villain cards, and 2 wildlife cards. what is the r

balu736 [363]

There as 16 cards, 2 of which are wildlife cards, so the ratio is 16 : 2. We can simplify it by dividing both sides by 2, so we'll get the ratio of 8 : 1.

I hope this helps! :)

5 0

4 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

Graph the line that has a slope of 1/9 and includes the point (0,8)

Crank

Answer:

Step-by-step explanation:

y = mx + b

slope(m) = 1/9

y int (b) = 8.....or (0,8)

y = 1/9x + 8.....this is ur equation

ur x intercept is : (can be found by subbing in 0 for y

0 = 1/9x + 8

-1/9x = 8

x = 8 * -9

x = - 72....or (-72,0)

7 0

4 years ago

12 dogs decreased by 25%

masya89 [10]

Answer:

Step-by-step explanation:

12-.25(12)=12-3

12-3=9

7 0

3 years ago