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3 years ago

Simplify by combining like terms 5 4/7i+4 3/5i

Mathematics

1 answer:

Arturiano [62]3 years ago

7 0

Simplify by combining the real and imaginary parts of each expression

Answer: 356i/35

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Solve the initial value problem

tigry1 [53]

$9(t+1)\dfrac{\mathrm dy}{\mathrm dt}-7y=14t\implies\dfrac{\mathrm dy}{\mathrm dt}-\dfrac7{9(t+1)}y=\dfrac{14t}{9(t+1)}$

Look for an integrating factor $\mu(t)$ :

$\ln\mu=\displaystyle-\frac79\int\frac{\mathrm dt}{t+1}=-\frac79\ln(t+1)\implies\mu=(t+1)^{-7/9}$

Multiply both sides by $\mu$ :

$(t+1)^{-7/9}\dfrac{\mathrm dy}{\mathrm dt}-\dfrac79(t+1)^{-16/9}y=\dfrac{14}9t(t+1)^{-16/9}$

Condense the left side as the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[(t+1)^{-7/9}y\right]=\dfrac{14}9t(t+1)^{-16/9}$

Integrate both sides:

$(t+1)^{-7/9}y=\displaystyle\frac{14}9\int t(t+1)^{-16/9}\,\mathrm dt$

For the integral on the right, substitute

$u=t+1\implies t=u-1\implies\mathrm dt=\mathrm du$

$\displaystyle\int t(t+1)^{-16/9}\,\mathrm dt=\int(u-1)u^{-16/9}\,\mathrm du$

$\displaystyle=\int\left(u^{-7/9}-u^{-16/9}\right)\,\mathrm du=\frac92u^{2/9}+\frac97u^{-7/9}+C$

$\implies(t+1)^{-7/9}y=\dfrac{14}9\left(\dfrac92(t+1)^{2/9}+\dfrac97(t+1)^{-7/9}+C\right)$

$\implies(t+1)^{-7/9}y=7(t+1)^{2/9}+2(t+1)^{-7/9}+C$

$\implies y=7(t+1)+2+C(t+1)^{7/9}=7t+9+C(t+1)^{7/9}$

Given that $y(0)=12$ , we get

$12=9+C\implies C=3$

$\implies\boxed{y(t)=7t+9+3(t+1)^{7/9}}$

6 0

3 years ago

Solve using elimination. -3x + 4y = 9 3x – 10y = 9 - PLEASE HELP

Art [367]

Answer:

x= -7

Y= -3

Step-by-step explanation:

4 0

2 years ago

Samuel exercises everyday. She spends 40% of his exercise on the treadmill. If he uses the treadmill 40 minutes each day, how ma

padilas [110]

Samuel exercises for 100 minutes each day. Or in other words, 1 hour and 40 minutes.

3 0

3 years ago

Which of the following is the correct factored form of the given equation? 6x^2 -13x - 8 = 0

tester [92]

Answer:

the 2nd

Step-by-step explanation:

8 0

3 years ago

Yea I need a lot of help

kolbaska11 [484]

Answer:

8. $356,250

9. 50,000 Birds

Step-by-step explanation:

8. $75,000*12.5%=$9375

30*$9375=281250

$75,000+$281,250=$356,250

9. 200,000*0.75%=1500

100*1500=150,000

200,000-150,00=50,000

8 0

3 years ago