T) -7x+10y=20. M) -3x+y=-2 - ,
2(8x-5y)=35(2) -1(x+y)=-6(-)
-7x+10y=20. -3x+y=-2
16x-10y=70. -x-y=6
9x=90. -4x=4
[x=10] [x= -1]
-7(10)+10y=20. -3(-1)+y=-2
-70+10y=20. 3+y=-2
10y=90. [y= -5]
[y=9]
<h3>
Answer: 12 square units</h3>
Explanation:
Rectangle ABDE is 4 units across the horizontal, and 2 units tall.
The area of this rectangle is length*width = 4*2 = 8 square units.
Triangle BCD has a base of 4 and height 2. The area of which is base*height/2 = 4*2/2 = 4 square units.
The total area is
rectangle + triangle = 8 + 4 = 12 square units
You have to build the triangles.
They are such that:
h is the common height
x is the horizontal distance from the plane to one stone
Beta is the angle between x and the hypotenuse
Then in this triangle: tan(beta) = h / x ......(1)
1 - x is the horizontal distance from the plane to the other stone
alfa is the angle between 1 - x and h
Then, in this triangle: tan (alfa) = h / [1 -x ] ...... (2)
from (1) , x = h / tan(beta)
Substitute this value in (2)
tan(alfa) = h / { [ 1 - h / tan(beta)] } =>
{ [ 1 - h / tan(beta) ] } tan(alfa) = h
[tan(beta) - h] tan(alfa) = h*tan(beta)
tan(beta)tan(alfa) - htan(alfa) = htan(beta)
h [tan(alfa) + tan(beta) ] = tan(beta) tan (alfa)
h = tan(beta)*tan(alfa) / (t an(alfa) + tan(beta) )
The equation is:
h ( t ) = - 16 t² + 60 t + 3
The toy rocket will reach the ground when: h ( t ) = 0
- 16 t² + 60 t + 3 = 0
t 1 = - 0.05
t 2 = 3.8
Answer:
C ) 3.80 s
2x + 3x + 140 = 360 (being complete turn angle)
5x + 140 = 360
5x = 360-140
5x = 220
x = 44
now 2x = 2 × 44 = 88
3x = 3 × 44 = 132
