Question

point a has an x - coordinate of 7 and lies below the x - axis on a circle with a center at (0, 0) and a radius of 8. to the nearest tenth, what is the y - coordinate for point a? -4.0 -3.9 -3.8 -3.7

Explanation:

Step1: Recall the equation of a circle

The standard - form equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2+(y - k)^2=r^2$. Here, $h = 0$, $k = 0$, and $r = 8$, so the equation is $x^{2}+y^{2}=64$.

Step2: Substitute the x - coordinate

We know that $x = 7$. Substitute $x = 7$ into the equation $x^{2}+y^{2}=64$, we get $7^{2}+y^{2}=64$, which simplifies to $49 + y^{2}=64$.

Step3: Solve for $y^{2}$

Subtract 49 from both sides of the equation: $y^{2}=64 - 49=15$.

Step4: Solve for $y$

Take the square root of both sides: $y=\pm\sqrt{15}$. Since the point lies below the $x$ - axis, $y<0$, so $y =-\sqrt{15}\approx - 3.9$.

Answer:

-3.9