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natita [175]
2 years ago
10

Find the general solution of the given differential equation. cos^2(x)sin(x)dy/dx+(cos^3(x))y=1 g

Mathematics
1 answer:
eimsori [14]2 years ago
7 0

If the given differential equation is

\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1

then multiply both sides by \frac1{\cos^2(x)} :

\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)

The left side is the derivative of a product,

\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)

Integrate both sides with respect to x, recalling that \frac{d}{dx}\tan(x) = \sec^2(x) :

\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx

\sin(x) y = \tan(x) + C

Solve for y :

\boxed{y = \sec(x) + C \csc(x)}which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}.

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On a map, 1 centimeter represents a distance of 15 kilometers. How many kilometers are represented by 7 centimeters?
marishachu [46]

Answer:

105

Step-by-step explanation:

15 times 7 =105

5 0
2 years ago
Suppose you have three consecutive integers.The greatest of the three integers is twice as great as the sum of the first two.Wha
vredina [299]

Answer:

0, 1, 2

Step-by-step explanation:

So, since there are three consecutive integers, you have the equations

x, x+1, x+2 where x is the smallest number.

The greatest of the three integers= x+2

Finish setting up your equation;

2(x+x+1)=x+2

Combine like terms;

2(2x+1)=x+2

Distribute;

4x+2=x+2

3x=0

x=0

x+1=1

x+2=2

Hope this helps:) Have a good day!

8 0
3 years ago
A woman is randomly selected from the 18-24 age group. For women of this group, systolic blood pressures (in mm Hg) are normally
dybincka [34]

Answer:

0.0274

Step-by-step explanation:

The mean is \mu =114.8 and the standard deviation is \sigma =13.1.

Calculate

Z=\dfrac{X-\mu}{\sigma}

for X=140:

Z=\dfrac{140-114.8}{13.1}\approx 1.9237.

If X\sim N(114.8,\ 13.1), then Z\sim N(0,1)

and

Pr(X>140)=Pr(Z>1.9237).

Use table for normal distribution probabilities to get that

Pr(Z>1.9237)=1-Pr(Z\le 1.9237)=1-0.9726=0.0274.

7 0
3 years ago
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3 years ago
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igor_vitrenko [27]

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