Find the general solution of the given differential equation.y^(4)+18y"+81y=0

Step-by-step explanation:

Taking the provided equation ,

[tex]\implies \dfrac{3x+4}{5}-\dfrac{2}{x+3} =\dfrac{8}{5} [/tex]

1) Here denominator of two fractions are 5 and x +3 . So their LCM will be 5(x+3)

[tex]\implies \dfrac{(x+3)(3x+4)-(2)(5)}{5(x+3)}=\dfrac{8}{5} [/tex]

2) Transposing 5(x+3) to Right Hand Side . And 5 to Left Hand Side .

[tex]\implies 5(3x^2+4x+9x+12 -10) = 40(x+3)[/tex]

3) Multiplying the expressions.

[tex] \implies 5(3x^2+13x+2) = 40x + 120 [/tex]

4) Opening the brackets .

[tex]\implies 15x^2+ 65x + 10 = 40x + 120 [/tex]

5) Transposing all terms to Left Hand Side .

[tex]\implies 15x^2 + 65x - 40x + 10 - 120 = 0 \\\\\implies 15x^2 +25x - 110 = 0[/tex]

6) Solving the quadratic equation .

[tex]\implies 5(3x^2+5x -22) = 0 \\\\\implies 3x^2+13x-22 = 0 \\\\ \implies x = \dfrac{-b\pm \sqrt{b^2-4ac}}{4ac} \\\\\implies x = \dfrac{-5\pm \sqrt{5^2-4(-22)(3)}}{2(3)} \\\\\implies x = \dfrac{-5\pm \sqrt{289}}{6}\\\\\implies x =\dfrac{-5\pm 17}{6} \\\\\implies x = \dfrac{17-5}{6},\dfrac{-17-5}{6}\\\\\implies x = \dfrac{12}{6},\dfrac{-22}{6} \\\\\underline{\boxed{\red{\bf\implies x = 2 , \dfrac{-11}{3}}}}[/tex]

Answer:

[tex]x=2\\x=-\frac{11}{3}[/tex]

Step-by-step explanation:

Solve the rational equation:

[tex]\displaystyle \frac{3x+4}{5}-\frac{2}{x+3}=\frac{8}{5}[/tex]

To eliminate denominators, multiply by 5(x+3) (x cannot have a value of 3):

[tex]\displaystyle 5(x+3)\frac{3x+4}{5}-5(x+3)\frac{2}{x+3}=5(x+3)\frac{8}{5}[/tex]

Operate and simplify:

[tex]\displaystyle (x+3)(3x+4)-5(2)=(x+3)(8)[/tex]

[tex]\displaystyle 3x^2+4x+9x+12-10=8x+24[/tex]

Rearranging:

[tex]\displaystyle 3x^2+4x+9x+12-10-8x-24=0[/tex]

Simplifying:

[tex]\displaystyle 3x^2+5x-22=0[/tex]

Rewrite:

[tex]\displaystyle 3x^2-6x+11x-22=0[/tex]

Factoring:

[tex]\displaystyle 3x(x-2)+11(x-2)=0[/tex]

[tex]\displaystyle (x-2)(3x+11)=0[/tex]

Solving:

[tex]x=2\\x=-\frac{11}{3}[/tex]

Answer:

5/10= 1/2            4/12=1/3

3/9= 1/3

Step-by-step explanation:

Answer:

5/10 = 1/2

4/12 = 1/3

3/9 = 1/3

i believe these are the answers

Answer:

2.4

Step-by-step explanation:

For one person, it would take 4/5 of an hour (4 divided by 5). Three people would take 12/5 or 2.4 hours because that's just 3*(4/5). Hope this helps!

Answer:

26

Step-by-step explanation:

13+13=26

6 weeks until she reaches 60 kilo

Answer:

b > 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

3b + 12 > 27 - 2b

Step 2: Solve for b

Here we see that any value b greater than 3 would work as a solution to the inequality.

Answer:

3rd answer choice

Step-by-step explanation:

The problem says "no more than" so automatically the first and second answer choices are wrong

Now looking at the last choice, it subtracts 5, but 5 shouldn't be subtracted since all of Janet's purchases should be combined. So that just leaves the third choice

Answer:

3y+5 ≤ 17

Step-by-step explanation:

ok so we need she is buying a certain amount of markers but we don't know exactly how many so it would be 3y

we also know that she brought ONE notebook for 5 dollars which is why it would be 3y + 5

because the total amount will soon add up

now the reason it is ≤ 17

is because the symbol "≤" means less than or equal to

she did NOT spend MORE than 17 but we do not know if she spent exactly 17 or less.

Answer:

24 : 12,       36 : 18,        48 : 24.

Step-by-step explanation:

hope this helps :)

Answer:

24:12

Step-by-step explanation:

Answer:

The slope is

[tex] - \frac{3}{2} [/tex]

Step-by-step explanation:

Remember:

[tex]Slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

All we have to do is plug the points in.

[tex]Slope = \frac{ - 7 - ( - 1)}{5 - 1} = \frac{ - 6}{4} = - \frac{ 3}{2} [/tex]

Therefore, your slope is

[tex] - \frac{3}{2} [/tex]

Answer:

X= 3.5

Step-by-step explanation:

4(6x-9.5)=46

24x-38=46

X=3.5

Answer:

c edg 2020

Step-by-step explanation:

Gothcu

Answer:

x=8/3

Step-by-step explanation:

1. 3/2=4/x [Rewrite the eqaution]

2. 3x=8[Cross multiply]

3. x=8/3[Just divide]

Answer:

The answer is "Their values are reliable or accurate in the distribution of the test".

