Answer:
Step-by-step explanation:
Prove: That the sum of the squares of 4 consecutive integers is an even integer.
An integer is a any directed number that has no decimal part or indivisible fractional part. Examples are: 4, 100, 0, -20,-100 etc.
Selecting 4 consecutive positive integers: 5, 6, 7, 8. Then;
= 25
= 36
= 49
= 64
The sum of the squares = 25 + 36 + 49 + 64
= 174
Also,
Selecting 4 consecutive negative integers: -10, -11, -12, -13. Then;
= 100
= 121
= 144
= 169
The sum of the squares = 100 + 121 + 144 + 169
= 534
Therefore, the sum of the squares of 4 consecutive integers is an even integer.
Answer:
Value of k is 
Step-by-step explanation:
We are given the following information in the question:
where x is the time elapses between the end of the hour and the end of the lecture.
We have to find the values of k.
Since, f(x) is the pdf, then,
![\displaystyle\int^\infty_{-\infty} f(x) = 1\\\\\displaystyle\int^2_{0} f(x) = 1\\\\\displaystyle\int^2_{0} kx^2 = 1\\\\k\bigg[\frac{x^3}{3}\bigg]^2_0 = 1\\\\k\times \frac{8}{3} = 1\\\\k = \frac{3}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5E%5Cinfty_%7B-%5Cinfty%7D%20f%28x%29%20%3D%201%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E2_%7B0%7D%20f%28x%29%20%3D%201%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E2_%7B0%7D%20kx%5E2%20%3D%201%5C%5C%5C%5Ck%5Cbigg%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5Cbigg%5D%5E2_0%20%3D%201%5C%5C%5C%5Ck%5Ctimes%20%5Cfrac%7B8%7D%7B3%7D%20%3D%201%5C%5C%5C%5Ck%20%3D%20%5Cfrac%7B3%7D%7B8%7D)
Hence, value of k is
Answer:
m = -2
Step-by-step explanation:
First, let's move all variables to one side of the equation. (Don't forget to change the signs when you move the numbers to the other side.)
18m + 7m = -60 + 2 + 8
Now we simplify to get this:
25m = -50
Now we divide -50 by 25 which gets us -2.
Therefore, m = -2
Hope this helps!
Answer:
x = 29
Step-by-step explanation:
I think this because they give you 78 degrees. The angle across from it (3x - 9) must equal 78 degrees as well. So solve as (3x - 9) = 78. 78 + 9 is 87. 87 divided by 3 is 29.
Hope it helps and is correct!
Answer:
El área del gimnasio sería 2000 metros cuadrados
Step-by-step explanation:
Un lado del gimnasio será igual al lado de la cancha y el otro lado será igual al lado de la piscina.
Dado que tanto la cancha como la piscina tienen forma cuadrada. El lado de la cancha será raíz cuadrada de 2.500 m2 y el de la piscina será raíz cuadrada de 1.600 m2
Por lo tanto, el lado del gimnasio sería 50 y 40.
El área del gimnasio sería 50 * 40 = 2000 metros cuadrados
