Refer to image and please attach working out

Refer To Image And Please Attach Working Out

Answers

Answer 1

The solution to the initial value problem is determined as y = e³ˣ.

Form auxiliary equation

The auxiliary equation is determined as follows;

y'' - 7y' + 12y = 0

m² - 7m + 12 = 0

m² - 3m - 4m + 12 = 0

m(m - 3) - 4(m - 3) = 0

m = 3 or 4

[tex]y = c_1e^{3x} + c_2e^{4x}\\\\y(0) = 1\\\\1 = c_1e^{3\times 0} + c_2e^{4\times 0}\\\\1 = c_1 + c_2 \ --(i)\\\\y' = 3c_1e^{3x} + 4c_2e^{4x}\\\\y'(0) = 3\\\\3 = 3c_1e^{3\times 0} + 4c_2e^{4\times 0}\\\\3 = 3c_1 + 4c_2 \ \ --(ii)[/tex]

solve (i) and (ii)

3 = 3c₁ + 4(1 - c₁)

3 = 3c₁ + 4 - 4c₁

3 = -c₁ + 4

c₁ = 1

c₂ = 0

[tex]y = e^{3x}[/tex]

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Related Questions

pls help it’s the last day of school

Answers

Answer:

12.56ftcube

Step-by-step explanation:

if V=(3.14×1^2)×4= 3.14 ×4=12.56

Fabian mixes orange juice with 4 cans of pineapple juice to make punch. Each can of pineapple juice holds 2 liters. He makes a total of 19 liters of punch.

How many liters of orange juice did Fabian use to make the punch?

A.
9 L

B.
11 L

C.
13 L

D.
15 L

Answers

Step-by-step explanation:

Total= 19

Each holds 2 litres .

So it means, 19 -4= 15

You need 15 litres of oranges.

6230000 in standard form​

Answers

Answer:

6.23*10^6

Step-by-step explanation:

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

1) write the first number and add a decimal point(.) and copy down the numbers behind the first number (DO NOT WRITE 0):

