5b. Solve the differential equations using Laplace transforms

y"+y' - 2y = x², y(0) = 0 and y'(0) = 0

​

Answer:

8

Step-by-step explanation:

Let us label these coordinates for our own ease:

A(0,0)

B(0,4)

C(4,5)

Area= [Ax(By-Cy)+Bx(Cy-Ay)+Cx(Ay-By)]÷2

Area = [0(4-5)+0(5-0)+4(0-4)]÷2

Area= [0+0-16]÷2

Area = -8

But since the value can not be negative we have consider a modulus in the formula, thus the value is 8

Answer:

She will earn 720 in December(Sorry, can't use the dollar sign.)

Step-by-step explanation:

1/5 of 600 is 120, so you want to add 120 to 600, which would be 720. Hope this helps!

Answer:

-x = 12

Step-by-step explanation:

x = -12

if you multiply both sides of the equation by -1, you get

-1x = -12 * -1

-x = 12

Answer:

12

Step-by-step explanation:

So what we know is that x is equal to negative 12. To make this easier you can say that -x is the same as -1 times x like shown below,

-1 × [tex]x[/tex]  is the same as -X

We can replace the x with -12 and a negative times a negative is a positive so the answer would be 12.

If you want me to explain it more let me know, but hopefully this helps and have a great day!

Answer:

Colin spends 1/8 of an hour practicing each song

Step-by-step explanation:

Colin's piano lesson is 3/4 of an hour, long.

In that period, he practices 6 different songs, spending an equal amount of time on each one.

This means that each song gets the sixth part of the lesson duration. The fraction that expresses that amount is:

[tex]\displaystyle \frac{\frac{3}{4}}{6}=\frac{3}{24}=\frac{1}{8}[/tex]

Colin spends 1/8 of an hour practicing each song

Answer:

1/8

Step-by-step explanation:

Answer:

20 D is 72%

Step-by-step explanation:

Answer:

16.2

Step-by-step explanation:

0.6 * 27

Answer:

Step-by-step explanation:

Completing the square

The blanks are

Answer:

(x^2-4)^2 = 9

Step-by-step explanation:

First, isolate the constant:

x^2-8x = -7

Then, since (a-b)^2 = a^2-2ab+b^2, you should add 16(4^2) to both sides:

x^2-8x+16 = 9

Now, we can rewrite the right-hand side as (a-b)^2:

(x-4)^2 = 9

Answer:

t = 9 cm

Step-by-step explanation:

Use Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle)

Given:

⇒ 12² + t² = 15²

⇒ 144 + t² = 225

⇒ t² = 225 - 144

⇒ t² = 81

⇒ t = √81

⇒ t = ±9

⇒ t = 9 only as length is always positive

Solution:

Pythagoras theorem can only be used in:

Since this is a scalene right triangle, we can use Pythagoras theorem to solve the missing length of the triangle.

Finding a, b, and c:

Setting up the equation:

Simplifying the squares:

Subtracting (12)(12) both sides:

Taking a square root both sides:

Since the length cannot be negative, the value of t must be positive.

The final answer is...

Answer:

2.813 m

Step-by-step explanation:

x = 9.2   θ = 17    AB=?

Looking at our angle we have an adjacent side & need to find the opposite side.

So tan θ = opp/adj

tan 17 = AB/9.2

AB = 9.2tan17

AB = 2.813 m

Answer:

59890

you just subtract

459909-400019

Step-by-step explanation:

please pass this on... ( #helpsavelives )

Who ever is reading this:

I love u.

U matter.

The world needs u

hang in there ik it may be bad but u deserve the world <3

ur beautiful no matter ur shape, size, color, gender.. anything

don't give up i need u to live.

i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me

Pls pass this on. Everyone deserves to know this. ♥️♥️

just copy and paste its not hard pls this could save someones life

Answer:

59890

Step-by-step explanation:

459909-400019

Answer:  [tex]y=\frac{1}{3} x[/tex]

Answer:

16/45 for fraction, or 0.35 for decimal

Step-by-step explanation:

4/7 x 4/5 × 7/9

reduce numbers with greatest common factor 7

4 × 4/5 × 1/9

calculate the product = 4 × 4 × 1 = 16

5 × 9 = 45

16/45 or 0.35

Answer:

Option C, 20 is the answer.

Step-by-step explanation:

Let g(x) = 2x and h(x) = x² + 4

We have to evaluate (h ο g) ( -2 )

Since ( h ο g )x = h [ g(x) ]

                       = ( 2x)² + 4

                       = 4x² + 4

( h ο g ) ( -2 )  = 4 ( -2 )² + 4

                       = 4 × 4 + 4

                       = 16 + 4

                       = 20

Answer:

8(15-m)

Step-by-step explanation:

just took the test

Answer:

$4

Step-by-step explanation:

It was 4 dollars because you bought one notebook worth two dollars and six-packs of crayons. 26-2 is 24, and 6x4 is 24, so it is worth four dollars.

Answer:

5*4=9 and if thats -5*7=35 and adding those together gets 35+9=44

Step-by-step explanation:

Answer:

Hello there buddy

Your answer is

35+9=44

Hope it’s helps you buddy

Step-by-step explanation:

~Awesome Jayden

Answer:

25

Step-by-step explanation:

we find how many problems 1% is first by solving 10/40, which gives us .25

then, we multiply by 100, which results in 25.

i could try to explain better if you'd like

Answer:

The two factor pairs for 72 are the following:

Step-by-step explanation:

Of you take the answer to each equation only these two equal 72, leaving them as factors.

