All categories

3 years ago

AC is the diameter. Calculate the area of the sector (to the nearest whole number) created by ∠CDB.

Mathematics

1 answer:

TiliK225 [7]3 years ago

3 0

Area of the circle is πr² which corresponds to an angle of 360° subtended at the center. Thus, the area of a sector subtending angle $\theta$ at the centre is:

$Area= \frac{\theta}{360}\times \pi r^2$

In this case put $\theta$ equal to 30°

You might be interested in

Which of the following graphs shows the solution set for the inequality below? 3|x + 1| < 9

Bas_tet [7]

Step-by-step explanation:

The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as

$f(x) \ = \ |x| \ = \ \left\{\left\begin{array}{ccc}x, \ \text{if} \ x \ \geq \ 0 \\ \\ -x, \ \text{if} \ x \ < \ 0\end{array}\right\}$ .

This definition of the absolute function can be explained geometrically to be similar to the straight line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ where $\textbf{\textit{x}} \ < \ 0$ (shown as the orange dotted line), the segment of the line is reflected across the x-axis.

First, we simplify the expression.

$3\left|x \ + \ 1 \right| \ < \ 9 \\ \\ \\\-\hspace{0.2cm} \left|x \ + \ 1 \right| \ < \ 3$ .

We, now, can simply visualise the straight line, $y \ = \ x \ + \ 1$ , as a line having its y-intercept at the point $(0, \ 1)$ and its x-intercept at the point $(-1, \ 0)$ . Then, imagine that the segment of the line where $x \ < \ 0$ to be reflected along the x-axis, and you get the graph of the absolute function $y \ = \ \left|x \ + \ 1 \right|$ .

Consider the inequality

$\left|x \ + \ 1 \right| \ < \ 3$ ,

this statement can actually be conceptualise as the question

$``\text{For what \textbf{values of \textit{x}} will the absolute function \textbf{be less than 3}}"$ .

Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).

Case 1 (when $x \ \geq \ 0$ )

$x \ + \ 1 \ < \ 3 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 3 \ - \ 1 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 2$

Case 2 (when $x \ < \ 0$ )

$-(x \ + \ 1) \ < \ 3 \\ \\ \\ \-\hspace{0.15cm} -x \ - \ 1 \ < \ 3 \\ \\ \\ \-\hspace{1cm} -x \ < \ 3 \ + \ 1 \\ \\ \\ \-\hspace{1cm} -x \ < \ 4 \\ \\ \\ \-\hspace{1.5cm} x \ > \ -4$

*remember to flip the inequality sign when multiplying or dividing by

negative numbers on both sides of the statement.

Therefore, the values of x that satisfy this inequality lie within the interval

$-4 \ < \ x \ < \ 2$ .

Similarly, on the real number line, the interval is shown below.

The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.

3 0

3 years ago

Which graph equals ƒ(x) = -x + 6?

KIM [24]

The last graph is the answer

6 0

3 years ago

Read 2 more answers

If sin(theta) =4/5 and is in quadrant 2, the value of cot(theta

iren [92.7K]

$\sin\theta= \frac{4}{5} 
\\
\\\sin^2\theta+\cos^2\theta=1
\\ \cos\theta=\pm \sqrt{1-\sin^2\theta} =\pm \sqrt{1-( \frac{4}{5})^2 } =\pm \sqrt{1- \frac{16}{25} } =\pm \sqrt{\frac{9}{25} }=\pm \frac{3}{5}}$

$\theta \in II \Rightarrow \cos\theta\ \textless \ 0 \Rightarrow \cos\theta=-\frac{3}{5}$

$\cot\theta= \frac{\cos\theta}{\sin\theta}= \frac{-\frac{3}{5}}{\frac{4}{5}} =- \frac{3}{4}$

5 0

3 years ago

A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at th

natali 33 [55]

Answer:

9 represents the initial height from which the ball was dropped

Step-by-step explanation:

Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:

$f(n)=9(0.7)^{n}$

The general formula for the geometric progression modelling this scenario is:

$f(n)=f_{0}(r)^{n}$

Here,

$f_{0}$ represents the initial height i.e. the height from which the object was dropped.

r represents the percentage the object covers with respect to the previous bounce.

Comparing the given scenario with general equation, we can write:

$f_{0}$ = 9

r = 0.7 = 70%

i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.

7 0

3 years ago

Business math pls help

Oksi-84 [34.3K]

Answer:

your pic hahaha

Step-by-step explanation:

4 0

3 years ago