6.23

2) check how many numbers are they behind the first number

6230000

~~~~~~

in here, it's 6numbers, so 10^6

3) all in all, your answer is

6.23*10^6

Mary's total bill for a used car is $2,700.00. If she pays an equal amount each month for an entire year, how much will she have to pay each month?

Answers

Answer:

  $225

Step-by-step explanation:

When Mary pays the cost in 12 equal payments, each is 1/12 of the total amount.

__

  1/12 × $2700 = $225

Mary will have to pay $225 each month.

I NEED HELP NOWWWW PLSSS
From this data, how many male, female, adult, and baby moose do you predict are in the park?


Elk Mountain Goat Deer Moose
Male 105 71 42 52
Female 120 93 63 34
Adult 173 103 72 58
Baby 52 61 33 28

Answers

The data shows that the number of male, female, adult, and baby moose that are in the park will be 52, 34, 58, and 28 respectively.

What is data?

It should be noted that data simply means the facts and statistics that are given which are used for analysis.

In this case, the data shows that the number of male, female, adult, and baby moose that are in the park will be 52, 34, 58, and 28 respectively. This can be seen from the information in the table.

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4 GET EVE ⠀ Directions: ​

Answers

Answer:

not a solution.. simple not needed to explain too

Not a solution , that is the answer

GIVEN F(x) = 4/x , FIND THE FOLLOWING VALUES.
1. x= 0
2. x= 2
3. x= 1
4. x = 2x

Answers

Hopes this helps:

Answer: x = 0 the equal sign has to have a line going through it.

The denominator must not equal 0. So the domain is x = 0 the equal sign has to have a line going through it.

The equation of this circle is (x +
)2 + (y +
)2 =
.

Answers

Answer:

x2 + y2 = r2, and this is the equation of a circle of radius r whose center is the origin O(0, 0). The equation of a circle of radius r and center the origin is x2 + y2 = r2.

I think this is the answer.

A cone has a height of 8 yards and a radius of 3 yards. What is its volume?

Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

cubic yards
Submit

Answers

Given:h= 8 ydr= 3 ydNote that:h= Height r= Radius To find:

The volume of the given cone.

Solution:

[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]

[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]

Let's solve!

Substitute the values according to the formula.

[tex]V= \frac{1}{3}×3.14×{3}^{2}×8[/tex]

[tex]\large\boxed{V= 75.36 \: {yd}^{3}}[/tex]

Therefore, the volume of the given cone is 75.36 cubic yards.

Of the following fractions: 1/4, 7/9, 7/12, and 9/16, which is the largest?

Answers

Answer:

1/4, 7/8, 7/12, 9/16

LCM of 4,8,12,16 = 48

1/4= 1×12/4×12= 12/48

7/8= 7×6/8×6= 42/48

7/12= 7×4/12×4= 28/48

9/16= 9×3/16×3= 27/48

hence, 7/8 is the largest fraction. I hope it helps ya!!

The largest fraction is 7/8.

What is  Least Common Multiple?

Least Common Multiple is defined as the smallest number that is a multiple of two or more numbers.

Given fractions,

1/4, 7/8, 7/12, 9/16

LCM of 4,8,12,16 = 48

1/4= 1×12/4×12= 12/48

7/8= 7×6/8×6= 42/48

7/12= 7×4/12×4= 28/48

9/16= 9×3/16×3= 27/48

Since the largest will be the fraction

NUMERATOR > DENOMINATOR

Hence, the largest fraction is 7/8.

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2x-y=3, x=-2y-2 solve for substitution

Answers

Answer:

-1.25

Step-by-step explanation:

2x - 7 = 3

x = -2y - 2

3 + 7 = 2x

x = 5

5 = -2y - 2

5 = -4y

5 = -4 times y

-

What the equation of the line that passes through the points (-4, 3) and is parallel to y = ½ x - 7?

Answers

The equation of the parallel line is: y = 1/2x + 5.

What is the Equation of Parallel Lines?

The slope (m) of parallel lines are the same.

Given the equation, y = 1/2x - 7, the slope (m) is 1/2. Therefore, the slope of the line that passes through (-4, 3) would be m = 1/2.

To find the y-intercept (b), substitute m = 1/2 and (x, y) = (-4, 3) into y = mx + b.

3 = 1/2(-4) + b

3 = -2 + b

3 + 2 = b

5 = b

