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3 years ago

Write a real world example, then solve. 5x + 4 = 2x +14

Mathematics

2 answers:

Brrunno [24]3 years ago

8 0

Answer:

x=10/3

Step-by-step explanation:

gregori [183]3 years ago

5 0

Answer: 10/3

Step-by-step explanation:

Let's solve your equation step-by-step.

Step 1: Subtract 2x from both sides.

Step 2: Subtract 4 from both sides.

Step 3: Divide both sides by 3.

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) Use the Laplace transform to solve the following initial value problem: y′′−6y′+9y=0y(0)=4,y′(0)=2 Using Y for the Laplace tra

artcher [175]

Answer:

$y(t)=2e^{3t}(2-5t)$

Step-by-step explanation:

Let Y(s) be the Laplace transform Y=L{y(t)} of y(t)

Applying the Laplace transform to both sides of the differential equation and using the linearity of the transform, we get

L{y'' - 6y' + 9y} = L{0} = 0

(*) L{y''} - 6L{y'} + 9L{y} = 0 ; y(0)=4, y′(0)=2

Using the theorem of the Laplace transform for derivatives, we know that:

$\large\bf L\left\{y''\right\}=s^2Y(s)-sy(0)-y'(0)\\\\L\left\{y'\right\}=sY(s)-y(0)$

Replacing the initial values y(0)=4, y′(0)=2 we obtain

$\large\bf L\left\{y''\right\}=s^2Y(s)-4s-2\\\\L\left\{y'\right\}=sY(s)-4$

and our differential equation (*) gets transformed in the algebraic equation

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0$

Solving for Y(s) we get

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0\Rightarrow (s^2-6s+9)Y(s)-4s+22=0\Rightarrow\\\\\Rightarrow Y(s)=\frac{4s-22}{s^2-6s+9}$

Now, we brake down the rational expression of Y(s) into partial fractions

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4s-22}{(s-3)^2}=\frac{A}{s-3}+\frac{B}{(s-3)^2}$

The numerator of the addition at the right must be equal to 4s-22, so

A(s - 3) + B = 4s - 22

As - 3A + B = 4s - 22

we deduct from here

A = 4 and -3A + B = -22, so

A = 4 and B = -22 + 12 = -10

It means that

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

and

$\large\bf Y(s)=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

By taking the inverse Laplace transform on both sides and using the linearity of the inverse:

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}$

we know that

$\large\bf L^{-1}\left\{\frac{1}{s-3}\right\}=e^{3t}$

and for the first translation property of the inverse Laplace transform

$\large\bf L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=e^{3t}L^{-1}\left\{\frac{1}{s^2}\right\}=e^{3t}t=te^{3t}$

and the solution of our differential equation is

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=\\\\4e^{3t}-10te^{3t}=2e^{3t}(2-5t)\\\\\boxed{y(t)=2e^{3t}(2-5t)}$

5 0

3 years ago

Find the value of the variable What is x?

yaroslaw [1]

Answer:

x = 7

Step-by-step explanation:

I think there may be other ways to do this ... but this is one I guess....

one angle= 90 ( given)

the other = 45 (given)

the third = 90 + 45 + a = 180

(all angles of triangles is 180 [angle sum property])

a = 180 - 135

= 45

The base angles are equal so that means it is a isoscles triangle. In isoscles triangle, two sides are equal , so

if one side is 7

the x is 7 too

(as it cant be the hypothenus)

I think this is right

5 0

3 years ago

Explain which city is warmer.

Naddik [55]

Answer:

City P is warmer than City Q because -4 is closer to 0 than -8 is. when in the negatives and talking about temp. the number closer to 0 is always warmer than a number far away.

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

The ratio of girls to boys in a particular classroom is 8: 7. How many boys are in the class if there are 45 students?

Dmitry [639]

9514 1404 393

Answer:

Step-by-step explanation:

Rearranging the given ratio, we can find the ratio of boys to the total.

boys : (boys +girls) = 7 : (7+8) = 7 : 15

Then the number of boys is ...

(7/15)(45) = 21

There are 21 boys in the classroom.

8 0

2 years ago

Factor the expression 18x^2 - 8

diamong [38]

Answer:

2(3x-2(3x+2)

Step-by-step explanation:

1) 18x^2-8

2) 2(9x^2-4)

3) 2(3x-2)(3x+2)

6 0

3 years ago