In the problem 62 times 45 the partial numbers are 6 and 5
Answer:
Step-by-step explanation:
General form of quadratic equation:
ax^2+bx+c=0
ax^2+bx=-c
To complete the square, we will divide the coefficient of x in the general quadratic equation as written above and divide by 2
I'm the question;
x^2-20x+13=0
x^2-20x=-13
The coefficient of x =-20
Divide the coefficient by 2 and square the result afterwards
-20/2= - 10
(-10)^2= 100
Add 100 to both sides of the equation
x^2-20x+100=-13+100
x^2-20x+100=87
x^2-10x-10x+100=87
x(x-10)-10(x-10)=87
(x-10)(x-10)=87
(x-10)^2=87
Answer is 10,87
Solution
Given the quadratic equation

we need to find the zeros of the equation
To do that, we use the completing the square method
Step 1. Add 38 to both sides

Step 2: add the square of half of the coefficient of x to both sides
That is;

Step 3: Simplify the above expression;
Answer:
<em>27 feet for the south wall and 18 feet for the east/west walls</em>
Maximum area= 
Step-by-step explanation:
<u>Optimization</u>
This is a simple case where an objective function must be minimized or maximized, given some restrictions coming in the form of equations.
The first derivative method will be used to find the values of the parameters that control the objective function and the maximum value of that function.
The office space for Billy-Sean will have the form of a rectangle of dimensions x and y, being x the number of feet for the south wall and y the number of feet for the west wall. The total cost of the space is
C=8x+12y
The budget to build the office space is $432, thus

Solving for y

The area of the office space is

Replacing the value found above

Operating

This is the objective function and must be maximized. Taking its first derivative and equating to 0:

Operating

Solving


Calculating y


Compute the second derivative to ensure it's a maximum

Since it's negative for x positive, the values found are a maximum for the area of the office space, which area is

Answer:
1/2 or 50% of the population has heard the rumor when it is spreading fastest.
Step-by-step explanation:
We need to take the derivative with respect to y from the r(y) = dy/dt = 2y(1-y) and equal to zero. At this condition we maximize the function and will get the maximum of the rumor spreading.

Therefore we just need to find y:

So 1/2 or 50% of the population has heard the rumor when it is spreading fastest.
I hope it helps you!