Ok first we calculate the length of board without losses:
4 * 11.5 = 46 inches
then, we have 1 inch of waste allowed fir each piece, so the total waste is 4*1 = 4 inches
finally, we will add the length of the waste to the desired length to get the total length of the board as follows:
total length of board = 46+4 = 50 inches
Step-by-step explanation:
For a quadratic equation y = ax² + bx + c, the vertex (the maximum or minimum point) is at x = -b/(2a).
1) y = -0.5t² + 2t + 38
The maximum is at:
t = -2 / (2 × -0.5)
t = 2
The maximum height is:
y = -0.5(2)² + 2(2) + 38
y = 40
The coordinates of the vertex are (2, 40). That means the missile reaches a maximum height of 40 km after 2 minutes.
2) y = -4.9t² + 12t + 1.6
The maximum is at:
t = -12 / (2 × -4.9)
t = 1.22
The maximum height is:
y = -4.9(1.22)² + 12(1.22) + 1.6
y = 8.95
The coordinates of the vertex are (1.22, 8.95). That means the missile reaches a maximum height of 8.95 m after 1.22 seconds.
3) y = -0.04x² + 0.88x
The maximum is at:
x = -0.88 / (2 × -0.04)
x = 11
The maximum height is:
y = -0.04(11)² + 0.88(11)
y = 4.84
The maximum height of the tunnel is 4.84 meters.
The maximum width is when y = 0.
0 = -0.04x² + 0.88x
0 = -0.04x (x − 22)
x = 22
The maximum width is 22 feet.
y = 8 -2x
x + 2 (8 - 2x) = 1
x + 16 - 4x = 1
x - 4x = -15
-3x = -15
x = 5
If x = 5, then we can substitute in...
5 + 2y = 1
2y = -4
y = -2
Now let us check that by substituting those values in to the equation
2x + y = 8
2 (5) + (-2) = 8
That is correct so we have the right values for x and y/
20,000 + 3,000 + 400 + 30 + 6
The line passes through two points that have the same x-coordinate.
It is a vertical line. To find the slope of a line, use any two points. Subtract the y-coordinates. Subtract the x-coordinates in the same order. Then divide the difference of the y-coordinates by the difference of the x-coordinates. Since in this case, the x-coordinates are both -6, the difference between the x-coordinates is zero. Division by zero is not defined, so the slope of this line is undefined. You can't write its equation in point-slope form, because there is no slope for this line.
