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Semenov [28]
2 years ago
12

Estimate a 15% tip for a $26.80 meal.

Mathematics
1 answer:
storchak [24]2 years ago
4 0
10% of 26.80 = 2.68

5% of 2.68 = 1.34

2.68 + 1.34 = 4.02

Your best estimate is 4.05
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3y''-6y'+6y=e*x sexcx
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 20 children in the cast of a class play, and 8 of the children are boys. of the boys, 4 have a speaking part in the pl
kotykmax [81]
<span>it all looks confusing when we try to juggle with all those numbers in the head. The problem can be solved systematically by constructing a contingency table.
 </span>role/gender B G total
 speaking...... 4 4 8
<span> silent............ 4 8 12
 total............. 8 12 20
 </span>Probability of a child having a speaking part is therefore
 (4+4)/20=8/20=2/5
  a. 2/5
5 0
3 years ago
Read 2 more answers
13. A shop owner spent $540 to purchase a stock of
Daniel [21]

Answer:

Step--by--step explanation:

3 0
3 years ago
Find the value of x such that 365 based seven + 43 based x = 217 based 10.
Pepsi [2]

We need to find the base x in the following equation:

365_7+43_x=217_{10}

First, lets convert 365 from base 7 to base 10. This is given by

365_7=3\times7^2+6\times7^1+5\times7^0

where the upperindex denotes the position of eah number. This gives

\begin{gathered} 365_7=3\times49+6\times7+5\times1 \\ 365_7=147+42+5 \\ 365_7=194_{10} \end{gathered}

that is, 365 based 7 is equal to 194 bases 10.

Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:

43_x=4\times x^1+3\times x^0

where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives

43_x=(4x+3)_{10}

Now, we have all number in base 10. Then, our first equation can be written in base 10 as

194_{10}+(4x+3)_{10}=217_{10}

For simplicity, we can omit the 10 and get

194+4x+3=217

so, we can solve this equation for x. By combining similar terms. we have

197+4x=217

and by moving 197 to the right hand side, we obtain

\begin{gathered} 4x=217-197 \\ 4x=20 \end{gathered}

Finally, we get

\begin{gathered} x=\frac{20}{4} \\ x=5 \end{gathered}

Therefore, the solution is x=5

8 0
10 months ago
Evaluate the expression if g+2, r+3, and t=11.<br> g+6t
Ivahew [28]

Answer:

I think you copied this wrong

Step-by-step explanation:

Most likely g = 2

Therefore (2) + 6(11)

2+66=68

5 0
3 years ago
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