The simultaneous equations are
2x - 7y = 4 (1)
3x + y = -17 (2)
Write (2) as
y = - 3x - 17 (3)
Substitute (3) into (1).
2x - 7(-3x - 17) = 4
2x + 21x + 119 = 4
23x = -115
x = -5
This is the equation obtained after substituting y from the second equation into the first equation.
The solution for y is
y = -3(-5) - 17 = -2
Answer: x = -5
Note: The solution is x = -5, y = -2.
Circumference: 37.7 yards
Area: 113.1 yards^2
Answer: 16 feet
Step-by-step explanation:
Looking at the shape, one can notice that the unknown side can be found by adding the sides that are circled because they will give the same distance.
The length of the unknown side is therefore:
= 8 + 8
= 16 feet
Answer:
Dimensions of the poster
Width 29.10 cm
Height 38.80 cm
A(min) = 1129.08 cm²
Step-by-step explanation:
Printed area = 390 cm² = Ap
Lets call x and y dimensions of printed area
x width
y height
Then Ap = x*y and
y = Ap/x ⇒ y = 390/x
Then total area of the poster is:
A(t) = ( x + 12 ) * ( y + 16 ) and y = 390/x
A as a function of x
A(x) = ( x + 12 ) * ( 390/x + 16 ) ⇒ A(x) = 390 + 16x + 4680/x + 192
A(x) = 582 + 16x + 4680/x (1)
Taking derivatives
A´(x) = 16 - (4680/x²) ⇒ A´(x) = 0
[ 16x² -4680] /x² = 0 16x²- 4680 = 0 ⇒ x² = 4680/16
x = 17.10 cm and y = 390/x y = 390/17.10 y = 22.80 cm
A(t) = ( 17.10 + 12 ) * ( 22.80 + 16 )
A(t) = 29.10 * 38.80
A(t) = 1129.08 cm²
If we substitute in equation (1) the value of x ( 17.10) we see A(x) > 0
Then there is a minimun at the point x = 17.10
cos (angle) = adjacent leg / hypotenuse
cos (50) = 6 / x
x = 6 / cos(50)
x = 9.3
