Consider the curve given by the equation 4x^(2)+48 x+9y^(2)-36 y=-144". " It can be shown that (dy)/(dx)=(4(x+6))/(9(2-y))". " Find the x-coordinate of the point where the line tangent to the curve is the x-axis. x=

Find Tangent Line Slope: The slope of the tangent line to the curve at any point is given by the derivative (dy)/(dx). A horizontal line has a slope of 0. Therefore, we need to find the x-coordinate where (dy)/(dx) = 0.Set Derivative to 0: We are given that (dy)/(dx) = (4(x+6))/(9(2-y)). To find where the tangent line is horizontal, we set (dy)/(dx) to 0 and solve for x. 0 = (4(x+6))/(9(2-y))Solve for x: Since the fraction equals zero, the numerator must be zero (as long as the denominator is not zero). Therefore, we set the numerator equal to zero and solve for x. 4(x+6) = 0Final Solution: Solving for x gives us: x + 6 = 0 x = -6

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Consider the curve given by the equation

4x^(2)+48 x+9y^(2)-36 y=-144". "
It can be shown that

(dy)/(dx)=(4(x+6))/(9(2-y))". "
Find the
x-coordinate of the point where the line tangent to the curve is the
x-axis.

x=

Consider the curve given by the equation $4 x^{2}+48 x+9 y^{2}-36 y=-144 \text {. }$ It can be shown that $\frac{d y}{d x}=\frac{4(x+6)}{9(2-y)} \text {. }$ $\newline$ Find the $x$ -coordinate of the point where the line tangent to the curve is the $x$ -axis. $\newline$ $x=$

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Algebra 2

Write equations of cosine functions using properties

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Q. Consider the curve given by the equation

4 x^{2}+48 x+9 y^{2}-36 y=-144 \text {. }

It can be shown that

\frac{d y}{d x}=\frac{4(x+6)}{9(2-y)} \text {. }

\newline

Find the

x

-coordinate of the point where the line tangent to the curve is the

x

-axis.

\newline

x=

Find Tangent Line Slope: The slope of the tangent line to the curve at any point is given by the derivative $(dy)/(dx)$ . A horizontal line has a slope of $0$ . Therefore, we need to find the $x$ -coordinate where $(dy)/(dx) = 0$ .
Set Derivative to $0$ : We are given that $(\frac{dy}{dx}) = \frac{4(x+6)}{9(2-y)}$ . To find where the tangent line is horizontal, we set $(\frac{dy}{dx})$ to $0$ and solve for $x$ . $0 = \frac{4(x+6)}{9(2-y)}$
Solve for x: Since the fraction equals zero, the numerator must be zero (as long as the denominator is not zero). Therefore, we set the numerator equal to zero and solve for x. $\newline$ $4(x+6) = 0$
Final Solution: Solving for $x$ gives us: $\newline$ $x + 6 = 0$ $\newline$ $x = -6$