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White raven [17]
3 years ago
8

Solve the given differential equation by using an appropriate substitution. The DE is of the form dy/dx = f(Ax + By + C), which

is given in (5) of Section 2.5. dy/dx = tan2(x + y)
Mathematics
1 answer:
pashok25 [27]3 years ago
8 0

\dfrac{\mathrm dy}{\mathrm dx}=\tan^2(x+y)

Let v=x+y, so that \frac{\mathrm dv}{\mathrm dx}=1+\frac{\mathrm dy}{\mathrm dx}:

\dfrac{\mathrm dv}{\mathrm dx}-1=\tan^2v

Recall that \tan^2v+1=\sec^2v:

\dfrac{\mathrm dv}{\mathrm dx}=\sec^2v

Separate the variables and integrate both sides:

\cos^2v\,\mathrm dv=\mathrm dx

\dfrac v2+\dfrac{\sin(2v)}4=x+C

Solve in terms of y:

\dfrac{x+y}2+\dfrac{\sin(2x+2y)}4=x+C

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In parallelogram ABCD, DB =28 cm. AN and CM are perpendicular to BD. AN = CM =10 cm. Find the area of the parallelogram.
tatiyna

Answer: 280 cm

Step-by-step explanation:

The base of each of the congruent triangles ABD and CBD is BD= 28 cm. The height of each is the perpendicular 10cm.

A=(2)(bh/2) works out to A= bh since the 2/2 cancel

So 10cm × 28cm = 280cm²

4 0
3 years ago
If Samantha can pay off her loan in 36 months at a 10% interest rate rather than in 48 months at a 12% interest rate, how much m
Ymorist [56]
Hi there
The simple interest formula is
I=prt
I interest changes
P amount of the loan 6000
R interest rate
T time( number of months/12 months)

The interest in 36 months at a 10%
I=6,000×0.1×(36÷12)=1,800
The interest in 48 months at a 12%
6,000×0.12×(48÷12)=2,880
she will save
2,880−1,800=1,080

Good luck!
7 0
3 years ago
30 red marbles is 40% of ____ marbles.
g100num [7]
Answer - 75

Sorry if it is wrong
7 0
3 years ago
The point (2, -1) is on the line 2x + y = 5.
malfutka [58]

Answer:

No

Step-by-step explanation:

Substitute by x = 2 and y = - 1

You will get 2*2 + (-1) = 3 not 5

Then it doesn't lie

3 0
3 years ago
PLEASE HELP ASAP<br> will mark brainliest <br><br> also, ignore what i already put
madam [21]

Answer:

-2x^2-11x^3

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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