Ask question

Ask question

All categories

schepotkina [342]

3 years ago

6

2. John earns a 3% commission for every car he sells. Today he sold a car for $13,600. How much commission did he receive? (To f

ind commission you just change your percent to a decimal and multiply it times the sales.)

1 answer:

OlgaM077 [116]3 years ago

7 0

Answer:

$408

Step-by-step explanation:

Find 3% of $13,600:

3 * 13,600 / 100 = $408

You might be interested in

What is the perimeter of this tile 4in 1in

UNO [17]

Answer:

10 inches

Step-by-step explanation:

Assuming a rectangular tile

P = 2(l+w) where l is the length and w is the width

P = 2(1+4)

= 2(5)

= 10 inches

8 0

3 years ago

Explain, with a test, why the two triangles in each figure are similar. Find the

frutty [35]

Answer:

x = 3, y = 6

Step-by-step explanation:

In the figure attached,

If ΔADE and ΔABC are similar triangles, their corresponding sides will be in the same ratio.

By this property,

$\frac{AB}{AD}=\frac{AC}{AE}=\frac{BC}{DE}$

$\frac{AB}{AD}=\frac{AC}{AE}$

$\frac{AD+BD}{AD}=\frac{AE+EC}{AE}$

$\frac{3}{2}=\frac{x+1.5}{x}$

3x = 2x + 3

3x - 2x = 3

x = 3

Similarly, $\frac{AB}{AD}=\frac{BC}{DE}$

$\frac{3}{2}=\frac{y}{4}$

y = $\frac{3\times 4}{2}$

y = 6

7 0

3 years ago

In the diagram, if KL=10, and MK=2, and JM=6 determine the value of MN. Show your work or explain how you arrived at your answer

kodGreya [7K]

Answer:

6

Step-by-step explanation:

JM is 6 riiite

and JMN should be an equilateral triangle so

4 0

3 years ago

Can someone helllllppp me on 5 more problems like this n I’ll give u 20 dollars in cashapp plzzz I’m being serious

Vlada [557]

Answer:

y = x - 5

Step-by-step explanation:

$\rm Solve \: for \: y: \\ \rm \longrightarrow x - y= 5 \\ \\ \rm Subtract \: x \: from \: both \: sides: \\ \rm \longrightarrow x - y - x = 5 - x \\ \\ \rm \longrightarrow -y = 5 - x \\ \\ \rm Multiply \: both \: sides \: by \: -1: \\ \rm \longrightarrow - y \times ( - 1) = (5 - x) \times ( - 1) \\ \\ \rm \longrightarrow y = x - 5$

5 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