b = 5

Substitute m = 1/2 and b = 5 into y = mx + b:

y = 1/2x + 5

The equation is: y = 1/2x + 5.

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a. The velocity, v, of an object is moving in a medium at time t is given by

t = √ 30² +50+2 du. Evaluate t.
+

Answers

The value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.

Velocity of the object moving in the medium

The velocity of the object moving in the medium is given as;

t = ∫(3u² + 5u + 2)du

the value of t is obtained by integrating the function as follows;

t = (3u³)/3 + (5u²)/2 + 2u

t = u³ + 2.5u² + 2u

Thus, the value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.

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TYPES OF CARS WORKED ON German cars 25% Other 10% American 50% Japanese 15% These are the types of cars worked on in the auto service.

6) What is the probability that the next car worked on will be Japanese or German?

7) If the mechanics work on 6,000 cars next year, how many cars would probably be Japanese?

I really would appreciate help on this! Thank you​

Answers

Answer:

6) 40%7) 900 cars

Step-by-step explanation:

German  25%

Other 10%

American 50%

Japanese 15%

……………………………………………

6) the probability that the next car worked on

will be Japanese or German :

p(J∪G) = p(J) + p(G) = 15% + 25% = 40%.

…………………………………………………………

7) the probable number of Japanese cars :

[tex]6000\times \frac{15}{100} = 900[/tex]

only answer if you know (no guesses) no spams! :)

Answers

Answer:

3/4

Step-by-step explanation:

I actually took this quiz a day ago!

Please show how you solved

Answers

Answer:

x = 7 degrees

Step-by-step explanation:

The unlabelled angle at M   PLUS   12x + 24 = 180

  then   the unlabelled interior angle is  180 - (12x+24)

The sum of the interior angles then = 180

 80 + 4x  +     180-(12x+24) = 180

236 -8x = 180

x = 7

x+14/x=-9

Help please and if possible could someone be so kind as to make a step by step please

Answers

Answer:

X = 1.4

Step-by-step explanation:

x + 14/x = -9

x + 14 = -9x

x + 9x = -14

10x = -14

X = -14/10

X = -1.4

What fraction is equivalent to 046464646

Answers

Answer:

46/99

explanation shown in the picture

If f(x) = x + 1 and g(x) = 2x – 7, which expression is equivalent to [f o g](3)? (3 + 1)(2(3) –7) 2(3)2 – 6 2(3 + 1) – 7 (2(3) – 7) + 1

Answers

Answer:

Solution

-1

f

x=

1

-X+

2

Step-by-step explanation:

f(x=2x-7

Solving Steps

y=2x-7

Interchange the variables

x=2y-7

Swap the sides

2y-7=X

Move the constant to the right

2y=X+7

Divide both sides

1

y=

>+*.

7

2

Solution

-1

f

x=

1

-X+

2

Please help me! Thanks.

Answers

Answer: Answer:

The perimeter of the polygon are

PQ = 5

RS = 5

PR = √74 = 8.60

QS = √74 = 8.60

QR = 7

Step-by-step explanation:

To calculate the perimeter of a polygon, polygon is like a coordinate with points, to find the length, we use this formula

d = √(x _2 - x_1)^2 + (y_2 - y_1)^2

Let's start from the first two vertices P ( 0 , 4) and Q(5 , 4)

x_1 = 0

y_1 = 4

x_2 = 5

y_2 = 4

PQ = √ ( 5 - 0)^2 + ( 4 - 4)^2

= √ 5^2 + 0^2

= √ 25

= 5

Between R( 5 , -3) and S ( 0 , -3)

x_1 = 5

y_1 = -3

x_2 = 0

y_2 = -3

RS = √ ( 0 - 5)^2 + ( -3 - (-3))^2

= √( -5)^2 + ( -3 + 3)^2

= √ 25 + 0

= √ 25

= 5

Between P( 0 , 4) and R (5 , -3)

x_1 = 0

y_1 = 4

x_2 = 5

y_2 = -3

PR = √( 5 - 0)^2 + ( -3 - 4)^2

= √ 5^2 + (-7)^2

= √ 25 + 49

= √ 74

= 8.60

Between Q ( 5 , 4) and S(0 ,-3)

x_1 = 5

y_1 = 4

x_2 = 0

y_2 = -3

QS = √ ( 0 - 5)^2 + ( -3 - 4)^2

= √ -5^2 + -7^2

= √ 25 + 49

= √ 74

= 8.60

Between Q( 5,4) and R(5 , -3)

x_1 = 5

y_1 = 4

x_2 = 5

y_2 = -3

QR = √ (5 - 5)^2 + ( -3 - 4)^2

= √ 0^2 + (-7)^2

= √ 0 + 49

= √ 49

= 7

Step-by-step explanation:

Which number is the largest 1.2 x 10^4, 4.5 x 10^-3,3.8x10^3,7.5^3

Answers

1.2x10^4

Step-by-step explanation:

2.

negative exponent means it's a fraction so

4.5x10^-3 is 1/4500 or 0.0045 so

it's a very small number

1.

^4 means means move the decimal 4 spots

