valor.21ict
2022-04-01

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asked 2022-04-10

Transform this into a polynomial: $-{x}^{2}+6x-9$

Is there a formula?

What number $k}^{2$ can be a negative number?

I thought that only $-{k}^{(\mathrm{odd}\mathrm{number})}$ could be negative, but it is a binomial so...

asked 2022-03-25

How a solving a nonlinear PDE with Self-similar Solution?

I want to solve the problem :

$\frac{\mathrm{\partial}u}{\mathrm{\partial}t}={\left|\mathrm{\nabla}u\right|}^{-2p}(\frac{{\mathrm{\partial}}^{2}u}{\mathrm{\partial}{\xi}^{2}}+(1-p\left)\frac{{\mathrm{\partial}}^{2}u}{\mathrm{\partial}{\eta}^{2}}\right)$

We search for a self-similarity solution, the general form of which is as follows

$u(x,y,t)=f\left(\xi \right),\text{}\text{with}\text{}\xi =d\frac{{({x}^{2}+{y}^{2})}^{n}}{a\left(t\right)}$

from which we obtain

$\alpha \xi =(1-p){\left(2n\right)}^{-2p+2}((\frac{1}{2n(1-p)}+\frac{2n-1}{2n}){\left(d\frac{df}{d\xi}\right)}^{-2p}+\xi {\left(d\frac{df}{d\xi}\right)}^{-2p-1}d\frac{{d}^{2}f}{d{\xi}^{2}})$

Now, I am very confused on how to solve the above equation and find the exact solution of $f\left(\xi \right)$, thereby finding the exact solution of $u(x,y,t)$. So my question is, does anyone know how to solve this ordinary differential equation?

asked 2022-03-19

Assuming that, on average, 4 out of 5 planes at Mactan International Airport arrive on schedule for a particular time period, what is the probability that out of 8 planes, chosen at random:

1.1) all 8 planes arrive on schedule?

1.2) 5 arrive on schedule?

1.3) at least 6 arrive on schedule?

asked 2022-03-17

If a student jumps straight up to a height of 0.440m, what is his initial speed as it leaves the ground? How long is he in the air?

asked 2022-05-11

Belinda is thinking about buying a car for $18,500. The table below shows the projected value of two different cars for three years:

Number of years | 1 | 2 | 3 |
---|---|---|---|

Car 1 (value in dollars) | 17,390 | 16,346.60 | 15,365.80 |

Car 2 (value in dollars) | 17,500 | 16,500 | 15,500 |

**Part A:** What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)**Part B:** Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)**Part C:** Belinda wants to purchase a car that would have the greatest value in nine years. Will there be any significant difference in the value of either car after nine years? Explain your answer, and show the value of each car after nine years. (4 points)

asked 2022-03-30

Prove: if $p{x}^{2}-(p+q)x+p=0$ has an integer root, $p{x}^{2}+qx+{p}^{2}-q=0$ has an integer root too, for com' $p,q\in \mathbb{N}$

asked 2022-05-13

Determine the equation of a cosine function for the following graph of a sinusoidal function.