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3 years ago

Find a formula for the described function. Express the surface area of a cube as a function of its volume v.

Mathematics

1 answer:

Digiron [165]3 years ago

4 0

Let the side of the cube=a

So the volume will be=V=a³

Then surface area of the cube will be=6a²= $\frac{6a^3}{a}$ = $\frac{6V}{a}$

The above expression showing surface area as a function of Volume. (Answer)

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f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

A rectangle's length is three times its width. Let w denote the rectangle's width. What polynomial represents the rectangle's ar

Ket [755]

<span>A = l x w
Since
l = 3w

Substitute the l with 3w
The formula will be

A = 3w + w
A = 4w

An example:
The given known values are: Length of 4 cm Width is unknown Perimeter is 34 cm Find the dimensions of the rectangle. Since the geometric formula for perimeter is: </span>
P= 2 (l + w)
L = 2w – 4 cm
W =?
Derivation and solution:
34 = 2 (2w - 4) + 2w <span>
34 = 4w – 8 + 2w</span>
42 = 6w 42/6 = w
W = 7 cm

34 = 2l + 2(7)
34 = 2l + 14
2l = 34 – 14
2l = 20
L = 20/2
L = 10 cm<span> <span>
</span></span>

7 0

3 years ago

My crush cole doesn't really like me,am i doing something wrong?

kap26 [50]

Answer:

well maybe you just have to do something that he likes with him and get a little closer to him as a friend before you try something

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Find the volume of this sphere.

Sholpan [36]