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3 years ago

Is this question rlly that easy?

Mathematics

2 answers:

AleksAgata [21]3 years ago

4 0

Answer:

yes

Step-by-step explanation:

PtichkaEL [24]3 years ago

4 0

Answer:

yes

Step-by-step explanation:

lol

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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

4 years ago

What is the midpoint of BC

Alex_Xolod [135]

Answer:

(5, 6 )

Step-by-step explanation:

Using the midpoint formula

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

with (x₁, y₁ ) = B(2, 1) and (x₂, y₂ ) = C(8, 11)

midpoint = [ 0.5(2 + 8), 0.5(1 + 11) ] = (5, 6 )

5 0

3 years ago

. The ratio of the area of circle A to the area of circle B is 12/5. What is the ratio of their circumferences?

N76 [4]

Answer:

1.5

Step-by-step explanation:

a : b = 1 : 12/5

Area of a circle = πr²

Where : = π = pi = 22/7

R = radius

Let the radius of circle a = 1

Area of circle A = 1π

Radius of circle A = square root of 12/5 = 1.5

The circumference of a circle = 2nr

n = 3.14

circumference of circle A = 2 x n x 1 = 2n

circumference of circle B = 2 x n x 1.5 = 3n

ratio of circumference = 3n / 2n = 1.5

4 0

3 years ago

A composite figure is formed by combining a square and a triangle. Its total area is 32.5ft sqaured. The area of the triangle is

NeTakaya

Answer:

The length of each side of square is 5ft.

Step-by-step explanation:

Given:

A composite figure is formed by combining a square and a triangle. Its total area is 32.5ft squared.

The area of the triangle is 7.5ft squared.

Now, to find the length of each side of square.

Now, we need to get the area of the square first:

Area of combined figure - area of triangle = area of square.

32.5 ft squared - 7.5 ft squared = 25 ft squared.

So, area of square = 25 ft squared.

Now, by putting the formula for getting the length of each side:

Let the side = a.

Area of square = 25 ft squared

Area of square = a²

$25 =a^{2}$

Using square root both sides we get:

$5=a$

So, the side = 5 ft.

Therefore, the length of each side of square is 5ft.

3 0

3 years ago

Solve: 12 + (-13) - 12 - 5 A: 14 B: -12 C: -18 D: 45

Drupady [299]

Answer:

-18

(i think this is right, sorry if i'm wrong)

6 0

3 years ago