Answer:
see the explanation
Step-by-step explanation:
Let
L ---> the length of rectangle in cm
W ---> the width of rectangle in cm
The area of rectangle is
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
![A=991\ cm^2](https://tex.z-dn.net/?f=A%3D991%5C%20cm%5E2)
so
---> equation A
we know that
<u><em>Prime numbers</em></u> only have factors of 1 and themselves.
So a rectangle with an area of 991 cm² can only be either
or ![L=1\ cm, W=991\ cm](https://tex.z-dn.net/?f=L%3D1%5C%20cm%2C%20W%3D991%5C%20cm)
It would be: 5x - 8 = 75
5x = 75 + 8
5x = 83
x = 83 / 5
x = 16.6
So, the number & your final answer is 16.6
Hope this helps!
Answer:
x'-5x=0, or x''-25x=0, or x'''-125x=0
Step-by-step explanation:
The function
is infinitely differentiable, so it satisfies a infinite number of differential equations. The required answer depends on your previous part, so I will describe a general procedure to obtain the equations.
Using rules of differentiation, we obtain that
. Differentiate again to obtain,
. Repeating this process,
.
This can repeated infinitely, so it is possible to obtain a differential equation of order n. The key is to differentiate the required number of times and write the equation in terms of x.
![\log50+\log\dfrac x2=2](https://tex.z-dn.net/?f=%5Clog50%2B%5Clog%5Cdfrac%20x2%3D2)
Condense the logarithms on the left into one:
![\log\left(50\cdot\dfrac x2\right)=\log(25x)=2](https://tex.z-dn.net/?f=%5Clog%5Cleft%2850%5Ccdot%5Cdfrac%20x2%5Cright%29%3D%5Clog%2825x%29%3D2)
Assuming the base of the logarithm is 10, write both sides as powers of 10. This lets us eliminate the logarithm:
![10^{\log(25x)}=10^2\implies25x=100](https://tex.z-dn.net/?f=10%5E%7B%5Clog%2825x%29%7D%3D10%5E2%5Cimplies25x%3D100)
Divide both sides by 24 to solve for
:
![x=\dfrac{100}4\implies\boxed{x=25}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B100%7D4%5Cimplies%5Cboxed%7Bx%3D25%7D)
A set of ordered pairs, like the ones shown, represents a function only if each of the first coordinates is not repeated.
For example {(2, 5), (7, 8)} is a function, but {(2, 3), (6, 8), (2, -1)} is not because 2 is repeated.
We can check that each set of pairs we are given, are functions.
The inverses of each of these sets would be :
<span>{(–2, –1), (4, 0), (3, 1), (14, 5), (4, 7)} 4 repeats
{(2, -1), (4, 0), (5, 1), (4, 5), (2, 7)} 4 and 2 repeat
{(3, -1), (4, 0), (14, 1), (6, 5), (2, 7)} no repetition of 1st coordinates
{(4, -1), (4, 0), (2, 1), (3, 5), (1, 7)} 4 repeats
</span>
So only the inverse of <span>{(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} is also a function</span>