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3 years ago

PLEASE HELP MEEEEE!!

Mathematics

1 answer:

vovangra [49]3 years ago

7 0

It appears you are doing well. You have already gotten the eighth answer! If you need any other help you can ask me.

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Determine whether the equation is exact. If it is, then solve it. e Superscript t Baseline (7 y minus 3 t )dt plus (2 plus 7 e

umka21 [38]

Answer:

$F(t,y)=(2+7e^t)y+3(1-t)e^t +C$

Step-by-step explanation:

You have the following differential equation:

$e^t(7y-3t)dt+(2+7e^t)dy=0$

This equation can be written as:

$Mdt+Ndy=0$

where

$M=e^t(7y-3t)\\\\N=(2+7e^t)$

If the differential equation is exact, it is necessary the following:

$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial t}$

Then, you evaluate the partial derivatives:

$\frac{\partial M}{\partial y}=\frac{\partial}{\partial t}e^t(7y-3t)\\\\\frac{\partial M}{\partial t}=7e^t\\\\\frac{\partial N}{\partial t}=\frac{\partial}{\partial t}(2+7e^t)\\\\\frac{\partial N}{\partial t}=7e^t\\\\\frac{\partial M}{\partial t} = \frac{\partial N}{\partial t}$

The partial derivatives are equal, then, the differential equation is exact.

In order to obtain the solution of the equation you first integrate M or N:

$F(t,y)=\int N \partial y = (2 +7e^t)y+g(t)$ (1)

Next, you derive the last equation respect to t:

$\frac{\partial F(t,y)}{\partial t}=7ye^t+g'(t)$

however, the last derivative must be equal to M. From there you can calculate g(t):

$\frac{\partial F(t,y)}{\partial t}=M=(7y-3t)e^t=7ye^t+g'(t)\\\\g'(t)=-3te^t\\\\g(t)=-3\int te^tdt=-3[te^t-\int e^tdt]=-3[te^t-e^t]$

Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:

$F(t,y)=(2+7e^t)y+3(1-t)e^t +C$

where C is the constant of integration

8 0

3 years ago

At a store clearance, a woman spent less than $200 on shirts that were labeled $15 each. How many shirts did she buy? Identify t

Roman55 [17]

divide 200 by 15

200/15 = 13.33

so she bought 13 shirts

13 x 15 = 195

8 0

3 years ago

Convert 2.94 ×10^7 to standard notation

ratelena [41]

You just convert 10 decimal places to the right, adding zeros when the points after the decimal end, leaving you with 29400000.

5 0

3 years ago

Robert wants to install windows in a bus barn to improve the airflow in the summer months. If Robert makes his own screens, he c

navik [9.2K]

Well since the area of one screen in 11 ft2 you would times it by 4 which is 44
and 5 which is 55 twice so its actually 154 ft2
hope this helps
(If I got it wrong plz tell me, I think I got it right, but just in case)

7 0

3 years ago

Due in an hour pls help me

kaheart [24]

1 over 91^1/12 - I used a surds calculator online! Hope this helps. Please mark as brainliest if this answer is correct

6 0

2 years ago

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