All categories

3 years ago

A cone fits inside a square pyramid as shown. For

Mathematics

1 answer:

likoan [24]3 years ago

6 0

Answer:

Answer on Question #47534 – Math – Geometry

How to prove the volume formula of con is 1/3×π×r^2×h;without using

integration?

Solution.

Suppose we take a slice of the pyramid with the cone inside, from some way up

the pyramid. This will look like a square with a circle fitting inside. Radius of the

cone at this point, will be x.

The area of the circle is

The area of the square is × =

The ratio of the circle to the square is

The same is true for every slice we take: the area of the circle is

of the area

of the square.

So, the volume of the cone will be

the volume of the pyramid.

The pyramid's volume is

So the cone's volume is

∗

You might be interested in

Lucy draws a rectangle that is not a square. The perimeter of the rectangle can be

shusha [124]

Answer is i think c
I think C

8 0

2 years ago

Pweaseee help!!!!!!!!!!!!!!!

liraira [26]

To simplify this expression would be 4x-3

8 0

3 years ago

Will mark brainlist for anyone who answers these parts correctly and properly showed their work.

dalvyx [7]

Answer:

The rise is -5 the run is 4

Step-by-step explanation:

Slope (m) =

ΔY

ΔX

-5

-1.25

θ =

arctan(

ΔY

) + 360°

ΔX

308.65980825409°

ΔX = 2 – -2 = 4

ΔY = -1 – 4 = -5

Distance (d) = √ΔX2 + ΔY2 = √41 = 6.4031242374328

Equation of the line:

y = -1.25x + 1.5

y =

When x=0, y = 1.5

When y=0, x = 1.2

Please give brainliest PLZPLZ

I really hope this helps have a beautiful day

3 0

3 years ago

Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodo

Shkiper50 [21]

Answer:

a) $P(X\leq 4)=0.0183+0.0733+ 0.1465+0.1954+0.1954=0.6288$

$P(X< 4)=P(X\leq 3)=0.0183+0.0733+ 0.1465+0.1954=0.4335$

b) $P(4\leq X\leq 8)=0.1954+0.1563+0.1042+0.0595+0.0298=0.5452$

c) $P(X \geq 8) = 1-P(X$

d) $P(4\leq X \leq 6)=0.1954+0.1563+0.1042=0.4559$

Step-by-step explanation:

Let X the random variable that represent the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. We know that $X \sim Poisson(\lambda=4)$

The probability mass function for the random variable is given by:

$f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda=4$ , $Var(X)=\lambda=2$ , $Sd(X)=2$

a. Compute both P(X≤4) and P(X<4).

$P(X\leq 4)=P(X=0)+P(X=1)+ P(X=2)+P(X=3)+P(X=4)$

Using the pmf we can find the individual probabilities like this:

$P(X=0)=\frac{e^{-4} 4^0}{0!}=e^{-4}=0.0183$

$P(X=1)=\frac{e^{-4} 4^1}{1!}=0.0733$

$P(X=2)=\frac{e^{-4} 4^2}{2!}=0.1465$

$P(X=3)=\frac{e^{-4} 4^3}{3!}=0.1954$

$P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954$

$P(X\leq 4)=0.0183+0.0733+ 0.1465+0.1954+0.1954=0.9646$

$P(X< 4)=P(X\leq 3)=P(X=0)+P(X=1)+ P(X=2)+P(X=3)$

$P(X< 4)=P(X\leq 3)=0.0183+0.0733+ 0.1465+0.5311=0.7692$

b. Compute P(4≤X≤ 8).

$P(4\leq X\leq 8)=P(X=4)+P(X=5)+ P(X=6)+P(X=7)+P(X=8)$

$P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954$

$P(X=5)=\frac{e^{-4} 4^5}{5!}=0.1563$

$P(X=6)=\frac{e^{-4} 4^6}{6!}=0.1042$

$P(X=7)=\frac{e^{-4} 4^7}{7!}=0.0595$

$P(X=8)=\frac{e^{-4} 4^8}{8!}=0.0298$

$P(4\leq X\leq 8)=0.1954+0.1563+ 0.1042+0.0595+0.0298=0.5452$

c. Compute P(8≤ X).

$P(X \geq 8) = 1-P(X$

d. What is the probability that the number of anomalies exceeds its mean value by no more than one standard deviation?

The mean is 4 and the deviation is 2, so we want this probability

$P(4\leq X \leq 6)=P(X=4)+P(X=5)+P(X=6)$

$P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954$

$P(X=5)=\frac{e^{-4} 4^5}{5!}=0.1563$

$P(X=6)=\frac{e^{-4} 4^6}{6!}=0.1042$

$P(4\leq X \leq 6)=0.1954+0.1563+0.1042=0.4559$

4 0

3 years ago

Ipod: $89.00 Discount: 17% Tax: 5%

Degger [83]

Step-by-step explanation:

This sales tax table (also known as a sales tax chart or sales tax schedule) lists the amount of sales tax due on purchases between $0.00 and $59.70 for a 5% sales tax rate.

...

5% Sales Tax Chart ($0.00 - $59.70)

Price 20.10

Tax 1.01

Price 30.10

Tax 2.01

Tax 2.51

4 0

3 years ago