INVERSE TRIG COMMON ANGLES IM DESPERATE FOR HELP PLS

Urgent!!!!!In a class of students, the following data table summarizes the gender of the students

Setler79 [48]

Answer:

.85%

Step-by-step explanation:

You add up all the students who have an A whether they are male or female. 3 + 17 = 20. You have 17 males right? Divide 17 by 20 to get .85

7 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

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

Roman55 [17]

Answer:

Standard error (S.E) = 0.048 ≅ 0.05

Step-by-step explanation:

Explanation:-

Given sample size 'n'=76

Given the dean who randomly selects 76 students and finds that 58 out of 76 are receiving financial aid.

Sample proportion

$p = \frac{x}{n} = \frac{58}{76} = 0.7631$

The standard error is determined by

$S.E = \sqrt{\frac{p(1-p)}{n} }$

$S.E = \sqrt{\frac{0.763(0.2369}{76} }$

Standard error is 0.048 ≅ 0.05

3 0

3 years ago

10 to the 6th power multiplied by what equals 10 to the 18th power

m_a_m_a [10]

You're asking

(10⁶) times (10^p) = 10¹⁸ .

When you multiply two numbers that have the same base
but different exponents, you just add the exponents.

So        6 + p = 18

Subtract 6 from each side:       p = 12 .

   10⁶ x 10¹² = 10¹⁸ .

8 0

3 years ago

Which inequality is shown in this graph?

Aneli [31]

Answer:

(A). $y\leq -3x+3$

Step-by-step explanation:

The equation of any straight line; a linear equation, can be interpreted as $y=mx+b$ , where 'm' is the slope of the line, 'b', is the y-intercept, and the values of 'x' and 'y' are simply coordinates!

Let's find the slope of the straight line, and that can be done in various ways. Since they gave us two points, I would use the following formula to find slope: $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Let's assign each coordinate(s) to correspond to the formula (It doesn't matter what order, as long as you follow the rule that you've set up).

$(x_{1},y_{1}), (x_{2}, y_{2})$ So now that know this, we can just plug in the values that we know, which we already know everything.

$(0,3) (2,-3)$

$m=\frac{-3-3}{2-0}$ → This then gives us; $m=-3$ , which means the slope is -3! Now we have one part of the equation. This means that we can easily eliminate options B and D since they give a slope of positive three, which is false.

Now, let's move onto the y-intercept. How do we solve that? The y-intercept is generally known as a point that crosses the y-axis. This means that the x value is always going to be zero. This means that we know the point on the graph is: $(0,y)$ . So all we have to do is use that information, and look at the graph! It looks like there is a point that does an x-value of zero.

We can see that the point we are looking at is; $(0,3)$ , and the y-value is only what we are looking for. So now, we know that several components of the graph. We know so far that the slope is -3 and the line crosses the y-axis at (0,3), now we move on to determine the inequality part of the graph.

There are rules that determine how a graph is shaded—and let's figure that out.

Shading above the line is represented when 'y' is greater than the inequality itself.

Shading below the line is represented when 'y' is less than the inequality.

The shading occurs below the line, right? That means y is less than the inequality, and since the line is solid, the line can also equal the inequality. Now; with all of this to mind, y is less than or equal to -3x +3 is written or known as; $y\leq -3x+3$ , which means the answer is A.

6 0

3 years ago