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lord [1]
2 years ago
9

Which of the following represents 32/100? A. thirty-two hundredths B. 0.032 C. 0.23 D. thrity-two tenths​

Mathematics
1 answer:
ryzh [129]2 years ago
8 0

Answer:

A

Step-by-step explanation:

32 hundredths is 32/100

Side note

32/100 can be simplified to 8/25.

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y= -3x/5

Step-by-step explanation:

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Simora [160]
From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

3r^2-6r+6=0\iff r^2-2r+2=0

which has roots at r=1\pm i. This admits the two fundamental solutions

y_1=e^x\cos x
y_2=e^x\sin x

The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

y_p=u_1y_1+u_2y_2

where

u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx

and W(y_1,y_2) is the Wronskian of the fundamental solutions. We have

W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}

and so

u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx
u_1=\dfrac13\ln|\cos x|

u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx
u_2=\dfrac13x

Therefore the particular solution is

y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x

so that the general solution to the ODE is

y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x
7 0
3 years ago
There are 25 students in a class. 16 of those students are boys. What percent of the class are girls?
fomenos

Answer:

36 %

Step-by-step explanation:

9 girls = 36%

25 students = 100

7 0
2 years ago
Read 2 more answers
Need help asap!!!!!!!
Neporo4naja [7]

Answer:

a) Linear function

b) Linear function

c) Exponential function

d) Exponential function

Step-by-step explanation:

a) The number of hours in a day increases constantly with 60 minute intervals

b) Constant speed = same distance traveled per given time - so it's linear

c) If a population doubles every y years, it means that the population is being raised exponentially - not at a constant rate, but more each year

d) Same as c

7 0
3 years ago
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