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1 year ago

Which function(s) are linear? Select all that apply.

Mathematics

1 answer:

Georgia [21]1 year ago

6 0

Answer:

3/5 x +1 and 7.5 x -7

Step-by-step explanation:

any equation in the form y= mx+b is linear the other 2 in this question are not in this form thus they are not linear

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Solve the following differential equation: (1− 5 y +x) dy/dx +y= 5/x −1 .<br><br> C=

Ganezh [65]

Answer:

$y(1+x)+x-5\ln xy=C$

Step-by-step explanation:

Consider the given differential equation is

$(1-\frac{5}{y}+x)\frac{dy}{dx}+y=\frac{5}{x}-1$

$(1-\frac{5}{y}+x)\frac{dy}{dx}=\frac{5}{x}-1-y$

$(1-\frac{5}{y}+x)dy=(\frac{5}{x}-1-y)dx$

Taking all variables on right sides.

$(1-\frac{5}{y}+x)dy-(\frac{5}{x}-1-y)dx=0$

$(-\frac{5}{x}+1+y)dx+(1-\frac{5}{y}+x)dy=0$

Let as assume,

$M=-\frac{5}{x}+1+y$ and $N=1-\frac{5}{y}+x$

Find partial derivatives $\frac{\partial M}{\partial y}$ and $\frac{\partial N}{\partial x}$

$\frac{\partial M}{\partial y}=1$ and $\frac{\partial N}{\partial x}=1$

Since $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$ , therefore the given differential equation is exact.

The solution of the exact differential equation is

$\int Mdx+\int N(\text{without x)}dy=C$

$\int (-\frac{5}{x}+1+y)dx+\int (1-\frac{5}{y})dy=C$

$yx-5\ln x+x+y-5\ln y=C$

$y+x+xy-5\ln x-5\ln y=C$

$y(1+x)+x-5(\ln x+\ln y)=C$

$y(1+x)+x-5\ln xy=C$

7 0

3 years ago

a large container holds 4 gallons of chocolate milk that has to be poured into bottes. each bottle holds 2 pints.

timama [110]

U can pour it into 16 bottes

5 0

3 years ago

Read 2 more answers

Can anyone explain what Literal Equations are? PLZ.

melisa1 [442]

Answer:

A literal equation is an equation that consists of multiple variables or letters.

A linear equation is an equation that consists of one variable

Step-by-step explanation:

Literal EX:

a = 1/2h(a + b)

ax + b = c

u = ak/b

Linear EX:

5(3a + 8) = 12a

4a = 8

11(3a - 18) = 12a

4 0

3 years ago

Read 2 more answers

How do you write 43% as a decimal?

vesna_86 [32]

0.43 abababababababab

4 0

2 years ago

Read 2 more answers

James puts $3,500 into a savings account that earns 2.5% simple interest. He does not touch that account for 3 years. What would

miskamm [114]

Given :

James puts $3,500 into a savings account that earns 2.5% simple interest.

He does not touch that account for 3 years.

To Find :

The new balance of the account be after 3 years.

Solution :

Interest on $3500 after 3 years is :

$I = \dfrac{P_o\times r\times t}{100}\\\\I = \dfrac{3500\times 2.5\times 3}{100}\\\\I = \$262.5$

So, new balance of the account after 3 years is $( 3500+262.5 ) = $3762.5 .

Hence, this is the required solution.

3 0

3 years ago