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Eduardwww [97]
3 years ago
5

Find the solution of the differential equation that satisfies the given initial condition. (du)/(dt) = (2t + sec^2 t)/(2u), u(0)

= -1
Mathematics
1 answer:
Delicious77 [7]3 years ago
3 0
Ah okay so in differential equations you usually want the top variable isolated. To do this, multiply by dt and 2u and you get
2udu = 2t + { \sec(t) }^{2} dt
Now just integrate both sides. The integral of 2u with respect to u is u². The integral of (2t + sec²(t) with respect to t is t² + ∫sec²(t)dt. The last part is just tan(x) because d/dt(tan(t)) is sec²(t) so just integrating gets us back. Now we have
{u}^{2}   + c =  {t}^{2}  +  \tan(t)  + k
Where c and k are arbitrary constants. Subtracting c from k and you get
{u}^{2}  =  {t}^{2}  +  \tan(t)  + b
Where b is another constant. To find b, just plug in u(0) = -1 where u is -1 and t is 0. This becomes
1 =  \tan(0)  + b
tan(0) is 0 so b = 1. Take the plus or minus square root on both sides and you finally get
u =  \: { {t}^{2} }  +  \tan(t)  + 1
But Brainly didn't let me do but juat remember there is a plus or minus square root on the left.
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(Score for Question 3: ___ of 5 points) The measure of ∠2=8x+10 and the measure of ∠4=42+6x. Find the measure of ∠4. Show your w
Svetradugi [14.3K]

Answer:

∠4 = 78°, assuming out measurements have been taken in degrees.

Step-by-step explanation:

If ∠2 = 8x + 10 and

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We will assume that x in both cases is represented by the same number, therefore, we will first need to solve for x. We will do so by equating both angle measurement expressions.

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x = 16

Knowing x, we can solve for the measure of ∠4 by plugging in 16 for x

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4 0
3 years ago
Which is a true statement?
Shkiper50 [21]
A) -15 > -5 is false.
B) -4 > 0 is 0 < -4
C) -12 < -3 is always true. There are many solutions.
D) 2 < -5 is false.

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