1.27, think money.
100 pennies is $1
27 cents left
$1.27
Step 1:
Start by putting
![\frac{d}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%20)
in front of each term
![\frac{d}{dx}[y cos x]= \frac{d}{dx}[5x^2]+ \frac{d}{dx}[ 3y^2]](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5By%20cos%20x%5D%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B5x%5E2%5D%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%203y%5E2%5D)
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Step 2:
Deal with the terms in 'x' and the constant terms
![\frac{d}{dx}[ycosx]= 10x+ \frac{d}{dx} [3y^2]](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bycosx%5D%3D%2010x%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5B3y%5E2%5D%20%20)
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Step 3:
Use the chain rule for the terms in 'y'
![\frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bycosx%5D%3D10x%2B6y%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20)
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Step 4:
Use the product rule on the term in 'x' and 'y'
![(y) \frac{d}{dx} cos x+(cos x) \frac{d}{dx}y =10x+6y \frac{dy}{dx} ](https://tex.z-dn.net/?f=%28y%29%20%5Cfrac%7Bd%7D%7Bdx%7D%20cos%20x%2B%28cos%20x%29%20%5Cfrac%7Bd%7D%7Bdx%7Dy%20%3D10x%2B6y%20%5Cfrac%7Bdy%7D%7Bdx%7D%0A)
![y(-siny)+(cosx) \frac{dy}{dx} =10x+6y \frac{dy}{dx}](https://tex.z-dn.net/?f=y%28-siny%29%2B%28cosx%29%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D10x%2B6y%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
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Step 5:
Rearrange to make
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
the subject
![-y sin(y)+cos(x) \frac{dy}{dx} =10x+6y \frac{dy}{dx}](https://tex.z-dn.net/?f=-y%20sin%28y%29%2Bcos%28x%29%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D10x%2B6y%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
![cos(x) \frac{dy}{dx}-6y \frac{dy}{dx}=10x+y sin(y)](https://tex.z-dn.net/?f=cos%28x%29%20%20%5Cfrac%7Bdy%7D%7Bdx%7D-6y%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D10x%2By%20sin%28y%29%20%20)
![[cos(x) - 6y] \frac{dy}{dx}=10x + y sin(y)](https://tex.z-dn.net/?f=%5Bcos%28x%29%20-%206y%5D%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D10x%20%2B%20y%20sin%28y%29%20)
![\frac{dy}{dx}= \frac{10x+ysin(y)}{cos(x)-6y}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B10x%2Bysin%28y%29%7D%7Bcos%28x%29-6y%7D%20%20)
⇒ Final Answer
Answer:
$58.25
Step-by-step explanation:
142.20 - 24.50 = 117.50
117.50 / 2 = 58.25
Perimeter of a triangle = all 3 sides added together
x + (x - 4) + (x - 4) = 19
3x - 8 = 19
3x = 19 + 8
3x = 27
x = 27/3
x = 9 <==
Answer:
t3 = 8, t5 = 14
Step-by-step explanation:
t3 = 2 + (3-1) × 3
t3 = 2 + (2) × 3
t3 = 2 + 6
t3 = 8
t5 = 2 + (5-1) × 3
t5 = 2 + (4) × 3
t5 = 2 + 12
t5 = 14