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kifflom [539]
3 years ago
14

A circle has a radius of 3. An arc in this circle has a central angle of 20. What is the length of the arc?

Mathematics
2 answers:
seropon [69]3 years ago
7 0

Answer:

Step-by-step explanation:

1/3 pi

Ede4ka [16]3 years ago
5 0
Circumference of whole circle =
\pi \times 3 \times 2
360÷20=18
\frac{1}{18}  \times 6\pi = \frac{1}{3} \pi
hence length of arc = 1/3 pi
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Factor the polynomial, x2 + 5x + 6
patriot [66]

Answer:

Choice b.

x^{2} + 5\, x + 6 = (x + 3)\, (x + 2).

Step-by-step explanation:

The highest power of the variable x in this polynomial is 2. In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to 0.)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to 0. The discriminant of this polynomial is (5^{2} - 4 \times 1 \times 6) = 1.

\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}.

Similarly:

\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}.

By the Factor Theorem, if x = x_{0} is a root of a polynomial, then (x - x_0) would be a factor of that polynomial. Note the minus sign between x and x_{0}.

  • The root x = -2 corresponds to the factor (x - (-2)), which simplifies to (x + 2).
  • The root x = -3 corresponds to the factor (x - (-3)), which simplifies to (x + 3).

Verify that (x + 2)\, (x + 3) indeed expands to the original polynomial:

\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}.

4 0
2 years ago
What type of relationship does this equation represent?
Klio2033 [76]

Answer:

Nonproportional

Step-by-step explanation:

hope it helps.

8 0
2 years ago
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Length and breadth of a rectangle is 28 and 20 respectively. It's perimeter is ....... *
vampirchik [111]

Answer:

96

Step-by-step explanation:

Because the perimeter of a rectangle is 2 * (length) + 2 * (breadth),

P = 2 * 28 + 2 * 20

P = 56 + 40 = 96

3 0
3 years ago
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¿cuál es el vértice de una parábola que corta los ejes en los puntos (-1,0) , (5,0), (0,-10) ?​
kvasek [131]

Answer:

vertex: (2,-18)

Step-by-step explanation:

y = ax² + bx + c

(-1,0) : a - b + c = 0       ...(1)

(5,0) : 25a +5b +c = 0  ...(2)

(0,-10): 0a + 0b + c = -10        c=-10

(1) x5: 5a - 5b + 5c = 0  ...(3)

(2)+(3): 30a + 6c = 0          30a = -6c = 60        a = 2

(1): 2 - b -10 = 0     b = -8

Equation: y = 2x² - 8x -10 = 2 (x² -4x +4) - 18 = 2(x-2)² -18

equation: y = a(x-h)²+k     (h,k): vertex

vertex: (2,-18)

3 0
2 years ago
What is a common denominator for 1/6 and 3/5
d1i1m1o1n [39]

Answer:

30

Step-by-step explanation:

8 0
3 years ago
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