Answer:
a) 400 meters
b) 67 meters
c) 124.790 meters
Step-by-step explanation:
Given data :
g1 = - 0.4 %
g2 = +2 %
change of grade of sag curve ( a ) = 0.6 %
Elevation of PVI ( h2 ) = 124.80 m
a) compute the length of the curve using the relation below
a = . hence ; L = ( g2 - g1 ) / a
L = ( 2 -(-0.4 ) / 0.6
= 2.4 / 0.6 = 4
= <em>400 meters</em>
<u>b) compute the elevation of the lowest point of the curve</u>
slope of the vertical curve = 0
0 = 2ax l + b
= 2( ) x + g1
∴ x = = ( 0.4 * 4 ) / ( 2 + 0.4 ) = 1.6 / 2.4 = 0.67 stations
therefore x ( elevation of the lowest point ) = <em>67 meters</em>
C<u>) compute the elevation at Sta. 12 + 125.60</u>
Given that the rate of change of elevation is the same at all points
= = 0.4 -------- ( 1 )
where h2 = 124.80
h1 = ? ( elevation of p0 ) at 12 + 125.60
PVI = 12 + 150.06
p0 = 12 + 125.60
back to the above equation
- h1 = 0.4 ( PVI - P0 ) - h2
= 0.4 ( 12.150 - 12.1256 ) - 124.80
-h1 = -124.790
hence h1 = 124.790 m
The answer is 238.5
hopes this helps
Answer:
136 cm^2
Step-by-step explanation:
The area of a trapezoid is found by
A = 1/2 (b1+b2) *h where b1 and b2 are the lengths of the bases and h is the height
A = 1/2 ( 12+22) *8
= 1/2 (34) * 8
= 136 cm^2
Answer: -42
Step-by-step explanation: 2*2 matrices are easy to find the determinant with. Its just ad-bc, so (5*-2)-(4*8), which is -42
Answer:
percentage applied to pants and sweater is 80%, and that applied to shirt and shoes is 70%
Step-by-step explanation:
<u>Question in English</u>
Leticia and Marta have gone Shopping in the sales. The First has bought $ 42 pants and a $ 24 shirt, and the second has bought a $ 28 sweater and $ 60 shoes. After applying the discounts, Leticia has paid $ 50.4 and Marta $ 64.4. Calculate the percentages of discounts applied knowing that the percentage applied to the pants and the sweater matched and that applied to the shirt and shoes as well.
<u>Solution</u>
Leticia = 42 + 24 = 50.4
Marta = 28 + 60 = 64.4
The percentage applied to the pants and the sweater coincided (that is, it is x) and that applied to the shirt and shoes also (that is, it is y)
Thus,
1) 42x + 24y = 50.4
2) 28x + 60y = 64.4
obtaining and in 1 we have
y = 50.4 - 42x / 24
y = 2.1 - 1.75x
Substituting and in 2 we obtain
28x + 60y = 64.4
28x + 60 (2.1 - 1.75x) = 64.4
28x + 126 - 105x = 64.4
126 - 64.4 = 105x - 28x
x = 61.6 / 77
x = 0.8
Substituting x into 1 gives:
42x + 24y = 50.4
42 (0.8) + 24y = 50.4
33.6 + 24y = 50.4
y = 50.4 -33.6 / 24
y = 0.7
Therefore, the percentage applied to pants and sweater is 80%, and that applied to shirt and shoes is 70%