Complete the square and graph x+2(y-1)^2=4show all steps
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The standard form of the parabola is x = -4/3y² -40/3y -103/3
What is parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point and a line.
x = -4/3(y +5)² -1
Solve for x.
x = (4y² +40y +103)/(-3)
x = -4/3y² -40/3y -103/3 . . . . 'standard form' in the US
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Taking our clues from the graph*, we can write the vertex form equation as ...
x = -4/3(y +5)² -1 . . . . . . 'standard form' in other places
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* The vertex is (-1, -5), so for some leading coefficient, the equation will be ...
x = a(y -(-5))² +(-1) = a(y +5)² -1
The value of 'a' is the scale factor. Here, that is the difference between the parabola value (x = -2 1/3) and the vertex value (x = -1) one unit away from the vertex.
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Answer:
Lenghts of the sides:
Lenghts of the diagonals: and
Step-by-step explanation:
Look at the rhombus ABCD shown attached, where AC and BD de diagonals of the rhombus.
The sides of a rhombus have equal lenght. Then, since the perimeter of this one is 104 centimeters, you can find the lenght of each side as following:
You know that the diagonals are in the ratio
Then, let the diagonal AC be:
This means that AE is:
And let the diagonal BD be:
So BE is:
Since the diagonals of a rhombus are perpendicular to each other, four right triangles are formed, so you can use the Pythagorean Theorem:
Where "a" is the hypotenuse and "b" and "c" are the legs.
In this case, you can choose the triangle ABE. Then:
Substituting values and solving for "x", you get:
Therefore, the lenghts of the diagonals are:
