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3 years ago

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If fx) = Ix| + 9 and g(x) = -6, which describes the value of (f+ g(X)? O (f+g)(x) 2 3 for all values of x O(f+ g)x) s 3 for all

values of x O O (f+ 9g)(x) < 6 for all values of x Of+g) (x) 2 6 for all values of x

1 answer:

vaieri [72.5K]3 years ago

3 0

You'll need to write your question a bit clearer. It's difficult to understand because a lot of it seems jumbled together.

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Find an explicit solution of the given initial-value problem. (1 + x4) dy + x(1 + 4y2) dx = 0, y(1) = 0

MissTica

Answer:

a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4

Step-by-step explanation:

for the equation

(1 + x⁴) dy + x*(1 + 4y²) dx = 0

(1 + x⁴) dy = - x*(1 + 4y²) dx

[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx

∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx

now to solve each integral

I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁

I₂= ∫[-x/(1 + x⁴)] dx

for u= x² → du=x*dx

I₂= ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ = - tan⁻¹ (x²) +C₂

then

1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C

for y(x=1) = 0

1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C

since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for π*N , we will choose for simplicity N=0 . hen an explicit solution would be

1/2 * 0 = - π/4 + C

C= π/4

therefore

1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4

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yan [13]

Answer:

I inserted your equation into desmos calculator

, Hope this helps :)

Have a great day!!

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The ANGLE BISECTOR mentioned in the problem is simply just a line that separates an angle in half.

Meaning if it bisects ∠SUT which is 34. It just means that it divides the angle 34 into 2 equal parts.

Therefore ∠1 is just one-half of the ∠SUT.

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