3 × 18 is equal to 54

8 × 8 is equal to 65

Which leaves them being the wrong answer

Answer:

To Evaluate:

[tex] \\ { \displaystyle{ \rm \lim_{x \to1} \left \{ \frac{ {x}^{4 } - {3x}^{2} + 2 }{ {x}^{3} - {5x}^{2} + 3x + 1} \right \} }}\\ \\[/tex]

Using L'Hospital's Rule

Let f(x) and g(x) be two common functions which are differentiable on an open Interval , at a point a where,

[tex]\\{ \displaystyle{ \lim_{x \to a}{ \rm{f(x)} = { \displaystyle{ \lim_{x \to a}}} \: { \rm{g(x)}} = 0 \: or \: \pm \infty}}}\\ \\[/tex]

Then,

[tex]\\{ \displaystyle{ \lim_{x \to a} \frac{{ \rm{f (x)}}}{{ \rm{g(x)}}} = { \displaystyle{ \lim_{x \to a }}} \frac{{ \rm{f '(x)}}}{{ \rm{g'(x)}}}}}\\ \\[/tex]

As x to 0 , we have:

[tex]\\{ \displaystyle{ \lim_{x \to 1}}} \left( \large\rm\frac{ {x}^{4} - {3x}^{2} + 2 }{ {x}^{3} - {5x}^{2} + 3x + 1} \right) = \frac{0}{0}\\ \\[/tex]

Therefore,

[tex]\\{ \large{ \displaystyle{ \lim_{x \to1}}} \left( \large \rm\frac{ {x}^{4} - {3x}^{2} + 2}{ {x}^{3} - {5x}^{2} + 3x + 1 } \right) = { \displaystyle{ \lim_{x \to1} { \small{\frac{ {4x}^{3} - 6x}{ {3x}^{2} - 10x + 3 }}} = { \small{\frac{4 - 6}{3 - 10 + 3} }} = - \frac{2}{ - 4} = - \frac{1}{2} }}}\\ \\[/tex]

Hence,

[tex]\\{ \displaystyle{ \lim_{x \to1}{\rm{ \left( \frac{ {x}^{4} - 3 {x}^{2} + 2 }{ {x}^{3} - 5 {x}^{2} + 3x + 1 } \right) = { \boxed{ \red{ - \frac{1}{2} }}}}}}}\\ \\[/tex]

Without using L'Hopital's rule:

Factorize the numerator.

[tex]x^4 - 3x^2 + 2 = (x^2 - 2) (x^2 - 1) = (x^2 - 2) (x + 1) (x - 1)[/tex]

Factorizing cubics is usually a bit trickier. But we know x = 1 makes the denominator vanish, so x - 1 is a factor of the cubic. So for some constants a and b,

[tex]x^3 - 5x^2 + 3x + 1 = (x - 1)^3 + a(x - 1)^2 + b(x - 1)[/tex]

Expanding the right side gives

[tex]x^3 - 5x^2 + 3x + 1 = x^3 + (a - 3)x^2 + (-2a + b + 3)x + a - b - 1[/tex]

Then

[tex]a - 3 = -5 \implies a = -2[/tex]

[tex]-2a + b + 3 = 3 \implies b = -4[/tex]

So we rewrite the limit as

[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \lim_{x\to1} \frac{(x^2 - 2) (x + 1) (x - 1)}{(x-1)^3 - 2(x-1)^2 - 4(x-1)}[/tex]

x is approaching 1 so x ≠ 1 and we can cancel out factors of x - 1 :

[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \lim_{x\to1} \frac{(x^2 - 2) (x + 1)}{(x-1)^2 - 2(x-1) - 4}[/tex]

The simplified limand is continuous at x = 1, so we can now evaluate the limit by direct substitution.

[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \frac{(1^2 - 2) (1 + 1)}{(1-1)^2 - 2(1-1) - 4} = -\frac24 = \boxed{-\frac12}[/tex]

Answer: Yes!

Step-by-step explanation:

a proportion is when to ratios are equivalent to each other and that they are set equal to each other

If you see, $30 is divided by 2 to get $15. Same goes for the pounds, 46 is divided by 2 to get 23. They follow the same proportion

Answer: follow this you'll be able to solve it

Step-by-step explanation: mean = 98.11F

standard deviation = 0.56F

99.79 – 98.11 = 1.68 = 3 standard deviations

96.43 – 98.11 = –1.68 = –3 standard deviations

96.43F and ​99.79F are 3 standard deviations from the mean 98.11F.

By the empirical rule we know that 99.7% of the data lies within 3 standard deviation of the mean.

Approximately 68% of healthy adults in this group have body temperatures within 1 standard of the​ mean, or between 97.55F and 98.67F.

Answer:

the anser is 1.3

have a nice day!

Answer:

$2.57

Step-by-step explanation:

divide 5,140 by 20,

5,140/20=257=2.57

I'm not 100% sure but it's not u

Answer:

A) 310 cm²

Step-by-step explanation:

The surface area is the area of the two-dimensional surfaces of this three-dimensional figure.

Start by multiplying each 5x4 rectangle. There are four of them that are visible from the front.

Now, find the surface area of the large rectangle in the back and the left side of the figure.

Find the surface area of the top of this figure.

Find the surface area of the bottom of this figure (it's the same as the area of the top).

Add all of the surface areas together to find the total surface area of the figure.

Answer:

V = 3^3 = 5^3

Volume of each cube is side^3. To find the volume of both cubes just add the two volumes together.

Step-by-step explanation: Your welcome.

Answer:

total volume = 152 units³

given:

using this formula:

total volume = first cube volume + second cube volume

total volume = 3³ + 5³

total volume = 27 + 125

total volume = 152 units³

Answer: a = b*r/n

Step-by-step explanation: Hope this helps :^)

Answer:

=0

Step-by-step explanation: