Answer:
62.1467 square units (correct to four decimal places)
Step-by-step explanation:
Let's say the triangle is;
A(-7,5)
B(-4,1)
C(0,1)
Let's say also that AB = a , BC = b and AC = c
By measurement BC = 4 units , AB = 5 units (applying Pythagorean theorem) and AC = 8.1 units (correct to one decimal place) also through Pythagorean theorem.
Area of this triangle = , where p is half the perimeter of the triangle
p = units
Area = = 62.1467 square units (correct to four decimal places)
9514 1404 393
Answer:
Step-by-step explanation:
Rewriting the equations to make x the subject, we have ...
x = y² -1 . . . . . [eq1]
x = 1 - y . . . . . .[eq2]
At the points of intersection, the difference will be zero.
y² -1 -(1 -y) = 0
y² +y -2 = 0
(y -1)(y +2) = 0
The y-coordinates of points A and B are 1 and -2.
The corresponding x-coordinates are ...
x = 1 -{1, -2} = {1 -1, 1+2} = {0, 3}
Then A = (0, 1) and B = (3, -2).
__
A differential of area can be written ...
(x2 -x1)dy = ((1 -y) -(y² -1))dy = (2 -y -y²)dy
Integrating this over the interval y = [-2, 1] gives the area.
The area of the shaded region is 4.5 square units.
Answer:
The required equation is:
Explanation:
Let us assume that the hole is at y = 0m, with x as the time.
From the question we have (-1s, 8m) as the vertex (here x being the time variable is supposed to be in seconds and y being the distance variable is supposed to be in meters)
At x = 1s, the ball gets to the hole, therefore we have point (1s, 0m)
We know that the vertex of the parabola y = ax² + bx + c is at
therefore we have:
We then have the following equations:
From the 3rd equation we have
1 X 2a = b.
Therefore we have:
We can simplify both equations and get:
The first equation now becomes:
With a, we can find the values of c and b.
Then the equation is: