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The hole is 8 feet deep at ground level ⇒ 3rd answer
Step-by-step explanation:
The form of the quadratic function is y = ax² + bx + c, where
- a is the coefficient of x²
- b is the coefficient of x
- c is the y-intercept (at x = 0)
The vertex point of the quadratic is (h , k), where
and k is the value of y when x = h
The table:
→ x : -2 , 0 , 2
→ y : -6 , -8 , -6
∵ x represents distance from hole's center in feet
∵ y represents the depth from level ground
∴ The quadratic function is y = ax² + bx + c
∵ c is the value of y at x = 0 ⇒ y-intercept
- From the table at x = 0 ⇒ y = -8
∴ c = -8
- Substitute its value in the function model
∴ y = ax² + bx - 8
- To find the values of a and b substitute x and y in the model by
the coordinates of the point in the table
∵ x = -2 and y = -6
∴ -6 = a(-2)² + b(-2) - 8
∴ -6 = 4a - 2b - 8
- Add 8 to both sides
∴ 2 = 4a - 2b
- Switch the two sides
∴ 4a - 2b = 2 ⇒ (1)
∵ x = 2 and y = -6
∴ -6 = a(2)² + b(2) - 8
∴ -6 = 4a + 2b - 8
- Add 8 to both sides
∴ 2 = 4a + 2b
- Switch the two sides
∴ 4a + 2b = 2 ⇒ (2)
Now we have a system of equation to solve it
Add equations(1) and (2) to eliminate b
∵ 8a = 4
- Divide both sides by 8
∴ a = 0.5
- Substitute value of a in equation (1) or to to find b
∵ 4(0.5) + 2b = 2
∴ 2 + 2b = 2
- Subtract 2 from both sides
∴ 2b = 0
- Divide both sides by 2
∴ b = 0
Substitute the values of a and b in the function model
∴ y = 0.5x² + (0)x - 8
∴ y = 0.5x² - 8
∵ y represents the depth from level ground
∵ The vertex of the function model is (h , k)
∴ The deep of the hole at ground level is the value of k
∵
∴
∴ h = 0
∵ k is the value of y when x = h
- From the table at x = 0 ⇒ y = -8
∴ k = -8
- Ignore the sign (-) because the k represents the depth of the
hole in feet
∴ The deep of the hole at ground level is 8 feet
The hole is 8 feet deep at ground level
Learn more:
You can learn more about the quadratic function in brainly.com/question/1332667
#LearnwithBrainly
To solve this problem, we have to find the net displacement and the net force and the multiply the dot product together and get the work done.
The work done on moving the object is 27ft*lbs
<h3>Work done in moving the object from point A to point B</h3>To find the work done on this object, let's find the net force on the object.
Data;
- force = 4lb
- direction = 4, -2
- displacement = 7ft
- direction = (0, 4) to (5,1)
The unit vector of the force is
The net force acting on the object is
The displacement on the object is 7ft through (0,4) to (5, -1)
The unit vector on displacement is
The net displacement will be
The work done will be F.d
The work done on moving the object is 27ft*lbs
Learn more on work done on an object here;
#SPJ1