12×10^4 = 12,000

3.

^3 means move the decimal 3 spots

3.8 x 10^3 =

3800

4.

7.5x10^3 =

7500

Select the correct answer from each drop-down menu.
Alice is playing checkers against a computer and has won 8 games out of the 12 she's played so far.
Alice must win the next ✓consecutive games to reach a winning percentage of 80%. After that, losing
will bring her winning percentage down to 50%.
consecutive games

Answers

She must win the next 8 consecutive games to get 80% and after that loose the next 12 games to get to 50%.

How to find the probability of winning?

She has won 8 out of 12 days. Thus, percentage of winning is;

P(winning) = 8/12 * 100%

P(Winning) = 75%

To arrive at 80% winning, it means that the number of extra consecutive games she must win is;

(8 + x)/(12 + x) = 80/100

10(8 + x) = 8(12 + x)

80 + 10x = 96 + 8x

2x = 16

x = 8

Thus, she must win the next 8 consecutive games to get 80%.

For her to get to 50% after that, it means that;

(16 - x)/(20 - x) = 50/100

(16 - x)/(20 - x) = 1/2

2(16 - x) = 20 - x

32 - 2x = 20 - x

x = 12

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Find the distance between the points (-20,6) and (-20,-14)

Answers

Answer:

20.00 units

Step-by-step explanation:

The distance between two points with coordinates

(-20,6) and (-20,-14) is:

20.00 units

(results are in decimal form, rounded to the nearest 100th)

53 POINTS. Which expression gives the distance between the points (7, -2) and (3, -1)?
A.√4² +3²
B.√4² +1²
C. 10² +3²
D.√10² + 1²

Answers

the formula for distance between points is:

Distance = sqrt((x2-x1)^2 + (y2-y1)^2)

Using the points given:

Sqrt((3-7)^2 + (-1 - -2)^2)

Sqrt(-4^2 + 1^2)

None of the answer have a -4 but I think it should be B. Since it is the closest. Did you forget a negative sign when typing??


answer B.

solve u^2 = -4, where u is a real number. Simplify your answer as much as possible.

will mark brainliest if correct

Answers

Answer:

2i and -2i

Step-by-step explanation:

I'll change u to x to be easier to understand.

x^2 = -4

sqrt(x^2) = sqrt(-4)

sqrt(-4) = 2i, or -2i

What is the solution to the system of equations graphed below?

Answers

realmente no lo se bro per necesito completar este paso

Does anyone know the correct answer.

Answers

Answer:

The answer is B

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. 6, 4, 6, 8, 7, 7, 6, 3, 3, 8, 10, 4, 8 7, 8, 7, 5, 9, 5, 8, 4, 3, 8, 5, 5, 4 4, 4, 8, 4, 5, 6, 2, 5, 9, 9, 8, 4, 8 9, 9, 5, 9, 7, 8, 3, 10, 8, 9, 6 Develop, a, 95%, confidence, interval, estimate, of, the, population, mean, rating, for, Miami.

Answers

Using the t-distribution, it is found that the 95% confidence interval for the population mean rating for Miami is (5.73, 6.95).

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Considering the given sample, the other parameters are given as follows:

[tex]\overline{x} = 6.34, s = 2.16, n = 50[/tex]

Hence, the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6.34 - 2.0096\frac{2.16}{\sqrt{50}} = 5.73[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6.34 + 2.0096\frac{2.16}{\sqrt{50}} = 6.95[/tex]

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help please! thank you so much

Answers

Answer:

4 units ...................

Using horizontal strip, determine the area of the region bounded by curves x² + 4y - 8 = 0 and x =
2y​

Answers

The Area of the region bounded by curves = 9 sq.units.

What is Area ?

Area is the space occupied by a two dimensional figure on a two dimensional space coordinate.

The two curves given are

x² + 4y - 8 = 0 and x =2y​

Convert the two equation so ‘x’ is the dependent variable.

y = -(1/4) x² +2 and y = (1/2)x

Find the limit by the intersection point of both the graph

so (-4, 2) and (2, 1)

The x-values of the line are greater so subtract the parabola:

A = ∫ (1/2)x - (-(1/4) x² +2 ) in the limits of (-4 and 1)

The Area = 9 sq.units.

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