Answer:
31.41592...
Step-by-step explanation:
If the radius of the circle is 10 inches, the circle's circumference is 31.4 because you calculate circumference as follows:
x = r * pi (3.1415926535)
<h3>
Answer: C = 1.06P</h3>
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Explanation:
The sales tax is 6% of the price P
6% of P = 0.06P
Add on the original cost P to get P+0.06P = (1+0.06)P = 1.06P
The 1.06 indicates the final after tax cost is 106% of the original price.
You can think of it like 100% + 6% = 106% = 1.06
So that's how we end up with C = 1.06P
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An example using actual numbers:
Let P = $100 be the initial cost before tax
6% of P = 0.06*P = 0.06*100 = 6 dollars is the tax
100+6 = 106 is the final cost
Note how C = 1.06P = 1.06*100 = 106
I think it is A because the numbers decreased
Answer:
The bird will be at a ground distance of 10.04 units away.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
![f(x) = ax^{2} + bx + c](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ax%5E%7B2%7D%20%2B%20bx%20%2B%20c)
It's vertex is the point ![(x_{v}, y_{v})](https://tex.z-dn.net/?f=%28x_%7Bv%7D%2C%20y_%7Bv%7D%29)
In which
![x_{v} = -\frac{b}{2a}](https://tex.z-dn.net/?f=x_%7Bv%7D%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
![y_{v} = -\frac{\Delta}{4a}](https://tex.z-dn.net/?f=y_%7Bv%7D%20%3D%20-%5Cfrac%7B%5CDelta%7D%7B4a%7D)
Where
![\Delta = b^2-4ac](https://tex.z-dn.net/?f=%5CDelta%20%3D%20b%5E2-4ac)
If a<0, the vertex is a maximum point, that is, the maximum value happens at
, and it's value is
.
Equation for the height:
The height of the bird after x seconds is given by:
![h(x) = -0.114x^2 + 2.29x + 3.5](https://tex.z-dn.net/?f=h%28x%29%20%3D%20-0.114x%5E2%20%2B%202.29x%20%2B%203.5)
Which is a quadratic equation with
.
When the bird is at its highest?
Quadratic equation with
, and thus, at the vertex. The ground distance is the x-value of the vertex. Thus
![x_{v} = -\frac{b}{2a} = -\frac{2.29}{2(-0.114)} = 10.04](https://tex.z-dn.net/?f=x_%7Bv%7D%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D%20%3D%20-%5Cfrac%7B2.29%7D%7B2%28-0.114%29%7D%20%3D%2010.04)
The bird will be at a ground distance of 10.04 units away.