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Mathematics

1 answer:

Anni [7]3 years ago

5 0

Answer:

Step-by-step explanation:

IT IS CONVENTIONAL to let the letter s symbolize the length of an arc, which is called arc length. We say in geometry that an arc "subtends" an angle θ; literally, "stretches under."

Now the circumference of a circle is an arc length. And the ratio of the circumference to the diameter is the basis of radian measure. That ratio is the definition of π.

π = C

D .

Since D = 2r, then

π = C

or,

r = 2π .

arc lengthThat ratio -- 2π -- of the circumference of a circle to the radius, is called the radian measure of 1 revolution, which are four right angles at the center. The circumference subtends those four right angles.

arc length

Radian measure of θ = s

Thus the radian measure is based on ratios -- numbers -- that are actually found in the circle. The radian measure is a real number that indicates the ratio of a curved line to a straight, of an arc to the radius. For, the ratio of s to r does determine a unique central angle θ.

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Of a number is what percentage of that number?

bulgar [2K]

Answer:

=5*3

=15%

the percentage of the number is 15%

8 0

3 years ago

Three dice are rolled. Let the random variable x represent the sum of the 3 dice. By assuming that each of the 63 possible outco

tamaranim1 [39]

<h3>Answer: 1/8</h3>

In decimal form, 1/8 = 0.125 which converts to 12.5%

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Work Shown:

The 63 should be 6^3. There are 6 choices per slot, and 3 slots, so 6^3 = 216 different outcomes.

Here are all of the ways to add to 11 if we had 3 dice

sum = 1+4+6 = 11
sum = 1+5+5 = 11
sum = 1+6+4 = 11
sum = 2+3+6 = 11
sum = 2+4+5 = 11
sum = 2+5+4 = 11
sum = 2+6+3 = 11
sum = 3+2+6 = 11
sum = 3+3+5 = 11
sum = 3+4+4 = 11
sum = 3+5+3 = 11
sum = 3+6+2 = 11
sum = 4+1+6 = 11
sum = 4+2+5 = 11
sum = 4+3+4 = 11
sum = 4+4+3 = 11
sum = 4+5+2 = 11
sum = 4+6+1 = 11
sum = 5+1+5 = 11
sum = 5+2+4 = 11
sum = 5+3+3 = 11
sum = 5+4+2 = 11
sum = 5+5+1 = 11
sum = 6+1+4 = 11
sum = 6+2+3 = 11
sum = 6+3+2 = 11
sum = 6+4+1 = 11

There are 27 ways to add to 11 using 3 dice. This is out of 216 total outcomes of 3 dice being rolled.

So, 27/216 = (1*27)/(8*27) = 1/8 is the probability of getting 3 dice to add to 11.

7 0

3 years ago

A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.

Artist 52 [7]

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}$

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}$