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2 years ago

Salma pumped 49 gallons of water out of her pool. This was done over a period of 7 minutes

1 answer:

3 0

7 gallons for minute because 49 divided by 7 (which is the mins) would be 7. Leading to the answer of ) gallons per minute

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

How many one-third cubes are needed to fill the gap in the prism shown below?

attashe74 [19]

Answer:

The answer is 16 I've seen this before so I would know. and your welcome

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Julie gives 7 pieces of candy to each of her friends. If Julie gives all of her candy away, which amount of candy could have bee

True [87]

To find the answer to this problem, you just need to figure out which total amount of candy is divisible by 7.

161/7=23
162/7=23.1428571429
145/7=20.7142857143
128/7=18.2857142857

Obviously, Julie cannot give a fraction of an amount of candy to someone. So that rules out that she had 162, 145, or 128 pieces of candy.

The only amount of candies that Julie could have that is divisible by 7 is 161 candies, which means that 161 is your answer.

5 0

3 years ago

Read 2 more answers

What is the exact area of a circle having diameter 3 in.?

boyakko [2]

Answer:

2.25π square inches

Step-by-step explanation:

Area = π $r^{2}$