Question

1. solve these equations. if there is more than one solution, separate them with a comma.

a. \\(\sqrt{n + 2} - 4 = 0\\)
type the answer in the box below.
\\(n = \square\\)
b. \\(-4 = \sqrt3{m + 2}\\)
type the answer in the box below.
\\(m = \square\\)

1. the area of a circle is related to the radius by the equation \\(a = \pi \cdot r^2\\). if the area of a particular circle is 10 square meters, find the radius of this circle.

Explanation:

Step1: Isolate the square root

$\sqrt{n+2} = 4$

Step2: Square both sides

$(\sqrt{n+2})^2 = 4^2$
$n+2 = 16$

Step3: Solve for n

$n = 16 - 2$
$n = 14$

Step4: Isolate the cube root

$\sqrt[3]{m+2} = -4$

Step5: Cube both sides

$(\sqrt[3]{m+2})^3 = (-4)^3$
$m+2 = -64$

Step6: Solve for m

$m = -64 - 2$
$m = -66$

Step7: Substitute A into area formula

$10 = \pi r^2$

Step8: Isolate $r^2$

$r^2 = \frac{10}{\pi}$

Step9: Solve for radius r

$r = \sqrt{\frac{10}{\pi}}$

Answer:

1. a. $n=14$

b. $m=-66$

1. $r=\sqrt{\frac{10}{\pi}}$ meters