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Morehollie9428
20.10.2020 •
Mathematics
Can 7:13 be simplified
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Ответ:
No it's already in its simplest form
Step-by-step explanation:
Ответ:
A) h(2.4) is 2.53
B) The numerical value of the vertical intercept is 5.8
C) The numerical value of the vertex is![(\frac{60}{113},\frac{3439}{565})](/tpl/images/0265/4877/30fe0.png)
D) The shot put strike the ground at x = 2.98
Step-by-step explanation:
* Lets explain how to solve the problem
- The path of the longest shot put is modeled by
h(x)= -1.017x² + 1.08x + 5.8, where x is the horizontal distance from
start and h(x) is the height of the shot put above the ground
A)
- We need to find h(2.4), that means substitute x in the equation by 2.4
∵ h(x)= -1.017x² + 1.08x + 5.8
∵ x = 2.4
∴ h(2.4)= -1.017(2.4)² + 1.08(2.4) + 5.8 = 2.53
∴ h(2.4) = 2.53
* h(2.4) is 2.53
B)
- We need to find the numerical value of the vertical intercept
- That means the y-intercept of the graph of the path ⇒ h(0)
- To find the vertical intercept put x = 0 in the equation
∴ h(0) = 0 + 0 + 5.8
* The numerical value of the vertical intercept is 5.8
C)
- We need to find the numerical value of the vertex
∵ h(x)= -1.017x² + 1.08x + 5.8 is a quadratic function
∴ The coordinates of its vertex are (v , w), where v![\frac{-b}{2a}](/tpl/images/0265/4877/1510a.png)
and w = h(v), a is the coefficient of x² and b is the coefficient of x
∵ a = -1.017 and b = 1.08
∴ v =![\frac{-1.08}{2(-1.017)}=\frac{60}{113}](/tpl/images/0265/4877/0a921.png)
∵ w = f(v)
∴ w =![-1.017(\frac{60}{113})^{2}+1.08(\frac{60}{113}) + 5.8=\frac{3439}{565}](/tpl/images/0265/4877/89d9a.png)
* The numerical value of the vertex is![(\frac{60}{113},\frac{3439}{565})](/tpl/images/0265/4877/30fe0.png)
D)
- We need to find how far from start the shot put strike the ground
- That means h(x) = 0, because the height at the ground = 0
∴ -1.017x² + 1.08x + 5.8 = 0
- Use your calculator to find the value of x
∴ x = 2.977 and x = -1.915
- We will ignore the negative value of x because we need the final
put strike on the ground from the start
∴ x = 2.98
* The shot put strike the ground at x = 2.98