Answer:
El nieto de 14 años de edad recibirá la mayor cantidad.
Step-by-step explanation:
En este problema, debemos tener en mente que la cantidad aportada es directamente proporcional a la edad de quien recibe, esta cantidad es igual al producto de la cantidad total y la razón de la edad de quien recibe y la suma de todas las edades.
Bajo este razonamiento, podemos concluir que el nieto de 14 años de edad recibirá la mayor cantidad.
Answer:
6 and -14
Step-by-step explanation:
Area of the triangle = 1/2 ab
42 = 1/2 (x)(x+8)
42 *2 = x(x+8)
84 = x²+8x
x²+8x-84 = 0
x²+14x-6x-84 = 0
x(x+14)-6(x+14) = 0
x-6 = 0 and x+14 = 0
x = 6 and -14
Hence the values of x are 6 and -14
Answer:
Step-by-step explanation:
Consider the revenue function given by 
. We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).
From the first equation, we get, 
.If we replace that in the second equation, we get
From where we get that 
. If we replace that in the first equation, we get
So, the critical point is 
. We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that
We have the following matrix,
![\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Bmatrix%7D%20-10%20%26%20-2%20%5C%5C%20-2%20%26%20-16%5Cend%7Bmatrix%7D%5Cright%5D)
.
Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is 
and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum
Answer:
Diameter of sphere = 18 cm
Step-by-step explanation:
<h2>Volume of Cylinder and Sphere:</h2><h3> Cylinder:</h3>
Diameter = 18 cm
r = 18÷ 2 = 9 cm
h = 12 cm
= π * 9 * 9 * 12 cm³
<h3>Sphere:</h3>
Solid cylinder is melted and turned into a solid sphere.
Volume of sphere = volume of cylinder
![\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}](https://tex.z-dn.net/?f=%5Csf%20r%5E%7B3%7D%3D%20%5Cdfrac%7B%5Cpi%20%2A9%2A9%2A12%2A3%7D%7B4%2A%5Cpi%20%7D%5C%5C%5C%5C%20%20r%5E%7B3%7D%3D9%20%2A%209%20%2A3%20%2A3%5C%5C%5C%5C%5C%5Cr%20%3D%20%5Csqrt%5B3%5D%7B9%2A9%2A9%7D%5C%5C%5C%5C%20r%20%3D%209%20%5C%20cm%5C%5C%5C%5Cdiameter%20%3D%209%2A2%5C%5C%5C%5C%5Cboxed%7Bdiameter%20%5C%20of%20%5C%20%20sphere%20%3D%2018%20%5C%20cm%7D)
Answer:
distributivity/distributive property
