The sum of 7+14+21 + 150 terms

Mathematics

1 answer:

Genrish500 [490]2 years ago

5 0

192 I just calculated it

You might be interested in

Hi boys can you help me pls!!!!!!!

goblinko [34]

Answer: OPTION A.

Step-by-step explanation:

Given the following function:

$h(x)=-\frac{1}{4}x^2+\frac{1}{2}x+\frac{1}{2}$

You know that it represents the the height of the ball (in meters) when it is a distance "x" meters away from Rowan.

Since it is a Quadratic function its graph is parabola.

So, the maximum point of the graph modeling the height of the ball is the Vertex of the parabola.

You can find the x-coordinate of the Vertex with this formula:

$x=\frac{-b}{2a}$

In this case:

$a=-\frac{1}{4}\\\\b=\frac{1}{2}$

Then, substituting values, you get:

$x=\frac{-\frac{1}{2}}{(2)(-\frac{1}{4}))}\\\\x=1$

Finally, substitute the value of "x" into the function in order to get the y-coordinate of the Vertex:

$h(1)=y=-\frac{1}{4}(1)^2+\frac{1}{2}(1)+\frac{1}{2}\\\\y=0.75$

Therefore, you can conclude that:

<em> The maximum height of the ball is 0.75 of a meter, which occurs when it is approximately 1 meter away from Rowan.</em>

7 0

3 years ago

Rewrite as a simplified fraction 1.6 <-- repeating=?

Norma-Jean [14]

$1.6666...=1.\overline{6}=1.(6)\\\\x=1.6666...\ \ \ |multiply\ both\ sides\ by\ 10\\10x=16.6666...\\\\10x-x=16.6666...-1.6666...\\9x=15\ \ \ \ |divide\ both\ sides\ by\ 9\\\\x=\frac{15}{9}\\\\\boxed{x=1\frac{6}{9}}\\\\simplify\\\\x=1\frac{6:3}{9:3}=\boxed{1\frac{2}{3}}$