{:[d=sqrt((-11-(-2)^(2)+(10-7)^(2):})],[d=]:}

Use Distance Formula: Use the distance formula to find the distance between two points in a plane. The distance formula is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.Substitute Given Points: Substitute the given points $(-2, 7)$ and $(-11, 10)$ into the distance formula. Let $(-2, 7)$ be $(x_1, y_1)$ and $(-11, 10)$ be $(x_2, y_2)$. Then we have: \[ d = \sqrt{((-11) - (-2))^2 + ((10) - (7))^2} \]Simplify Expression: Simplify the expression inside the square root. \[ d = \sqrt{(-11 + 2)^2 + (10 - 7)^2} \] \[ d = \sqrt{(-9)^2 + (3)^2} \] \[ d = \sqrt{81 + 9} \]Find Distance: Add the values inside the square root and then take the square root to find the distance. \[ d = \sqrt{90} \] \[ d = 3\sqrt{10} \] (since $90 = 9 \times 10$ and $\sqrt{9} = 3$)

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Math Problems

Calculus

Find indefinite integrals using the substitution

Full solution

\begin{array}{c}d=\sqrt{\left(-11-(-2)^{2}+(10-7)^{2}\right.} \\ d=\end{array}

Use Distance Formula: Use the distance formula to find the distance between two points in a plane. The distance formula is given by: $\newline$ $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ $\newline$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
Substitute Given Points: Substitute the given points $(-2, 7)$ and $(-11, 10)$ into the distance formula. Let $(-2, 7)$ be $(x_1, y_1)$ and $(-11, 10)$ be $(x_2, y_2)$ . Then we have: $\newline$ $d = \sqrt{((-11) - (-2))^2 + ((10) - (7))^2}$
Simplify Expression: Simplify the expression inside the square root. $\newline$ $d = \sqrt{(-11 + 2)^2 + (10 - 7)^2}$ $\newline$ $d = \sqrt{(-9)^2 + (3)^2}$ $\newline$ $d = \sqrt{81 + 9}$
Find Distance: Add the values inside the square root and then take the square root to find the distance. $\newline$ $d = \sqrt{90}$ $\newline$ $d = 3\sqrt{10}$ (since $90 = 9 \times 10$ and $\sqrt{9} = 3$ )