Answer:
A)
B)
Step-by-step explanation:
<em>x</em> and <em>y</em> are differentiable functions of <em>t, </em>and we are given the equation:
First, let's differentiate both sides of the equation with respect to <em>t</em>. So:
![\displaystyle \frac{d}{dt}\left[xy\right]=\frac{d}{dt}[6]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bxy%5Cright%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6%5D)
By the Product Rule and rewriting:
![\displaystyle \frac{d}{dt}[x(t)]y+x\frac{d}{dt}[y(t)]=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Bx%28t%29%5Dy%2Bx%5Cfrac%7Bd%7D%7Bdt%7D%5By%28t%29%5D%3D0)
Therefore:
A)
We want to find dy/dt when <em>x</em> = 4 and dx/dt = 11.
Using our original equation, find <em>y</em> when <em>x</em> = 4:
Therefore:
Solve for dy/dt:
B)
We want to find dx/dt when <em>x</em> = 1 and dy/dt = -9.
Again, using our original equation, find <em>y</em> when <em>x</em> = 1:
Therefore:
Solve for dx/dt:
Answer:
The equation is y = 3/5x - 6
Step-by-step explanation:
First we have to find the slope of the line. In order to do so, solve the first equation for y.
3x - 5y = 7
-5y = -3x + 7
y = 3/5x + 7/-5
This gives us a slope of 3/5. Given that information, we now can plug the slope and point into point-slope form and get the final equation.
y - y1 = m(x - x1)
y - -6 = 3/5(x - 0)
y + 6 = 3/5x
y = 3/5x - 6
Answer:
3 1/5 minutes per meter
Step-by-step explanation:
To find the rate in minutes per meter, divide the number of minutes by the number of meters:
(2.4 min)/(0.75 m) = 3.2 min/m = 3 1/5 minutes per meter
Answer:
Step-by-step explanation: ion kno
The function is: f ( x ) = - x² + 60 x - 116 is in the form: f ( x ) = a x² + b x + c
Part A:
x = -b / 2 a = - 60 / ( - 2 ) = 30
Then we will charge it into the function:
f ( 30 ) = - 30² + 60 · 30 - 116 = - 900 +1,800 - 116 = 784
The vertex is ( 30, 784 ).
It means that the maximum profit is $784, when 30 windshields are repaired.
Part B:
x 1/2 = ( -60 +/- √(3600 - 464 )/ (- 2 ) = ( -60 +/- 56 ) / ( - 2 )
x 1 = 2, x 2 = 58
It means that a shop has to repair at least 2 windshields and not more than 58 windshields for making a profit.
