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Irina-Kira [14]
3 years ago
6

Simplify (−8 + 8i) − (5 + 4i)

Mathematics
2 answers:
Sunny_sXe [5.5K]3 years ago
7 0

Answer: 13 + 12i

Step-by-step explanation:

Travka [436]3 years ago
3 0

Answer:

-13+4i

Step-by-step explanation:

(-8+8i)-(5+4i)

(-8+8i)-5-4i

-8+8i-5-4i

-8-5+8i-4i

-13+4i

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Help someone out pls!
likoan [24]

Answer: the answer is D

Step-by-step explanation:V = pi (d/2)^2  *  h

V =  pi  (d^2  / 4)   * h

 h =  4V  /  ( pi  * d^2)       (meters) 

6 0
2 years ago
Use the substitution of x=e^{t} to transform the given Cauchy-Euler differential equation to a differential equation with consta
kherson [118]

By the chain rule,

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dt}=x\dfrac{\mathrm dy}{\mathrm dx}

which follows from x=e^t\implies t=\ln x\implies\dfrac{\mathrm dt}{\mathrm dx}=\dfrac1x.

\dfrac{\mathrm dy}{\mathrm dt} is then a function of x; denote this function by f(x). Then by the product rule,

\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dt}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm df}{\mathrm dx}

and by the chain rule,

\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}=\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dt^2}

so that

\dfrac{\mathrm d^2y}{\mathrm dt^2}-\dfrac{\mathrm dy}{\mathrm dt}=x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}

Then the ODE in terms of t is

\dfrac{\mathrm d^2y}{\mathrm dt^2}+8\dfrac{\mathrm dy}{\mathrm dt}-20y=0

The characteristic equation

r^2+8r-20=(r+10)(r-2)=0

has two roots at r=-10 and r=2, so the characteristic solution is

y_c(t)=C_1e^{-10t}+C_2e^{2t}

Solving in terms of x gives

y_c(x)=C_1e^{-10\ln x}+C_2e^{2\ln x}\implies\boxed{y_c(x)=C_1x^{-10}+C_2x^2}

4 0
3 years ago
julian want to buy a new ipod that costs $220. he goes into a store and sees that it is on sale and has a 35% discount. he will
tigry1 [53]

Answer:

The final cost for him is;

\text{ \$154.44}

Explanation:

Given that the ipod costs $220;

C=\text{ \$220}

The store gives a 35% discount, which means he will only pay 65% of the original cost;

100\text{\%- 35\% = 65\%}

The store price is;

\begin{gathered} P=\text{ 65\% of \$220} \\ P=\frac{65}{100}\times\text{ \$220} \\ P=\text{ \$143} \end{gathered}

Also he will need to pay additional 8% sales tax on the discounted price P;

\begin{gathered} t=8\text{\% of P} \\ t=8\text{\% of \$143} \\ t=\frac{8}{100}\times\text{ \$143} \\ t=\text{ \$11.44} \end{gathered}

The final cost he need to pay is the sum of the discounted price and the sales tax;

\begin{gathered} F=P+t \\ F=\text{ \$143 + \$11.44} \\ F=\text{ \$154.44} \end{gathered}

Therefore, the final cost for him is;

\text{ \$154.44}

5 0
1 year ago
Audrey uses 5/8 cup of fruit in each smoothie she makes. She makes 6 smoothies to share with her friends. How many cups of fruit
Karo-lina-s [1.5K]
C, 3 3/4 b/c 5/8•6 = 3 3/4
6 0
3 years ago
Read 2 more answers
Descibe how you would find the sum of 24,36, and 13. PLEASE HELP DUE TONIGHT
n200080 [17]
2436 + 13 = 2449. you would count up 13 from 2436, or using the way I do it, since there are to digits in 13, and the 1 is in the second digit, add 1 to the second digit of 2436, so the 3. this makes 4 in that place. then all you have left is to add 3 to 6, making 9. so you are left with 2449. Plz plz plz give me brainiest answer I only need 4 more to rank up. If u do I will show my work.

7 0
3 years ago
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