MATHEMATICS HIGH SCHOOL

In a circle with an 8-inch radius, a central angle has a measure of 60°. How long is the segment joining the endpoints of the arc cut off by the angle?

Answers

Answer 1

Answer:

Answer:

The length of segment joining the endpoints of the arc is $8\ in$

Step-by-step explanation:

we know that

In the triangle ABC

see the attached figure to better understand the problem

$AC=BC$ -----> is the radius of the circle

$m<CAB=m<CBA$

$m<ACB=60\°$ ----> given problem (central angle)

Initially the triangle ABC is an isosceles triangle

Remember that

the sum of the internal angles of triangle must be equal to $180\°$

For this particular case, the isosceles triangle ABC becomes an equilateral triangle, as the three angles are equal to $60\°$

The equilateral triangle has three equal sides and tree equal angles

$AC=BC=AB$

Hence

The length of segment joining the endpoints of the arc is $8\ in$

Answer 2

Answer: Given the radius, circumference can be solved by the equation, C = 2πr. The circumference of the circle above is C = 2π(8 in) = 16π in. To solve for the length of the segment joining the arc is the circumference times the ratio of central angle and 360 degrees.

Length of the segment = (16π in)(60/360) = 8/3 π in

Thus, the length of the segment is approximately 8.36 in.

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Two airplanes left the same airport and arrived at the same destination at the same time. The first airplane left at 8:00 a.m. and traveled at an average rate of 496 mph. The second airplane left at 8:30 a.m. and traveled at an average rate of 558 mph. How many hours did it take the first plane to travel to the destination?Let x represent the number of hours that the first plane traveled.
Enter an equation that can be used to solve this problem in the first box.
Solve for x and enter the number of hours in the second box.

Answers

First plane: 496x
Second plane: 558( x - 1/2)

Equation: 496x = 558( x - 1/2)

Solving x = 9/2 , or x = 4.5 hours.

Hope this helps.

Ten plus 8 to the third power divided by 16

Answers

Answer: 42

Step-by-step explanation:

10+8^3/10

Exponets first

8^3=512

Then Divide

512/16=32

Finally add

32+10=42

Use Order of Operations

How do you find the graph of f(x)= 5x-1/x-3 ?

Answers

$f(x)=(5x-1)/(x-3)=(5x-15+14)/(x-3)=(5x-15)/(x-3)+(14)/(x-3)=(14)/(x-3)+(5(x-3))/(x-3)=(14)/(x-3)+5\n\ny=(14)/(x)\n\n\Downarrow T_{\vec{a}=[3;\ 5]-translate\ 3\ units\ right\ and\ 5\ units\ up}\n\nf(x)=(14)/(x-3)+5$

$y=(14)/(x)\n\n\underline{x|-28|-14|-7|-2|\ -1\ |\ 1\ |\ 2\ |\ 7\ |14|28|}\ny|-(1)/(2)\ |\ -1\ |-2|-7|-14|14\ |\ 7\ |\ 2\ |\ 1|\ (1)/(2)\ |$

The element in group 15 and period 4

Answers

Final answer:

The element in group 15 and period 4 of the periodic table is Arsenic (As), which is classified as a metalloid due to its mixed properties of metals and non-metals.

Explanation:

The element that is found in group 15 and period 4 on the periodic table is Arsenic (As). Group refers to the vertical column and period refers to the horizontal row on the periodic table.

Arsenic belongs to the 'p-block' group of the periodic table and it is classified as a metalloid. This means it has properties of both metals and non-metals. For example, arsenic is brittle (like a non-metal) but can also conduct some electricity (like a metal).

Learn more about Arsenic here:

brainly.com/question/36984490

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Answer:

Arsenic

Step-by-step explanation:

Periods are vertical, groups are horizontal

Find the length of the third side. If necessary, write in simplest radical form

Answers

Answer:

$√(19)$

Step-by-step explanation:

Pythagoras

c² = a² + b²

with c being the Hypotenuse (= the side opposite of the 90 degree angle).

10² = 9² + b²

100 = 81 + b²

19 = b²

b = sqrt(19) (≈ 4.36)

Ana's statistics skills have been improving during her senior year at Fletcher High School. On her first end-of-the-week assessment she scored 57 points, then she scored 61 and 65 on her next two assessments. If her scores continued to increase at the same rate, what will be her score on the 9th assessment?

Answers

it will be 89 because it increases by 4 each time

Answer:
89%
Step-by-step explanation:
This is because it increases by 4 every time.

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