What does the irrational number 1.8693... fall?

Which explanation can be used to informally derive the formula for the volume of a cylinder? a cylinder is similar to a triangul

romanna [79]

The correct is one is; A cylinder is like a stack of circles. The volume of the cylinder would be the area of the circle multiplied by the height of the cylinder. The height of the cylinder represents how many circles are in the stack. Therefore, we get the formula πr²h, where πr² represents the area of the circle and h the height of the circle.

6 0

3 years ago

Read 2 more answers

Part 2: Use the information provided to write the vertex form equation of each parabola.

Serggg [28]

Answer: 1. x = -2(y - 4)² + 1

2. x = -y² + 5

3. y = -5(x + 1)² + 2

Step-by-step explanation:

Notes: The vertex formula of a parabola is x = a(y - k)² + h or y = a(x - h)² + k

(h, k) is the vertex
p is the distance from the vertex to the focus

$\bullet\quad a=\dfrac{1}{4p}$

1)

$\text{Vertex}=(1,4)\qquad \text{Focus}:\bigg(\dfrac{7}{8},4\bigg)\\\\\text{Given}: (h,k)=(1,4)\\\\\\p=focus-vertex=\dfrac{7}{8}-\dfrac{8}{8}=\dfrac{-1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{8})}=\dfrac{1}{-\frac{1}{2}}=-2$

Now input a = -2 and (h, k) = (1, 4) into the equation x = a(y - k)² + h

x = -2(y - 4)² + 1

***********************************************************************************

2)

$\text{Vertex}=(5,0)\qquad \text{Directrix}:x=\dfrac{21}{4}\\\\\text{Given}: (h,k)=(5,0)\\\\\\p=vertex-directrix=\dfrac{20}{4}-\dfrac{21}{4}=\dfrac{-1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{4})}=\dfrac{1}{-1}=-1$

Now input a = -1 and (h, k) = (5, 0) into the equation x = a(y - k)² + h

x = -1(y - 0)² + 5 → x = -y² + 5

***********************************************************************************

3)

$\text{Vertex}=(-1,2)\qquad \text{Directrix}:y=\dfrac{41}{20}\\\\\text{Given}: (h,k)=(-1,2)\\\\\\p=vertex-directrix=\dfrac{40}{20}-\dfrac{41}{20}=\dfrac{-1}{20}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{20})}=\dfrac{1}{-\frac{1}{5}}=-5$

Now input a = -5 and (h, k) = (-1, 2) into the equation y = a(x - h)² + k

y = -5(x + 1)² + 2

8 0

3 years ago

Solve ALL please . work needed 5x-1=x+115 3+5q=9+4q 2b+4=-18-9b

spin [16.1K]

1) 5x-1=x+115

5x-x=115+1
4x=116
x=116/4
x=29 (Answer)

2) 3+5q=9+4q

5q-4q=9-3
q=6 (Answer)

3) 2b+4=-18-9b

2b+9b=-18-4
11b=-22
b=-22/11
b=-2 (Answer)

Hope this helps

7 0

3 years ago

[6+4=10 points] Problem 2. Suppose that there are k people in a party with the following PMF: • k = 5 with probability 1 4 • k =

kirza4 [7]

Answer:

1). 0.903547

2). 0.275617

Step-by-step explanation:

It is given :

K people in a party with the following :

i). k = 5 with the probability of $\frac{1}{4}$

ii). k = 10 with the probability of $\frac{1}{4}$

iii). k = 10 with the probability $\frac{1}{2}$

So the probability of at least two person out of the 'n' born people in same month is = 1 - P (none of the n born in the same month)

= 1 - P (choosing the n different months out of 365 days) = $1-\frac{_{n}^{12}\textrm{P}}{12^2}$

1). Hence P(at least 2 born in the same month)=P(k=5 and at least 2 born in the same month)+P(k=10 and at least 2 born in the same month)+P(k=15 and at least 2 born in the same month)

= $\frac{1}{4}\times (1-\frac{_{5}^{12}\textrm{P}}{12^5})+\frac{1}{4}\times (1-\frac{_{10}^{12}\textrm{P}}{12^{10}})+\frac{1}{2}\times (1-\frac{_{15}^{12}\textrm{P}}{12^{15}})$