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jeka94
3 years ago
7

Hi, can somoene please check why my solution and explain why I get the wrong answer.

Mathematics
1 answer:
trapecia [35]3 years ago
4 0

Answer:

a_n=(1-n)2^n+3^n

Step-by-step explanation:

You are correct down to the part where you add the partial results:

a_n=a_n^h+a_n^p=A3^n+B2^n-n2^n\\\text{Using the given starter values, we can find A, B:}\\a_0=2=A\\a_1=7=3A+2B+2\\\text{has solution A=1, B=1, so ...}\\\\a_n=3^n+2^n-n2^n

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3 years ago
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

5 0
3 years ago
A pharmacist wants to make 36ml of a 65% hydrogen peroxide solution. how many pls of 75% hydrogen peroxide must he mix with 57%
faltersainse [42]

Answer:

16 mls of the 75% solution and 20 mls of the 0.57% solution.

Step-by-step explanation:

Set up a system of equations:

Let x = volume of 75% solution and y be volume of 57% solution

0.75x + 0.57y = 36*0.65

0.75x + 0.57y = 23.4.......(1)

x + y = 36.........(2)

From equation (2):

y = 36 - x

Substituting this into equation(1):

0.75x + (0.57(36 - x) = 23.4

0.75x + 20.52 - 0.57x = 23.4

0.18x = 23.40 - 20.52 = 2.88

x = 2.88/0.18

x = 16

so from equation (2): y = 36-16 = 20.

8 0
2 years ago
What is the image of the point (9,7) after a rotation of 180° counterclockwise
NeX [460]

Answer:

(-9,-7)

Step-by-step explanation:

(x,y)—>(-x,-y)

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5 0
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