Answer:
y=-0.215x^2+35
Step by Step:
Let, ,
,
,
We know that, the general equation of the parabola.
Substitute the value of in equation
and find the value of
Hence, the equation of the parabola is:
On a recent day, 8 euros were worth $11 and 32 euros were worth $44. Enter an equation of the form y = kx to show the relationsh
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Answer:
The area of the parallelogram is;
32 square units
Step-by-step explanation:
The given parameters are;
The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)
We note that the area of a parallelogram = Base length × Height
From the drawing of the parallelogram RSTU, we have;
The base length = The length of = The length of
= √((2 - (-4))² + (6 - 4)²) = 2·√10
The height of a parallelogram is perpendicular to its base length = The line
∴ Where, the slope of the base length = m, the slope of the height = -1/m
The slope, 'm' of = (6 - 4)/(2 - (-4)) = 1/3
Therefore, the slope of the height = -1/(1/3) = -3
We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;
y - 0 = -3·(x - 0)
∴ y = -3·x
Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of and
The equation of the line in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;
y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)
y = x/3 + 4/3 + 4 = x/3 + 16/3
y = x/3 + 16/3
We then have the coordinate at the point 'V' (x, y) is given as follows;
-3·x = x/3 + 16/3
-9·x = x + 16
-10·x = 16
x = -16/10 = -1.6
x = -1.6
∴ y = -3·x = -3 × -1.6 = -4.8
y = 4.8
The coordinate at the point, V = (-1.6, 4.8)
The length of the line = The height of the parallelogram = √((-1.6 - 0)² + (4.8 - 0)²) = 8/5·√10
The height of the parallelogram = 8/5·√10
The area of the parallelogram, A = Base length × Height
∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32
The area of the parallelogram, A = 32 square units.
