PLEASE HELP! I WILL GIVE BRAINLIEST FOR A RIGHT ANSWER

y'' + 5y' + 6y = 0

has characteristic equation

r² + 5r + 6 = (r + 2) (r + 3) = 0

with roots at r = -2 and r = -3, hence the differential equation's characteristic solution is

[tex]y(t) = C_1 e^{-2t} + C_2 e^{-3t}[/tex]

Given that y(0) = 1 and y'(0) = 2, we have

[tex]y(t) = C_1 e^{-2t} + C_2 e^{-3t} \implies 1 = C_1 + C_2[/tex]

[tex]y'(t) = -2C_1 e^{-2t} - 3C_2 e^{-3t} \implies 2 = -2C_1 - 3C_2[/tex]

and solving the resulting system of equations yields C₁ = 5 and C₂ = -4.

So the particular solution to the ODE is

[tex]\boxed{y(t) = 5 e^{-2t} - 4 e^{-3t}}[/tex]

Answer:

0.8

Step-by-step explanation:

Convert 71/100 into a decimal

.71

0.8 > .71

Answer:

the slope should be -4

Step-by-step explanation:

to find the slope we use the equation y2 - y1/ x2 - x1

-15 - (-7) / 5 - 3

-15 + 7 / 2

-8 / 2

-4

The profit function of the company is the difference between the cost and the revenue functions of the company

The given parameters are:

C(x) = 60x + 300 --- the cost function

R(x) = 100x - 0.5x^2 ---- the revenue function

The profit function is calculated as:

P(x) = R(x) - C(x)

So, we have:

[tex]P(x) = 100x - 0.5x^2 - 60x - 300[/tex]

Rewrite as:

[tex]P(x) = - 0.5x^2 + 100x - 60x - 300[/tex]

[tex]P(x) = - 0.5x^2 + 40x - 300[/tex]

This means that the expression of the profit function is [tex]- 0.5x^2 + 40x - 300[/tex]

This means that:

P(x) = 50

So, we have:

[tex]- 0.5x^2 + 40x - 300 = 50[/tex]

Subtract 50 from both sides

[tex]- 0.5x^2 + 40x - 350 = 0[/tex]

Multiply through by -2

[tex]x^2 - 80x + 700 = 0[/tex]

Expand

[tex]x^2 - 70x - 10x + 700 = 0[/tex]

Factorize

[tex]x(x - 70) - 10(x - 70) = 0[/tex]

Factor out x - 70

[tex](x - 10)(x - 70) = 0[/tex]

Solve for x

x = 10 or x = 70

Hence, the two values of x that creates a profit of $50 are x = 10 and x = 70

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Answer:

i believe the answer is 9.1

Step-by-step explanation:

6.5 x 40% or in other words .4 is 2.6.

then you add 2.6 to 6.5 and that gives you 9.1

Answer:

80

Step-by-step explanation:

The rule for triangles is that their angles must add up to 180. 30+50=80 and 180-80=100 so the angle next to 4 is 100. Since they are on a straight line the angle is 180 and 180-100 is 80

brainliest pls hardstuck ambitious.

Answer:

5.4

Step-by-step explanation:

x2-12x+36 = 90

=> 2x - 12x + 36 = *90

=> 2x - 12x = 90 - 36

=> -10x = 54

=> (-10x)/-10 = (54)/-10

=> x = 5.4

Answer:

X

Step-by-step explanation:

[tex]36 {}^{x} (6 {}^{x - 2} )[/tex]

[tex]36 {}^{x} ( \frac{6 {}^{x} }{6 {}^{2} } )[/tex]

[tex]36 {}^{x} ( {6}^{x} ) \frac{1}{6 {}^{2} } [/tex]

[tex]6 {}^{2} (6 {}^{x} )6 {}^{ - 2} [/tex]

[tex]6 {}^{x} [/tex]

F(x)=x.

Answer: f (x) = 3x-2

Step-by-step explanation:

Answer: Your answer is 3.53 as a Decimal.

Hope this helps!

Answer:

3.53

Step-by-step explanation:

If you have been wondering what is 353% in decimal form, or if you have been looking for how to change 353% to decimal, then you are definitively right here.

353%, 353 pct and 353 percent all mean 353 by the hundred. 353 percent as a decimal equals:

353% as a decimal = 3.53

353 percent as a decimal = 3.53

Answer:

~Male Y/n here~ I think that your A will be 77 feet in distance and your B would be 25 feet above ground.

(Hope this helps!)

Answer:

x = 15/8

Step-by-step explanation:

Let x = unknown number

Given:

some number minus -15 is equal to the product of the number and 9

⇒ x - -15 = x · 9

⇒ x + 15 = 9x

⇒ 15 = 9x - x

⇒ 15 = 8x

⇒ x = 15/8

Answer:

15/8

Step-by-step explanation:

Let's assume that the number is 'n'. Provided that number 'n' minus -15 is equal to the product of the number 'n' and 9. Simply jot down the above statement in mathematical form:

[tex] \implies\:\sf{\red{n \: - \: ( - 15) \: = \: n \: \times \: 9}}[/tex]

Now, simply solve the above equation.

[tex]\implies\:\sf{n \: + \: 15 \: = \: 9n}[/tex]

Take the like terms on one sides.

[tex]\implies\:\sf{9n \: - \: n \: = \: 15}[/tex]

Do the rest calculations.

[tex]\implies\:\sf{8n \: = \: 15}[/tex]

[tex]\implies\:\sf{\red{n \: = \: \dfrac{15}{8}}}[/tex]

Hence, the required value of n is 15/8.

Answer:

It is, in fact, a rational number.

Answer:

C. 240 in^2

Step-by-step explanation:

is it stated that two triangles are similar.

