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DedPeter [7]
3 years ago
6

Solve the equation (1 + x²)dy +xydx= 0​

Mathematics
1 answer:
Tatiana [17]3 years ago
7 0

Answer:

y=\frac{c}{\sqrt[]{x^2+1} }

Step-by-step explanation:

(1 + x²)dy +xydx= 0​

(1+x^2)dy=-xydx\\\frac{1}{y}dy=\frac{-x}{x^2+1}dx\\

Integrate both side

lny=-\frac{1}{2} ln(x^2+1)+c\\y=\frac{c}{\sqrt[]{x^2+1} }

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cluponka [151]

Answer:

47.5

Step-by-step explanation:

4 0
3 years ago
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There are nine empty seats in a theater, and six customers need to find places to sit. How many different ways can these six sea
dybincka [34]

Answer: 60480

Step-by-step explanation:

Given : The number of empty seats in a theater = 9

The number of customers need to find places to sit =6

Since order matters here, so we use permutations

The permutations of n things taking r at a time is given by :-

^nP_r=\dfrac{n!}{(n-r)!}

Then, the number of ways to arrange 6 seat in 9 seats :-

^9P_6=\dfrac{9!}{(9-6)!}=\dfrac{9\times8\times7\times6\times5\times4\times3!}{3!}\\\\=60480

Hence, the number of ways to arrange 6 seat in 9 seats = 60480

3 0
3 years ago
Which is the area of a circle with diameter 6.4 inches? use 3.14
Elodia [21]
The correct answer is 32.15 inches
3 0
3 years ago
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shtirl [24]

Answer:

y = 3

x = 1

y = 1.5

x = 2

Step-by-step explanation:

For the first x point, look at the graph where x is 0. When x is 0, y is 3. So the first one is 3. For the second one, there is a point on the graph where y is 4. Where y is 4, x is 1, so you the second answer is 1. For the third one, find the y point where x is -1. At the x value, -1, y is 1.5. For the last one, where y is 5, x is 2.

8 0
2 years ago
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Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?
Flura [38]

Answer:

The value to the given expression is 8

Therefore \left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8

Step-by-step explanation:

Given expression is (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed

Given expression can be written as below

\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3

To find the value of the given expression:

\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=\frac{((10^4)(5^2))^3}{((10^3)(5^3))^3}

( By using the property ((\frac{a}{b})^m=\frac{a^m}{b^m} )

=\frac{(10^4)^3(5^2)^3}{(10^3)^3(5^3)^3}

( By using the property (ab)^m=a^mb^m )

=\frac{(10^{12})(5^6)}{(10^9)(5^9)}

( By using the property (a^m)^n=a^{mn} )

=(10^{12})(5^6)(10^{-9})(5^{-9})

( By using the property \frac{1}{a^m}=a^{-m} )

=(10^{12-9})(5^{6-9}) (By using the property a^m.b^n=a^{m+n} )

=(10^3)(5^{-3})

=\frac{10^3}{5^3} ( By using the property a^{-m}=\frac{1}{a^m} )

=\frac{1000}{125}

=8

Therefore \left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8

Therefore the value to the given expression is 8

3 0
3 years ago
Read 2 more answers
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