3x - y = 9
y = -2x + 11
3x - (-2x + 11) = 9
3x + 2x - 11 = 9
3x + 2x = 9 + 11
5x = 20
x = 20/5
x = 4
y = -2x + 11
y = -2(4) + 11
y = -8 + 11
y = 3
solution (where the lines intersect) is (4,3)
<span>et us assume that the origin is the floor right below the 30 ft. fence
To work this one out, we'll start with acceleration and integrate our way up to position.
At the time that the player hits the ball, the only force in action is gravity where: a = g (vector)
ax = 0
ay = -g (let's assume that g = 32.8 ft/s^2. If you use a different value for gravity, change the numbers.
To get the velocity of the ball, we integrate the acceleration
vx = v0x = v0cos30 = 103.92
vy = -gt + v0y = -32.8t + v0sin40 = -32.8t + 60
To get the positioning, we integrate the speed.
x = v0cos30t + x0 = 103.92t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + 60t + 4
If the ball clears the fence, it means x = 0, y > 30
x = 0 -> 103.92 t - 350 = 0 -> t = 3.36 seconds
for t = 3.36s,
y = -16.4(3.36)^2 + 60*(3.36) + 4
= 20.45 ft
which is less than 30ft, so it means that the ball will NOT clear the fence.
Just for fun, let's check what the speed should have been :)
x = v0cos30t + x0 = v0cos30t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + v0sin30t + 4
x = 0 -> v0t = 350/cos30
y = 30 ->
-16.4t^2 + v0t(sin30) + 4 = 30
-16.4t^2 + 350sin30/cos30 = 26
t^2 = (26 - 350tan30)/-16.4
t = 3.2s
v0t = 350/cos30 -> v0 = 350/tcos30 = 123.34 ft/s
So he needed to hit the ball at at least 123.34 ft/s to clear the fence.
You're welcome, Thanks please :)
</span>
Step-by-step explanation:
It is given that the angels of a triangle have a sum of 180°. The angles of a rectangle have a sum of 360°. The angels of a pentagon have a sum of 540.
<u>Let me define the each terms.</u>
1. We know that each angle in a triangle is 60°, So there is a three angle in a regular triangle.
2. We know that each angle in a rectangle, is 90°, So there is a four angle in a regular rectangle.
Similarly,
- There is 8 angle in a regular octagon and each angle measurement is 135°.
So, sum of the angles of an octagon = 135° × 8
Sum of the angles of an octagon = 1080°
Therefore, the required sum of the angles of an octagon is 1080°
