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Katyanochek1 [597]
3 years ago
11

Need help due in 25 minutes

Mathematics
1 answer:
masha68 [24]3 years ago
7 0

Answer:

Area = 400  Perimeter = 80

Step-by-step explanation:

aree = 400

side = sqrt of 400 = 20

perimeter = 4*20 = 80

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Definition. A shape that only has two dimensions (such as width and height) and no thickness. Squares, Circles, Triangles, Hexagon, Rhombus etc are two dimensional objects. Also known as "2D".

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Rectangular prism rectangular prism
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There are 5 black marbles, 17 blue marbles, 10 brown marbles, and 12 white marbles. What is the ratio of white marbles to all th
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12:44

Step-by-step explanation:

u would add all the marbles up and then put the white marble amount in front of a colon and then put the total marbles

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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

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C 495 i know its right.
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