I need help!!!!!!!!!!!

If points A and B are randomly placed on the circumference of a circle with a radius of 2 cm, what is the probability that the l

OLga [1]

Answer:

The probability that the length of chord AB > 2 cm is 2/3 ⇒ D

Step-by-step explanation:

* Lets explain how to solve the problem

- Points A and B are randomly placed on the circumference of a

circle with a radius of 2 cm

- We need to find the probability that the length of chord AB is

greater than 2 cm

- Probability = required length of arc / circumference

- Assume that the length of the chord AB is 2 and the center of

the circle is labeled M

- The radius of the circle is 2 and AB = 2

- In Δ AMB

∵ MA= MB = 2 radii

∵ AB = 2

∴ Δ AMB is an equilateral triangle

∴ m∠AMB = π/3

∵ The length of an arc = r Ф , where r is the radius of the circle and

Ф is the central angle subtended by this arc

∵ r = 2 , Ф = π/3

∴ The length of arc AB = 2 × π/3 = 2π/3

- The arc AB is in the half of the circle then there are another arc

with the same length in the other half of the circle

- The length of the arc we must excluded from the length of the

circle to have the part of length of AB is greater than 2 is

2(2π/3) = 4π/3

∴ The length of the excluded arc is 4π/3

∵ The length of the circle is 2πr

∵ r = 2

∴ The length of the circle = 2π(2) = 4π

- The required arc = length circle - length excluded arc

∵ The length of the excluded arc = 4π/3

∵ The length of the circle = 4π

∴ The required arc = 4π - 4π/3 = 8π/3

- Probability = required length of arc / circumference

∴ Probability = (8π/3)/(4π) = 2/3

∴ The probability that the length of chord AB > 2 cm is 2/3

4 0

3 years ago

Welcome to the bread bank

Dimas [21]

Answer:

TOASTED. ROASTED.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Brad is 3 years older than Francis. The product of their ages is 154. Determine their ages.

Naya [18.7K]

Let Francis's age be x and Brad's age be 3x

The Product of their ages = 154

So ,

$\huge\blue{A}\red{n}\green{s}\red{w}\pink{e}\red{r}$

X × 3x = 154

4x = 154

x = 154÷4

x= 36

So Francis age = 36

Brad age = 36×3 = 108

<h3>HOPE IT HELPS YOU </h3>

6 0

3 years ago

Read 2 more answers

On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(-3,1), B(2,3), and

solniwko [45]

we have

A(-3,1), B(2,3), and C(4,-1)

we know that

the distance between two points is equal to the formula

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

so

Step 1

Find the distance AB

$d=\sqrt{(3-1)^{2}+(2+3)^{2}}$

$d=\sqrt{(2)^{2}+(5)^{2}}$

$dAB=\sqrt{29}\ units$

convert units to miles

$dAB=\sqrt{29}\ miles$

Step 2

find the distance BC

$dBC=\sqrt{(-1-3)^{2}+(4-2)^{2}}$

$dBC=\sqrt{20}\\dBC=2\sqrt{5}\ units$

convert unit to miles

$dBC=2\sqrt{5}\ miles$

Step 3

Find the minimum total distance the employee may have driven before getting stuck in traffic

Sum the distance AB and the half distance BC

$=\sqrt{29}\ miles+(0.5)*2\sqrt{5}\ miles\\ =5.4+2.2\\ =7.6\ miles$

therefore

the answer is

$7.6\ miles$

5 0

4 years ago

The quantity, Q, of a drug in the blood stream begins with 250 mg and decays to one-fifth its value over every 90 minute period.

Mazyrski [523]

Answer:

$a=250 \, mg\\\\b=5\\\\T= 90'$

Step-by-step explanation:

We have that $Q(t) = a\cdot b^{-\frac{t}{T}} \\$

Where t is the time (in minutes) and for the sake of dimensional consistency, let's assume that T is also in minutes, b is an adimensional number, and a is in mg. So we will have Q in mg as a consequence.

We now want to find out what values these constants might take. Let's see what happens when $t=0$ , that is, just as we start. At that point, we have that the amount of drug in the bloodstream must be equal to 250mg, thus:

$Q(0)= a\cdot b ^{-\frac{0}{T} }=250\,mg\\Q(0)= a=250\,mg$

We have found the constant $a$ ! It is the initial amount of drug! we have made use of the fact that any number raised to the 0th power is equal to one.

Now, we know that every 90 minutes, the amount of drug decreases to one fifth of its former value. How do we put this in mathematical form? Like so:

$Q(t+90')=Q(t)/5$

That is, 90 minutes after time t the amount of drug will be one fifth of the amount of drug at time t. Let's expand the last equation:

$Q(t+90')=Q(t)/5\\\\a\cdot b^{-\frac{t+90'}{T} }=a\cdot b^{-\frac{t}{T} }/5\\\\ b^{-\frac{t+90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{t}{T} }b^{-\frac{90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{90'}{T} }=\frac{1}{5}$

Now the last expression isn't enough to determine both T and b, but that also means that we have some freedom in how we choose them. What seems most simple is to pick $T=90'$ and thus we will get:

$b^{-1 }=\frac{1}{5}\\\\\frac{1}{b}= \frac{1}{5}\\\\b=5$

And that is our final result.

3 0

3 years ago