Let x and y be functions of t with y = 7x. If dx/dt = 2, what is dy/dt when x = π /2? Write an exact, simplified answer. ______

Identify Relationship: Identify the relationship between y and x. Given y = 7x, differentiate both sides with respect to t to find dy/dt.Differentiate with Respect: Differentiate y = 7x with respect to t. Using the chain rule, dy/dt = 7 * dx/dt.Substitute Value of dx/dt: Substitute the value of dx/dt. Given dx/dt = 2, substitute into dy/dt = 7 * dx/dt to get dy/dt = 7 * 2 = 14.Check Value of x: Check the value of x. Since x = π/2 does not affect the differentiation directly and we are given dx/dt, no need to use this value in our differentiation.

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Let $x$ and $y$ be functions of $t$ with $y = 7x$ . If $\frac{dx}{dt} = 2$ , what is $\frac{dy}{dt}$ when $x = \frac{\pi}{2}$ ? $\newline$ Write an exact, simplified answer.

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Algebra 2

Write and solve direct variation equations

Full solution

Q. Let

x

and

y

be functions of

t

with

y = 7x

. If

\frac{dx}{dt} = 2

, what is

\frac{dy}{dt}

when

x = \frac{\pi}{2}

\newline

Write an exact, simplified answer.

Identify Relationship: Identify the relationship between $y$ and $x$ . Given $y = 7x$ , differentiate both sides with respect to $t$ to find $\frac{dy}{dt}$ .
Differentiate with Respect: Differentiate $y = 7x$ with respect to $t$ . Using the chain rule, $\frac{dy}{dt} = 7 \cdot \frac{dx}{dt}$ .
Substitute Value of $dx/dt$ : Substitute the value of $dx/dt$ . Given $dx/dt = 2$ , substitute into $dy/dt = 7 \times dx/dt$ to get $dy/dt = 7 \times 2 = 14$ .
Check Value of x: Check the value of $x$ . Since $x = \frac{\pi}{2}$ does not affect the differentiation directly and we are given $\frac{dx}{dt}$ , no need to use this value in our differentiation.