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rowdycar313p0ao5k
23.07.2019 •
Mathematics
*urgent* answer a) calculate the perimeter of the excavation. b) determine the equation of the diagonal adc) use algebraic methods to show that ad is parallel to bc
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Ответ:
AB = 2 - (-4) = 6
AE = 4 - (-2) = 6
ED = 5 - (-4) = 9
CD = 2 - (-2) = 4
Now BC is a little trickier and we need to use the formula for the distance between two points: d = sq.root of((x2 - x1)^2 + (y2 - y1)^2)
Given that B has coordinates (2, 4) and C has coordinates (5, 2):
d = sq.root of((5 - 2)^2 + (2 - 4)^2)
= sq.root of (3^2 + (-2)^2)
= sq.root of(9 + 4)
= sq.root of(13)
= 3.606 (to three decimal places)
Perimeter = 6 + 6 + 9 + 4 + 3.606
= 28.606 m
(Or if we kept it as an exact value it would be 25 + sq.root of(13) m)
b) First we need to calculate the gradient of the line AD, using m = (y2 - y1)/(x2 - x1).
Given that A has coordinates (-4, 4) and D has coordinates (5, -2):
m = (-2 - 4)/(5 - (-4)
= -6/9
= -2/3
Now we can substitute this into the point-slope equation form y - y1 = m(x - x1) with another point, let's take A(-4, 4):
y - 4 = -2/3(x - (-4)
y = (-2/3)x - 8/3 + 4
y = (-2/3)x + 4/3
(This can also be rewritten as 3y + 2x = 4)
c) If AD is parallel to BC, then their gradients will be equal. First we need to find the gradient of BC using the same method that we used above, where m = (y2 - y1)/(x2 - x1)
Given that B has coordinates (2, 4) and C has coordinates (5, 2):
m = (2 - 4)/(5 - 2)
= -2/3
The gradient of AD = -2/3
Gradient of AD = gradient of BC = -2/3, therefor the two lines are parallel
Ответ:
Step-by-step explanation:
{y2+8y−128=0x=34⋅(y+4) ... The two right triangle are similar, so: BDAB=DEAC. From this, I obtain: ... AC=3x AB=4x (3x)²+(4x)²=225 x=3 BD=8 AB/AC=BD/DE 12/9=8/DE DE=6.