Is the square root of -1/4 rational.or irrational

MAVERICK [17]

The first graph.

The equation is x - 1 $\leq$ 3
In order to solve it, you need to get x by itself.
Add 1 to both sides. 3+1=4
x $\leq$ 4

Since this is your sign $\leq$ the arrow has to point towards the left, and the circle needs to be colored in.

3 0

3 years ago

The fastest speed at table tennis ball has been hit is 21.12 faster than the speed for the fastest swimmer. What is the speed fo

Juli2301 [7.4K]

Remark

You cannot give an answer to this unless you are give the fastest speed of a swimmer. That stat is not an easy one to decide upon. At what distance for example or do you eliminate distance? Since this is a college level question, I don't think it unreasonable that you have to research raw distance over fastest time.

The fastest speed I can find is 100 meters in 46.91 seconds. That means that the actual speed of the swimmer is 100 meters / 46.91 = 2.132 meters / second.

Givens

Set up a proportion with the numbers found and given

Speed of ball / speed of swimmer = 21.12 / 1

Speed of ball = x

Solution

Speed of swimmer = 2.132 m/s

x / 2.132 = 21.12 / 1 Multiply Both sides by 2.132

x = 21.12 * 2.132 / 1

x = 45.02 m/s

Answer

45.02 m/s

8 0

3 years ago

Read 2 more answers

Get all of them and get brainliest

Marina86 [1]

1. 21,150
2. 2.5193
3. 27.98
4. 11,100

8 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

Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?

TEA [102]

Answer:

The book is 270 pages long.

6 0

2 years ago