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4 years ago

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The cost for 4 dinners plus a 20% tip is $24.00. write an equation representing the situation if pp is the price of the dinner i

n dollars. you may asssume there is no tax

1 answer:

jek_recluse [69]4 years ago

6 0

To find the equation, simply write out what the problem states: the cost of 4 dinners plus the cost of 0.2 dinners (20%) is $24.00:

4pp + 0.2pp = 24

Simplify:

4.2pp = 24

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You roll a fair 6 sided die. what is p (roll less than 4)

Darina [25.2K]

Answer:

1/2

Step-by-step explanation:

Since this die has 6 sides, for each roll it has 6 outcomes.

Hence the probability of it landing on any specific number is 1/6.

Since there are only 3 outcomes wanted (roll less than 4 so it can be 1, 2, or 3) then we have to add the probability of each number being rolled so that is:

1/6 chance of rolling1

1/6 chance of rolling2

1/6 chance of rolling3

1/6 + 1/6 + 1/6

=3/6

=1/2

3 0

4 years ago

Which of the following circles have their centers in the second quadrant? Check all that apply.

steposvetlana [31]

<span>B. (x + 1)2 + (y - 7)2 = 16
</span>D. (x + 2)2 + (y - 5)2 = 9

3 0

4 years ago

Use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answ

olga_2 [115]

Answer:

Therefore the complete primitive is

$y=c_1 e^{2y}+c_2e^{3t}+e^{t}$

Therefore the general solution is

$y=c_1e^{2t}+c_2e^{3t}+e^t$

Step-by-step explanation:

Given Differential equation is

$y''-5y'+6y=2e^t$

<h3>Method of variation of parameters:</h3>

Let $y=e^{mt}$ be a trial solution.

$y'= me^{mt}$

and $y''= m^2e^{mt}$

Then the auxiliary equation is

$m^2e^{mt}-5me^{mt}+6e^{mt}=0$

$\Rightarrow m^2-5m+6=0$

$\Rightarrow m^2 -3m -2m +6=0$

$\Rightarrow m(m -3) -2(m -3)=0$

$\Rightarrow (m-3)(m-2)=0$

$\Rightarrow m=2,3$

∴The complementary function is $C_1e^{2t}+C_2e^{3t}$

To find P.I

First we show that $e^{2t}$ and $e^{3t}$ are linearly independent solution.

Let $y_1=e^{2t}$ and $y_2= e^{3t}$

The Wronskian of $y_1$ and $y_2$ is $\left|\begin{array}{cc}y_1&y_2\\y'_1&y'_2\end{array}\right|$

$=\left|\begin{array}{cc}e^{2t}&e^{3t}\\2e^{2t}&3e^{3t}\end{array}\right|$

$=e^{2t}.3e^{3t}-e^{2t}.2e^{3t}$

$=e^{5t}$ ≠ 0

∴ $y_1$ and $y_2$ are linearly independent.

Let the particular solution is

$y_p=v_1(t)e^{2t}+v_2(t)e^{3t}$

Then,

$Dy_p= 2v_1(t)e^{2t}+v'_1(t)e^{2t}+3v_2(t)e^{3t}+v'_2(t)e^{3t}$

Choose $v_1(t)$ and $v_2(t)$ such that

$v'_1(t)e^{2t}+v'_2(t)e^{3t}=0$ .......(1)

So that

$Dy_p= 2v_1(t)e^{2t}+3v_2(t)e^{3t}$

$D^2y_p= 4v_1(t)e^{2t}+9v_2(t)e^{3t}+ 2v'_1(t)e^{2t}+3v'_2(t)e^{3t}$

Now

$4v_1(t)e^{2t}+9v_2(t)e^{3t}+ 2v'_1(t)e^{2t}+3v'_2(t)e^{3t}-5[2v_1(t)e^{2t}+3v_2(t)e^{3t}] +6[v_1e^{2t}+v_2e^{3t}]=2e^t$

$\Rightarrow 2v'_1(t)e^{2t}+3v'_2(t)e^{3t}=2e^t$ .......(2)

Solving (1) and (2) we get

$v'_2=2 e^{-2t}$ and $v'_1(t)=-2e^{-t}$

Hence

$v_1(t)=\int (-2e^{-t}) dt=2e^{-t}$

and $v_2=\int 2e^{-2t}dt =-e^{-2t}$

Therefore $y_p=(2e^{-t}) e^{2t}-e^{-2t}.e^{3t}$

$=2e^t-e^t$

$=e^t$

Therefore the complete primitive is

$y=c_1 e^{2y}+c_2e^{3t}+ e^{t}$

<h3>Undermined coefficients:</h3>

∴The complementary function is $C_1e^{2t}+C_2e^{3t}$

The particular solution is $y_p=Ae^t$

Then,

$Dy_p= Ae^t$ and $D^2y_p=Ae^t$

$\therefore Ae^t-5Ae^t+6Ae^t=2e^t$

$\Rightarrow 2Ae^t=2e^t$

$\Rightarrow A=1$

$\therefore y_p=e^t$

Therefore the general solution is

$y=c_1e^{2t}+c_2e^{3t}+e^t$

4 0

3 years ago

Write 35/3 as a mixed number.

labwork [276]

Answer:

Answer is 11⅔

Step-by-step explanation:

if want convert improper fraction into mixed number you have divide numerator by denominator

35÷3=11 remainder 2

7 0

3 years ago

On the first day of June, there were about 17.71 h of daylight in a city. Five months later, there were about 5.30 h of daylig

Andru [333]

Answer:

Percentage increases and decreases, are found by setting the problem up proportionally.

You are trying to find what percentage of 17.37 is 8.30 first.

so What %/100 = 8.30/17.37

Now define a variable:

Let x = What%

x/100 = 8.30/17.37

17.37x = 830

x = 830/17.37

x ≈ 47.78

8.30 is approximately 47.78% of 17.37, so the percentage decrease is 100% - 47.78% = 52.22%

The percentage decrease is approximately 52.22%

7 0

4 years ago