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MatroZZZ [7]
3 years ago
8

Frank's Auto Corner recorded its sales for the second quarter (April, May and June) of 1999. April sales were 89 cars, May sales

were 98 cars, and June sales were 115 cars. During the same quarter in the previous year, 1998, the total sales were 287 cars. How many cars were sold at Frank's Auto Corner during the second quarter of 1999? How many more cars were sold during the second quarter in 1999 than in the second quarter of 1998? Explain how you got your answer.
Mathematics
1 answer:
scZoUnD [109]3 years ago
8 0
Because I’m smart why are all the teachers doubting me I’m smartttt
You might be interested in
Need help with this math
Rudiy27

10,171.07 pesos

To every US dollar, it equal 18.84 pesos.

7 0
3 years ago
Solve the following differential equation using using characteristic equation using Laplace Transform i. ii y" +y sin 2t, y(0) 2
kifflom [539]

Answer:

The solution of the differential equation is y(t)= - \frac{1}{3} Sin(2t)+2 Cos(t)+\frac{5}{3} Sin(t)

Step-by-step explanation:

The differential equation is given by: y" + y = Sin(2t)

<u>i) Using characteristic equation:</u>

The characteristic equation method assumes that y(t)=e^{rt}, where "r" is a constant.

We find the solution of the homogeneus differential equation:

y" + y = 0

y'=re^{rt}

y"=r^{2}e^{rt}

r^{2}e^{rt}+e^{rt}=0

(r^{2}+1)e^{rt}=0

As e^{rt} could never be zero, the term (r²+1) must be zero:

(r²+1)=0

r=±i

The solution of the homogeneus differential equation is:

y(t)_{h}=c_{1}e^{it}+c_{2}e^{-it}

Using Euler's formula:

y(t)_{h}=c_{1}[Sin(t)+iCos(t)]+c_{2}[Sin(t)-iCos(t)]

y(t)_{h}=(c_{1}+c_{2})Sin(t)+(c_{1}-c_{2})iCos(t)

y(t)_{h}=C_{1}Sin(t)+C_{2}Cos(t)

The particular solution of the differential equation is given by:

y(t)_{p}=ASin(2t)+BCos(2t)

y'(t)_{p}=2ACos(2t)-2BSin(2t)

y''(t)_{p}=-4ASin(2t)-4BCos(2t)

So we use these derivatives in the differential equation:

-4ASin(2t)-4BCos(2t)+ASin(2t)+BCos(2t)=Sin(2t)

-3ASin(2t)-3BCos(2t)=Sin(2t)

As there is not a term for Cos(2t), B is equal to 0.

So the value A=-1/3

The solution is the sum of the particular function and the homogeneous function:

y(t)= - \frac{1}{3} Sin(2t) + C_{1} Sin(t) + C_{2} Cos(t)

Using the initial conditions we can check that C1=5/3 and C2=2

<u>ii) Using Laplace Transform:</u>

To solve the differential equation we use the Laplace transformation in both members:

ℒ[y" + y]=ℒ[Sin(2t)]

ℒ[y"]+ℒ[y]=ℒ[Sin(2t)]  

By using the Table of Laplace Transform we get:

ℒ[y"]=s²·ℒ[y]-s·y(0)-y'(0)=s²·Y(s) -2s-1

ℒ[y]=Y(s)

ℒ[Sin(2t)]=\frac{2}{(s^{2}+4)}

We replace the previous data in the equation:

s²·Y(s) -2s-1+Y(s) =\frac{2}{(s^{2}+4)}

(s²+1)·Y(s)-2s-1=\frac{2}{(s^{2}+4)}

(s²+1)·Y(s)=\frac{2}{(s^{2}+4)}+2s+1=\frac{2+2s(s^{2}+4)+s^{2}+4}{(s^{2}+4)}

Y(s)=\frac{2+2s(s^{2}+4)+s^{2}+4}{(s^{2}+4)(s^{2}+1)}

Y(s)=\frac{2s^{3}+s^{2}+8s+6}{(s^{2}+4)(s^{2}+1)}

Using partial franction method:

\frac{2s^{3}+s^{2}+8s+6}{(s^{2}+4)(s^{2}+1)}=\frac{As+B}{s^{2}+4} +\frac{Cs+D}{s^{2}+1}

2s^{3}+s^{2}+8s+6=(As+B)(s²+1)+(Cs+D)(s²+4)

2s^{3}+s^{2}+8s+6=s³(A+C)+s²(B+D)+s(A+4C)+(B+4D)

We solve the equation system:

A+C=2

B+D=1

A+4C=8

B+4D=6

The solutions are:

A=0 ; B= -2/3 ; C=2 ; D=5/3

So,

Y(s)=\frac{-\frac{2}{3} }{s^{2}+4} +\frac{2s+\frac{5}{3} }{s^{2}+1}

Y(s)=-\frac{1}{3} \frac{2}{s^{2}+4} +2\frac{s }{s^{2}+1}+\frac{5}{3}\frac{1}{s^{2}+1}

By using the inverse of the Laplace transform:

ℒ⁻¹[Y(s)]=ℒ⁻¹[-\frac{1}{3} \frac{2}{s^{2}+4}]-ℒ⁻¹[2\frac{s }{s^{2}+1}]+ℒ⁻¹[\frac{5}{3}\frac{1}{s^{2}+1}]

y(t)= - \frac{1}{3} Sin(2t)+2 Cos(t)+\frac{5}{3} Sin(t)

3 0
3 years ago
The diameter of cold virus cell is about 3x10-9 meter,and the diameter of a streptoccus bacterium cell is about 9x10-7 meter. Wh
Archy [21]

Here we need to compare the orders of magnitude of two measures.

We will see that the bacteria is<em> 300 times larger than the virus.</em>

We know that:

The diameter of the virus-cell is:

D_v = 3 \cdot 10^{-9} m

The diameter of the bacteria cell is:

D_b = 9 \cdot 10^{-7} m

So, to compare them, first notice that both are in the same units, meters, so we only need to <u>compare the numbers</u>.

Is common sense to identify the one with the largest exponent as the largest number, and the largest exponent is -7, thus <u>the bacteria should be the larger one.</u>

But let's prove this with math, remember the property:

\frac{a^n}{a^m} = a^{n - m}

Let's take the quotient between the diameters and see what we get, I will use the <u>diameter of the bacteria in the numerator</u>, thus <u>if the quotient is larger than 1, it would mean that the bacteria is greater and by how much.</u>

quotient = \frac{ 9 \cdot 10^{-7} m}{ 3 \cdot 10^{-9} m}  = \frac{9}{3} \cdot 10^{-7 + 9}\\\\= 3*10^2

So we can say that the bacteria is 3*10^2 = 3*100 = 300 times larger than the virus.

If you want to learn more, you can read:

brainly.com/question/4953281

8 0
2 years ago
What number id 0.4% is 20
d1i1m1o1n [39]

0.4% x 20 = 0.08


Hope helps!-Aparri

6 0
3 years ago
Do the ratios 6:3 and 8:4 form a proportion?
Serhud [2]

Answer:

yes

Step-by-step explanation:

6:3 and 8:4

6:3

Divide by 3

6/3: 3/3

2:1

8:4

Divide by 4

8/4: 4/4

2:1

They are the same so they form a proportion

6 0
3 years ago
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