Answer:
X=-2
Step-by-step explanation:
The axis of symmetry for any parabola is the x value of the vertex. Dividing the parabola along the vertex will always yield two symmetric halves.
Answer:
- 892 lb (right)
- 653 lb (left)
Step-by-step explanation:
The weight is in equilibrium, so the net force on it is zero. If R and L represent the tensions in the Right and Left cables, respectively ...
Rcos(45°) +Lcos(75°) = 800
Rsin(45°) -Lsin(75°) = 0
Solving these equations by Cramer's Rule, we get ...
R = 800sin(75°)/(cos(75°)sin(45°) +cos(45°)sin(75°))
= 800sin(75°)/sin(120°) ≈ 892 . . . pounds
L = 800sin(45°)/sin(120°) ≈ 653 . . . pounds
The tension in the right cable is about 892 pounds; about 653 pounds in the left cable.
_____
This suggests a really simple generic solution. For angle α on the right and β on the left and weight w, the tensions (right, left) are ...
(right, left) = w/sin(α+β)×(sin(β), sin(α))
To determine what the line looks like, simply change it to y = mx + b form. Then simply either make a table of values. And substitute any points into the equation and obtain points to plot on the graph. Or you can simply plot the graph by using the slope of the equation.
Y = 8 - 6x/2
Y = 4 - 3x
Y = -3x + 4.
This would be the rearranged equation.
1 pizza should cost $5.65
Pizza is $5.65 then bottle of coke is $2.45
3 pizzas and coke: ($5.65*3) + $2.45 = $19.4
I solved this by setting up and solving a system of linear equations:
Variables: p = pizza, c = coke
p = c+3.2
3p+c = 19.4
Solve by substitution
3(c+3.2) + c = 19.4
4c+9.6 = 19.4
c = 2.45
Re-plug in:
p = 2.45+3.2
p = 5.65
Write the equation of the cost
p stands for the cost per pear, a stands for the cost per apple
6p + 3a = 3.9
2p + 5a = 3.3
Solve the equation system
To solve the equation system, we work on eliminating variable p so we will find the number of a. To eliminate, we have to change the coefficient of p to the same number (i will change it to coefficient 6)
6p + 3a = 3.9 (multiply 1)
2p + 5a = 3.3 (multiply 3)
---------------------------------
6p + 3a = 3.9
6p + 15a = 9.9
-------------------- - (substract)
-12a = -6
a = -6/-12
a = 0.5
To find the cost per pear, subtitute the number of a to one of the equation
2p + 5a = 3.3
2p + 5(0.5) = 3.3
2p + 2.5 = 3.3
2p = 3.3 - 2.5
2p = 0.8
p = 0.4
The cost of one pear is $0.4