Step-by-step explanation:

Given temperature:

[tex]37.8, \ 38.3, \ 38.1, \ 38.0, \ 37.6, \ 38.2, \ 38.0, \ 38.0, \ 37.4, \ 38.3[/tex]

Calculating the average value temperature:

[tex]\to \frac{37.8 + 38.3 + 38.1 + 38.0 + 37.6+ 38.2+ 38.0+ 38.0+37.4+ 38.3}{10}[/tex]

[tex]\to \frac{379.7}{10}\\\\\to 37.97\\\\\to 38[/tex]

Given:

Center of hyperbola is at (h,k).

To find:

The standard forms of a hyperbola.

Solution:

We know that, standard forms of a hyperbola are

1. For Horizontal hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]

2. For Vertical hyperbola:

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]

where, (h,k) is center of the hyperbola.

Therefore, the correct option is B.

Answer:

Maximum height = 500 feet

Land after = 20 seconds

Step-by-step explanation:

Let us follow the movement of the ball as it is thrown upwards.  We notice that we get to a point, where the change in the height of the ball with respect to time becomes = 0. This means that the ball is at its maximum position.

Hence, mathematically, at maximum height, [tex]dh/dt = 0[/tex]

Recall,

[tex]h = 100t - 5t^2[/tex]

[tex]dh/dt=100-10t[/tex]

From our problem, we can also deduce that at the maximum height, the velocity of the ball is = 0. i.e [tex]dh/dt = 0[/tex]

hence,

[tex]0 = 100-10t\\t =10 seconds[/tex]

The time the ball takes to reach a maximum height is 10 seconds.

The next step will be to substitute this time value into the equation for the height.

[tex]h = 100(10) -5(10)^2=500 feet[/tex]

The maximum height is 500 feet

The object will land after t X 2 seconds = 10 X 2 = 20 seconds. This is because it will have to go up and come back down. This should take twice the time.

Step-by-step explanation:

55 / 3 = 18.333.

Since it is a decimal, we round up to the nearest whole number.

It will take at least 19 battles to level up.

Answer:

Step-by-step explanation:

so divide 55 / 3 = 18.33333333  or 18 1/3 but.. you'll have to battle 19 times to level up

Answer:

x² + 4x - 7 = (x + 2)² - 11

Step-by-step explanation:

Let us solve the question

∵ The expression is x² + 4x - 7

∵ The form is (x + a)² - b

→ To express the equation in the given form quate them

∴ x² + 4x - 7 = (x + a)² - b

→ Simplify the right side then equate the like terms to find a and b

∵ (x + a)²  = (x + a)(x + a)

∴ (x + a)² = (x)(x) + (x)(a) + (a)(x) + (a)(a)

∴ (x + a)² = x² + ax + ax + a²

→ Add the like terms

∵ (x + a)² = x² + (ax + ax) + a²

∴ (x + a)² = x² + 2ax + a²

→ Substitute (x + a)² in the right side by x² + 2ax + a²

∵ x² + 4x - 7 = x² + 2ax + a² - b

→ Equate the coefficients of the like terms

∵ 4x and 2ax are like terms

∴ 4 = 2a

→ Divide both sides by 2

∴ 2 = a

∵ -7 and a² - b are like terms ⇒ constant terms

∴ -7 = a² - b

∵ a = 2

∴ -7 = (2)² - b

∴ -7 = 4 - b

→ Subtract 4 from both sides

∵ -7 - 4 = 4 - 4 - b

∴ -11 = -b

→ Divide both sides by -1

∴ 11 = b

→ Substitute the values of a and b in the given form

∴ (x + a)² - b = (x + 2)² - 11

∴ x² + 4x - 7 = (x + 2)² - 11

Answer:

C

Step-by-step explanation:

Answer:

45 pine tree. 5 5.01 - 2, 500 5.3 - 5 equal 80508 15233?. g of product of 3/8 to 8 elements is what technology of a day weather

Answer:

127.1

Step-by-step explanation:

This is easy, if you see the hundredth 0.07, that is above 5 so it rounds up to become 0.1 tenth, normally we check for things like 0.003 in the thousandth, but here it is less than 5 so it does nothing, not to mention it wouldnt change the outcome

Answer:

-10

Step-by-step explanation:

Find f(x) = - x^2 + 2x first

f(3) = -(3)^2 + 2(3)

f(3) = - 9 + 6

f(3) = - 3

Now do f(3) - 7

f(3) - 7 = - 3 - 7

f(3) - 7 = - 10

Answer:

Concept: % Values

Answer:

D

Step-by-step explanation:

her value is greater

Explanation:

The probability of rolling a "2" is 1/6

The probability of rolling a "4" is also 1/6

Multiplying those fractions leads to (1/6)*(1/6) = 1/36. We can multiply the probabilities because the events are independent. Each dice roll does not affect any others.

The probability of rolling a 2 the first time and a 4 the second time is 1/36

There are 6 faces on a die.

Of these 6 faces, one of them is 2 and one of them is 4

So, the probabilities of rolling a 2 and a 4 are:

P(2) = 1/6

P(4) = 1/6

The probability of rolling a 2 the first time and a 4 the second time is calculated as follows:

[tex]\mathbf{Pr = P(2) \times P(4)}[/tex]

This gives

[tex]\mathbf{Pr = \frac 16 \times \frac 16}[/tex]

Multiply

[tex]\mathbf{Pr = \frac 1{36}}[/tex]

Hence, the probability of rolling a 2 the first time and a 4 the second time is 1/36

Read more about probabilities at:

https://brainly.com/question/11234923

Answer:

185 times

Step-by-step explanation:

Answer:

185 times

Step-by-step explanation:

Just look it up

Answer:

the two numbers are 8 and 8

Answer:

The 2 numbers for the sum are 9 and 10

Answer:

Second answer is the correct answer