For implicit differentiation, you are using the chain rule
![f'(x) = g'(u(x))* \frac{du}{dx}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20g%27%28u%28x%29%29%2A%20%5Cfrac%7Bdu%7D%7Bdx%7D)
Except u(x) = y, So after every "y" term is differentiated it will be multiplied by dy/dx.
17)
![y^3 +4 = 3x \\ 3y^2 \frac{dy}{dx} +0 = 3](https://tex.z-dn.net/?f=y%5E3%20%2B4%20%3D%203x%20%5C%5C%203y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2B0%20%3D%203)
Then you solve for dy/dx as if its a variable.
![\frac{dy}{dx} = \frac{3}{3y^2} = \frac{1}{y^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B3%7D%7B3y%5E2%7D%20%3D%20%5Cfrac%7B1%7D%7By%5E2%7D%20)
18) Here lets review product rule:
![(fg)' = f'g + fg'](https://tex.z-dn.net/?f=%28fg%29%27%20%3D%20f%27g%20%2B%20fg%27)
Take derivative of each term
![2x^2 = -3y^3 +3x^2y^3 \\ 4x = -9y^2 \frac{dy}{dx} + (6x)(y^3) + (3x^2)(3y^2 \frac{dy}{dx}) \\ 4x = -9y^2 \frac{dy}{dx} +6xy^3 +9x^2y^2 \frac{dy}{dx}](https://tex.z-dn.net/?f=2x%5E2%20%3D%20-3y%5E3%20%2B3x%5E2y%5E3%20%20%5C%5C%204x%20%3D%20-9y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2B%20%286x%29%28y%5E3%29%20%2B%20%283x%5E2%29%283y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%20%20%5C%5C%204x%20%3D%20-9y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2B6xy%5E3%20%2B9x%5E2y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D)
Solve for dy/dx using factoring:
Answer:
The slope is $0.35/min and it gives the cost per minute of the phone used.
Step-by-step explanation:
We can model this situation with a linear equation of the form
![y =mx+b](https://tex.z-dn.net/?f=y%20%3Dmx%2Bb)
where
is monthly cost,
is the number of minutes,
is the flat monthly fee, and
is the slope of the equation, or in our case, the amount of money charged per minute.
The slope
is
![m= \dfrac{\$372.5-\$131}{990min-300min}](https://tex.z-dn.net/?f=m%3D%20%5Cdfrac%7B%5C%24372.5-%5C%24131%7D%7B990min-300min%7D)
,
in other words, the phone company charges $0.5 per minute.
With the slope in hand, the linear equation becomes
,
and we can find the monthly fee
from that fact that for 300 minutes the cost is $131:
![\$131 = 0.35(300min) +b](https://tex.z-dn.net/?f=%5C%24131%20%3D%200.35%28300min%29%20%2Bb)
.
Therefore,
![y = 0.35x+26](https://tex.z-dn.net/?f=y%20%3D%200.35x%2B26)
where the slope if the equation give the cost per minute of the phone used.
Dawn has to pay 10,990 for her college dorm room and tuition each year. About how much money does dawn spend the first 2 years of college
Answer: The amount of money Dawn has to pay for 1 year ![= 10,990](https://tex.z-dn.net/?f=%3D%2010%2C990)
Therefore, the amount of money Dawn has to pay for first 2 years of college is:
![2 \times 10,990 = 21,980](https://tex.z-dn.net/?f=2%20%5Ctimes%2010%2C990%20%3D%2021%2C980)
Respuesta:
Los 47.85m
Explicación paso a paso:
Altura máxima = u²sin²Ф / 2g
Dado
velocidad u = 40 m / s
Ф = 50 °
g = 9,81 m / s²
Sustituir'
H = 40²sin²50 / 2 (9,81)
H = 1600 (0,7660) ² / 19,62
H = 1600 (0,5868) /19,62
H = 938,8096 / 19,62
H = 47,85 m
Por lo tanto, la altura máxima es de 47,85 m.
Answer:
true
Step-by-step explanation:
because the ratios are both 60 miles in 1 hour