Angle G and Angle F are the same, which means that HF = GH
This means that x = 15
X = the number
14 + 2x = 6x - 7
21 + 2x = 6x
21 = 4x
5.25 = x
The number is 5.25.
The force in the rod when the temperature is 150 °F is 718.72 pounds-force.
<h3>How to determine the resulting the resulting force due to mechanical and thermal deformation</h3>
Let suppose that rod experiments a <em>quasi-static</em> deformation and that both springs have a <em>linear</em> behavior, that is, force (
), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to <em>temperature</em> increase creates a <em>spring</em> deformation additional to that associated with <em>mechanical</em> contact.
Given simmetry considerations, we derive an expression for the <em>spring</em> force (), in pounds-force, as a sum of mechanical and thermal effects by principle of superposition:
(1)
Where:
- Spring constant, in pounds-force per inch.
- Spring deformation, in inches.
- Rod elongation, in inches.
The <em>rod</em> elongation is described by the following <em>thermal</em> dilatation formula:
(2)
Where:
- Coefficient of linear expansion, in 
.
- Initial length of the rod, in inches. 
- Initial temperature, in degrees Fahrenheit.
- Final temperature, in degrees Fahrenheit.
If we know 
, 
, 
, 
, 
and 
, then the force in the rod at final temperature is:
![F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right]](https://tex.z-dn.net/?f=F%20%3D%20%5Cleft%281000%5C%2C%5Cfrac%7Blb%7D%7Bin%7D%20%5Cright%29%5Ccdot%20%5Cleft%5B0.7%5C%2Cin%20%2B%200.5%5Ccdot%5Cleft%286.5%5Ctimes%2010%5E%7B-6%7D%5C%2C%5Cfrac%7B1%7D%7B%5E%7B%5Ccirc%7DF%7D%20%5Cright%29%5Ccdot%20%2848%5C%2Cin%29%5Ccdot%20%28150%5C%2C%5E%7B%5Ccirc%7DF-30%5C%2C%5E%7B%5Ccirc%7DF%29%5Cright%5D)
The force in the rod when the temperature is 150 °F is 718.72 pounds-force. 
To learn more on deformations, we kindly invite to check this verified question: brainly.com/question/13774755
The vertex of the parabola is (0,4), because you can use -b/2a to find the x coordinate a of the vertex. There is no b so b=0 and 0/anything is 0. Then you can plug 0 into the equation to find the y coordinate of the vertex. When you plug in 0 you get 4, so the vertex is (0,4)
6.02 - 3.9 = 2.12 km
Convert 2.12 km to meters.
2.12 km = 2,120 meters.
