1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dybincka [34]
3 years ago
7

If a central angle of measure 30° is subtended by a circular arc of length 6 meters, as is illustrated below, how many meters in

length is the radius of the circle?
Mathematics
1 answer:
Nana76 [90]3 years ago
3 0
30 degrees = pi/6 radians
Arc Length = (radius)(angle in radians)
               6 = (radius)(pi/6)
       radius = 36/pi or approx. 11.5 m

You might be interested in
I really need this answer
otez555 [7]

Answer:

D

Step-by-step explanation:

If the lines are parallel, the slope of both of them are going to be the same. So if one line is 3, the other one will be too.

6 0
3 years ago
Read 2 more answers
Simplify the given expression. (4x2squared-15x-21)+3x2squared-10)
Bess [88]

Answer:

7x^{2} - 15x -31

Step-by-step explanation:

(4x^{2} - 15x -21) + 3x^{2}  - 10 = 4x^{2} + 3x^{2} - 15x -21  - 10 = 7x^{2} - 15x -31

4 0
3 years ago
How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y
son4ous [18]

Solution:

Given:

x^2=6y

Part A:

The vertex of an up-down facing parabola of the form;

\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}

Rewriting the equation given;

\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\  \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\  \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\  \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\  \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}

Therefore, the focus is;

(0,\frac{3}{2})

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}

Therefore, the directrix is;

y=-\frac{3}{2}

3 0
1 year ago
What does 2.89x0.79x1.35= equal?
fenix001 [56]

Answer: 3.082185x^2

Step-by-step explanation: Find the exact value using trigonometric identities

8 0
2 years ago
What is/are the classification of functions that has its inverse?
UNO [17]

Answer:

Invertible functions

Step-by-step explanation:

An inverse of a function is one that reverses the operation of the function such that the result of the function on a variable, is reversed back to the initial variable

Therefore, when we have the the result of the function, f on x as y given as follows;

f(x) = y

The inverse of the function, g on the result, y gives the initial variable, x as follows;

g(y) = x

Example of invertible functions includes;

f(x) = x²

An example of a non-invertible function includes;

f(x) = 2·x².

4 0
3 years ago
Other questions:
  • A small island in the middle of a river is eroding away. Each year, the island has 85% of the area from the previous year. After
    10·1 answer
  • The following factors are not prime: (x2- 7x)(7x+21).What remains to be factored? (can be more than one answer). A) Factor out t
    13·2 answers
  • Find the value of |-4 3| · 8
    8·1 answer
  • Which function represents a horizontal shift of f(x) = 5x by 4 units to the right?
    5·1 answer
  • Write the first five terms of the sequence defined by the recursive formula
    12·2 answers
  • Is 40, 25, 85 a pythagorean triple?<br>​
    6·2 answers
  • What are two different names for this line
    9·1 answer
  • Solve 4x-2y=6 for x in terms for y
    6·1 answer
  • Directions: Simplify the following monomials (if possible).
    9·1 answer
  • If you buy stock for $36.20 per share and sell that stock for $37.90 per share, what was your
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!