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 triangle is a right triangle.
Step-by-step explanation:
Since The Pythagorean Theorem only works on right triangles, we can use this knowledge to prove whether this triangle is right:
Therefore, the triangle is right.
Answer:
The number is 48
Step-by-step explanation:
First, let's call the number we are looking for n.
We can then write "two-thirds of the number" as 2/3n
We can also write "one-half of a number" as 1/2n
Finally, we are told 1/2n is the same as 2/3n −8 or: 1/2n = 23n −8
We can now solve for n: 1/2n − 2/3n = 2/3n −8 − 2/3n 1/2n − 2/3n = −8We next need to get the fractions over common denominators, in this case, 6 by multiplying each fraction by the necessary for of 1: (3/3) 1/2n − (2/2) 2/3n = −8 3/6n − 4/6n = −8 − 1/6n = −8.
We can finally solve for n by multiplying by -6 to isolate n −6 ⋅(−1/6)n = −8⋅ − 6
1n = 48
n =48
Answer:
96 people were teenagers
Step-by-step explanation:
2400*4%= 96
Answer:
the answer and steps are pictured above
