All categories

2 years ago

A circle has a radius if 20 centimeters and a central angle that measures 118 degrees. Find the length of the arc defined by thu

s central angle

Mathematics

1 answer:

babymother [125]2 years ago

4 0

$\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =118 \end{cases}\implies \begin{array}{llll} s=\cfrac{(118)\pi (20)}{180}\implies s=\cfrac{118\pi }{9} \\\\\\ s\approx 41.19~cm \end{array}$

You might be interested in

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

RoseWind [281]

Answer:

a. The equation of the parallel line to the given line is y = -4x + 19

b. The equation of the perpendicular line to the given line is y = $\frac{1}{4}$ x + 2

Step-by-step explanation:

Parallel lines have the same slopes

If the slope of one of them is m, then the slope of the other is m

The product of the slopes of the perpendicular lines is -1

If the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$

To find the slope of a perpendicular line to a given line reciprocal the slope of the given line and change its sign

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are the points on the line

The form of the equation of a line is y = m x + b, where

m is the slope

b is the y-intercept

Let us solve the question

∵ The given line passes through points (1, 6) and (2, 2)

∴ x1 = 1 and y1 = 6

∴ x2 = 2 and y2 = 2

→ Substitute them in the rule of the slope to find it

∵ m = $\frac{2-6}{2-1}=\frac{-4}{1}=-4$

∴ The slope of the given line is -4

∵ The line is parallel to the given line

∴ Their slopes are equal

∵ The slope of the given line = -4

∴ The slope of the parallel line = -4

→ Substitute its value in the form of the equation above

∴ y = -4x + b

→ To find b substitute x and y in the equation by the coordinates

of any point on the line

∵ The parallel line passes through the point (4, 3)

∴ x = 4 and y = 3

∵ 3 = -4(4) + b

∴ 3 = -16 + b

→ Add 16 to both sides

∴ 3 + 16 = -16 + 16 + b

∴ 19 = b

→ Substitute it in the equation

∴ y = -4x + 19

The equation of the parallel line to the given line is y = -4x + 19

∵ The line is perpendicular to the given line

∴ The product of their slopes is -1

→ Reciprocal the slope of the given line and change its sign

∵ The slope of the given line = -4

∴ The slope of the perpendicular line = $\frac{1}{4}$

→ Substitute its value in the form of the equation above

∴ y = $\frac{1}{4}$ x + b

→ To find b substitute x and y in the equation by the coordinates

of any point on the line

∵ The perpendicular line passes through the point (4, 3)

∴ x = 4 and y = 3

∵ 3 = $\frac{1}{4}$ (4) + b

∴ 3 = 1 + b

→ Subtract 1 from both sides

∴ 3 - 1 = 1 - 1 + b

∴ 2 = b

→ Substitute it in the equation

∴ y = $\frac{1}{4}$ x + 2

The equation of the perpendicular line to the given line is y = $\frac{1}{4}$ x + 2

4 0

3 years ago

Read 2 more answers

Simplify the expression and rewrite in rational exponent form.

Dahasolnce [82]

Answer:

$4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$

Step-by-step explanation:

The given expression: $4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}}$

Step 1: Change radical to fractional exponent.

Formula for fractional exponent: $\sqrt[n]{a}=a^{\frac{1}{n}}$

The power to which the base is raised becomes the numerator and the root becomes the denominator.

$\Rightarrow 4 x^{\frac{3}{5}} \cdot y^{4} \cdot x^{\frac{1}{2}} \cdot y^{\frac{5}{3}}$

Step 2: Apply law of exponent for a product $a^{m} \times a^{n}=a^{m+n}$

Multiply powers with same base.

$\Rightarrow 4 x^{\frac{3}{5}+\frac{1}{2}} \cdot y^{4+\frac{5}{8}}$

Take LCM for the fractions in the power.

$\Rightarrow 4 x^{\frac{6}{10}+\frac{5}{10}} \cdot y^{\frac{12}{3}+\frac{5}{3}}$

$\Rightarrow 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$

Hence the simplified form of $4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}} \text { is } 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$ .

5 0

3 years ago

tatuchka [14]

Answer:

angle 2

Step-by-step explanation:

alternate interior angles are angles formed when two parallel or non parallel line are intersected by a transversal ....

4 0

3 years ago

bru you just times the too numbers then you divide the answer by 2 then you times that by 4 then that your answer BIG BRAIN 1694

Salsk061 [2.6K]

Answer: SHEEEESHOOOOOO yesssirrrr big brainnnnnnn :clap clap:

6 0

3 years ago

Find the slope and standard form of the line that passes through the points (3, 6) and (4, 5).

qwelly [4]

Answer:

B) m = -1 , x + y = 9

Step-by-step explanation:

7 0

3 years ago