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3 years ago

9 is 3% of what number

2 answers:

7 0

3% is really the fraction 3/100. So we multiply both top and bottom of the fraction to get 9/300 which means 9 is 3% of 300.

butalik [34]3 years ago

6 0

9 is 3% of the number 300.

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Send help asap i hate school smh please i will give brainlist

inn [45]

Answer:

See below.

Step-by-step explanation:

The question tells us that 2.54 cm is equivalent to 1 inch. The next part wants to know what 5.08 cm is in inches. We can just divide 5.08 by 2.54 to figure that out.

5.08/2.54 = 2

This means that 5.08 cm is 2 inches.

The next one wants to know how many centimeters 10 inches is. We can 2.54 and multiply it by 10.

2.54 · 10 = 25.4

This means that 25.4 cm is 10 inches.

3 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

5 tripled and another question is a number plus 14 equals to 9

hjlf

Answer:

5 tripled is 15, x=5

Step-by-step explanation:

14-9=5 which is the number you're looking for, and 3×5=15

3 0

3 years ago

At a bakery, Victor makes 20 cupcakes. He puts themin equal rows with 10 cupcakes in each row. Whichcalculation can be used to f

Anna [14]

Calculation = 20/10

Number of cupcakes Victor makes = 20

He puts them in equal rows:

Each row contains = 10 cupcakes

To know the number of rows he placed the 20 cupcakes,

we would divide 20 by 10

$\begin{gathered} \text{Number of rows = }\frac{20}{10} \\ \text{number of rows = 2} \end{gathered}$

Calculation = 20/10

The number of rows of cupcakes Victor makes = 2

4 0

1 year ago

What are the solutions of the quadratic equation4x*2 − 8x − 12 = 0 ?A) x = −1 and x = −3B) x = −1 and x = 3C) x = 1 and x = −3D)

blsea [12.9K]

The solutions for the given quadratic equation are x = -1 and x = 3. So, option B is correct.

<h3>What are the solutions to an equation?</h3>

The solutions to an equation are the one that satisfies the equation and makes it true.
There are different methods to solve an equation and find its solutions.
These solutions are also called zeros or roots of the equation.

<h3>Calculation:</h3>

The given equation is 4x² - 8x - 12 = 0

Since it is a quadratic equation, it has 2 roots or solutions.

On factorizing the given equation,

4x² - 8x - 12 = 0

⇒ 4x² - 12x + 4x -12 = 0

⇒ 4x(x - 3) + 4(x - 3) = 0

⇒ (4x + 4)(x - 3) = 0

According to the zero-product rule,

4x + 4 = 0 or x - 3 = 0

So, x = -4/4 = -1 or x = 3

Therefore, the solutions of the given equation are -1 and 3.

So, option B) x = -1 and x = 3 is correct.

Learn more about solving an equation here:

brainly.com/question/25678139

#SPJ4

5 0

2 years ago