If they are similar then their area must be proportional too.

The side lengths' proportion is :

12/60 = 1/5 this can be used to find the area of the smaller triangle, ABC
Let x represent the are of triangle ABC

1/5 = x/1200 cross multiply both sides

5x = 1200 divide both sides by 5

x = 240 since the area is indicated with square value so the answer is

C. 240 in^2

Answer:

b

Step-by-step explanation:

Answer:

0, 3, -6, 7

Step-by-step explanation:

x(x − 3)(x + 6) (x – 7) = 0

so x = 0

or x - 3 = 0, x = 3

or x + 6 = 0, x = -6

or x - 7 = 0, x = 7

Answer: 0, 3, -6, 7

A confidence interval is simply the range of estimates for an unknown parameter, which is defined as an interval with a lower bound and an upper bound.

Your information is incomplete as the data is not given. Therefore, an overview of the confidence interval will be given.

A 90% confidence interval means that the researcher is 90% confident that the values of the results will simply fall between the upper and lower limits if the procedure is repeated again.

You can find a confidence level for data by simply taking half of the size of the confidence interval, then multiplying it by the square root of the sample size, and then dividing by the sample standard deviation.

Finally, look up the resulting ​Z​ or ​t​ score in a table in order to find the level.

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Answer: y=25x

Step-by-step explanation:

Answer:

768$

Step-by-step explanation:

I multiplied 24$ times 32.

Answer: none

Step-by-step explanation: there are no WHOLE numbers between 39

The polynomial that represents the length is:

h(x) = 11x + 1.

We know that the area of the top surface is given by:

f(x) = 66x^2 + 17x + 1

And the width of the top surface is:

g(x) = 6x + 1.

We can assume that the length, h(x), is another polynomial of degree 1, so we can write:

h(x) = a*x + b

Now, the area is the product of the width and the length, so we have:

f(x) = g(x)*h(x)

f(x) = (6x + 1)*(ax + b)

     =   6ax^2 + (6b)x + (a)x + b

     =   (6a)x^2 + (6b + a)x + b

Now let's compare this with f(x), correspondent coefficients must have the same value.

66x^2 + 17x + 1 = (6a)x^2 + (6b + a)x + b

Then we have:

66 = 6a

17 = 6b + a

1 = b

From the first equation we have:

66/6 = a = 11

And from the third:

b = 1

Then the length is:

h(x) = 11x + 1.

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Answer:

240 ounces is your answer

Answer:

The answer to this question is 60degree

Presumably, the first limit is some finite number

[tex]\displaystyle \lim_{x\to\pi} \frac{f(x)}{x-\pi} = c[/tex]

Since x - π clearly approaches 0 as x approaches π, we must also have f(x) approaching 0,

[tex]\displaystyle \lim_{x\to\pi} f(x) = 0[/tex]

Recall the double angle identity,

sin(2t) = 2 sin(t) cos(t)

and rewrite the limit as

[tex]\displaystyle \lim_{x\to\pi} \frac{\sin(2 f(x))}{x - \pi} = \lim_{x\to\pi} \frac{2 \sin(f(x)) \cos(f(x))}{x - \pi} = 2 \lim_{x\to\pi} \frac{\sin(f(x))}{f(x)} \times \frac{f(x) \cos(f(x))}{x - \pi}[/tex]

Recall that

[tex]\displaystyle \lim_{x\to0}\frac{\sin(x)}x=1[/tex]

which means

[tex]\displaystyle \lim_{x\to\pi}\frac{\sin(f(x))}{f(x)} = \lim_{f(x)\to0}\frac{\sin(f(x))}{f(x)} = 1[/tex]

and by continuity,

[tex]\displaystyle \lim_{x\to\pi} \cos(f(x)) = \cos\left(\lim_{x\to\pi} f(x)\right) = \cos(0) = 1[/tex]

Then

[tex]\displaystyle 2 \lim_{x\to\pi} \frac{\sin(f(x))}{f(x)} \times \frac{f(x) \cos(f(x))}{x - \pi} \\\\ = 2 \left(\lim_{x\to\pi}\frac{\sin(f(x))}{f(x)}\right) \left(\lim_{x\to\pi} \frac{f(x)}{x-\pi}\right) \left(\lim_{x\to\pi}\cos(f(x))\right) \\\\ = 2 \times 1 \times c \times 1 = \boxed{2c}[/tex]

Answer:

To find the x-intercept, substitute in 0 for

y and solve for x. To find the y-intercept, substitute in 0

for x and solve for y. x-intercept(s): (2^3,0) y-intercept(s):

(0,−2)

Answer:

x =(2+√40)/18=(1+√ 10 )/9= 0.462

or:

 x =(2-√40)/18=(1-√ 10 )/9= -0.240

Answer:

the answer is 48.139 in²

Step-by-step explanation:

I took the test.

48.139 in² of the figure area is painted yellow in color.

An area is amount of space occupied by a two dimensional shape or object.

The area of the figure = Area of the square + Area of the triangle

Area of the figure = (7 in * 7 in) + (1/2) * (12 * 7) = 91 in²

Since 52.9% of the area is painted yellow, hence:

Area painted yellow = 52.9% of 91 = 48.139 in²

48.139 in² of the figure area is painted yellow in color.

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Answer:

Step-by-step explanation:

this involves any number that when subtracted or added it gives each other the values of the family

7 + 6 equals 13, 13 - 6 equals 7,

please mark me brainiest

^_^

Answer:

7+6=13 6+7=13 13-6=7 13-7=6 7+6=13 13=7+6 13-6=7 7=13-6b

Step-by-step explanation:

I studied. :)

Answer:

6

Step-by-step explanation:

6 in hundred thousands place

Answer:

Six is the correct answer.