Answer: 50.24 cm^2
Step-by-step explanation:
This can be translated to:
An old coin is kept in a cubic box in such a way that the outline of the coin touches the 4 walls of the box, if the base of the box has a perimeter of 24 cm. What is the area of the coin?
The fact that the coin touches the interior of the box means that the diameter of the coin is equal to the side lenght of the box.
The perimeter of the box is 24 cm, and the perimeter of a square is equal to:
P = 4*L
where L is the side lenght of the square.
24 cm = 4*L
L = 24cm/4 = 8cm
Now we know that the diameter of the coin is 8cm
Now, the area of a circle (the coin) is equal to:
A = 3.14*(d/2)^2
where d is the diameter, so we have:
A = 3.14*(4cm)^2 = 50.24 cm^2
Answer:
Create the table and choose a set of x values. Substitute each x value (left side column) into the equation. Evaluate the equation (middle column) to arrive at the y value. An Optional step, if you want, you can omit the middle column from your table, since the table of values is really just the x and y pairs.
Step-by-step explanation:
Specify a name for the function.
Specify a name and data type for each input parameter.
Specify the routine attributes.
Specify the RETURNS TABLE keyword.
Specify the BEGIN ATOMIC keyword to introduce the function-body.
Specify the function body.
Answer:
f(x) = (x -6)² +14
Step-by-step explanation:
Completing the square involves writing part of the function as a perfect square trinomial.
<h3>Perfect square trinomial</h3>
The square of a binomial results in a perfect square trinomial:
(x -h)² = x² -2hx +h²
The constant term (h²) in this trinomial is the square of half the coefficient of the linear term: h² = ((-2h)/2)².
<h3>Completing the square</h3>
One way to "complete the square" is to add and subtract the constant necessary to make a perfect square trinomial from the variable terms.
Here, we recognize the coefficient of the linear term is -12, so the necessary constant is (-12/2)² = 36. Adding and subtracting this, we have ...
f(x) = x² -12x +36 +50 -36
Rearranging into the desired form, this is ...
f(x) = (x -6)² +14
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<em>Additional comment</em>
Another way to achieve the same effect is to split the given constant into two parts, one of which is the constant necessary to complete the square.
f(x) = x² -12x +(36 +14)
f(x) = (x² -12x +36) +14
f(x) = (x -6)² +14
Hello,
(tg(x))'=1/cos²(x)
(arcsin(x))'=1/√(1-x²)
cos²(arcsin(x))=1-sin²(arcsin(x))=1-x²
