the compound interest of the rate of 5 percent on an amount of 4000$ at the end of 2 years​

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Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

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Question a:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]

[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]

[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]

[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}}  + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]0A + 0B = 0[/tex]

[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.

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Question b:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]A + B = 3 \rightarrow B = 3 - A[/tex]

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[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]7A - \frac{1}{2}B = -5[/tex]

Using [tex]B = 3 - A[/tex]

[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]

[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]

[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]

[tex]15A = -7[/tex]

[tex]A = -\frac{7}{15}[/tex]

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Then, B is given by:

[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]

Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]

A similar problem is given at https://brainly.com/question/2456414

Answer:

B. x = -3 and x = 4

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x² - x - 12

Step 2: Solve for x

Answer:

72

Step-by-step explanation:

look at the prime factors of each number.

18 = 2*3^2

24 = 2^3*3

36 = 2^2*3^2

The most factors of 2 in any of these numbers is 3: 2^3

The most factors of 3 in any of these numbers is 2: 3^2

2^3*3^2 is 8*9 or 72.

72 is the lowest number exactly divisible by 18, 24, and 36.

For drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

For this case, the equation given to us is:

[tex]y = \dfrac{3}{4}x + 7[/tex]

Any equation of the form [tex]y = mx + c[/tex] where m and c are constants and x and y are variables is the equation of a straight line.

For a straight line to be characterized, only two points are sufficient.

For x = 0, the y-coordinate would be such that it would satisfy the equation [tex]y = \dfrac{3}{4}x + 7[/tex]

Putting x = 0, we get:

[tex]y = \dfrac{3}{4} \times 0 + 7 = 7[/tex]

Thus, y-coordinate of the point on this line whose x-coordinate is 0 is 7. Thus, (0,7) is one of the point's coordinate on the considered line.

Putting x = 3, we get:

[tex]y = \dfrac{3}{4} \times 3 + 7 = 9.25[/tex]

Thus, y-coordinate of the point on this line whose x-coordinate is 0 is 9.25 . Thus, (0,9.25) is another of the point's coordinate on the considered line.

Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.

Learn more about points lying on graph of a function here:

brainly.com/question/1979522

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent Atsu's current age. Then Agyappng is 3x. Three years ago the relationship was ...

  (3x -3) = 4(x -3)

  9 = x . . . . . . . . . . . . add 12-3x

Atsu is 9; Agyappng is 27.

Answer:

46

Step-by-step explanation:

200/2 = 100, and the x coordinate that line up with the y-coordinate of 100 is 46.

Answer:

40

Step-by-step explanation:

2x² - 5y + 7 when x = 2 and y = -5

2(2)² - 5(-5) + 7

= 2(4) -5(-5) + 7

= 8 + 25 + 7

= 40

Answer:

X= 8cm

Step-by-step explanation:

area of the square = s×s = 16×16 = 256cm

area of the rectangle = l×b = 32×x = 32x

Given , area of triangle = area of square

32x = 256

x= 256/32

x= 8cm

Answer:

[tex]x = 8cm[/tex]

Step-by-step explanation:

we are given a square and rectangle.we want to figure out x which is the width of the rectangle. we are also given a condition i.e

therefore,

[tex] \displaystyle \rm A _{square } = A _{rect}[/tex]

recall the formula of the area of square and rectangle so,

[tex] \displaystyle {s}^{2} = lw[/tex]

now assign variables

thus substitute:

[tex] \displaystyle 32cmx = {16cm}^{2} [/tex]

simplify square:

[tex] \displaystyle 32cmx = 256cm^2[/tex]

divide both sides by 32:

[tex] \displaystyle \boxed{x = 8cm}[/tex]

and we're done!

9514 1404 393

Answer:

  -8,257,536·u^5·v^10

Step-by-step explanation:

The expansion of (a +b)^n is ...

  (c0)a^nb^0 +(c1)a^(n-1)b^1 +(c2)a^(n-2)b^2 +... +(ck)a^(n-k)b^k +... +(cn)a^0b^n

Then the k-th term is (ck)a^(n-k)b^k, where k is counted from 0 to n.

The value of ck can be found using Pascal's triangle, or by the formula ...

  ck = n!/(k!(n-k)!) . . . . where x! is the factorial of x, the product of all positive integers less than or equal to x.

This expansion has 11 terms, so the middle one is the one for k=5. That term will be ...

  5th term = (10!/(5!(10-5)!)(2u)^(10-5)(-4v^2)^5

  = (252)(32u^5)(-1024v^10) = -8,257,536·u^5·v^10

Answer:

605 boys.

Step-by-step explanation:

5:7 means 5 parts consists of boys and 7 parts consist of girls.

Since 7 parts = 847, 1 part = 121 and 5 parts = 605

Hence there are 605 boys.

Hope you have a nice day :)

Answer:

-52

Step-by-step explanation:

-4(x + 10) - 6 = -3(x - 2)

Distribute the left side to get:

(-4x + -40) - 6

Now distribute the right side to get:

-3x + 6

Arrange the equation as the following:

-4x - 40 - 6 = -3x + 6

Add the like terms on each side:

-4x - 46 = -3x + 6

Do the inverse operation of each term:

-x = 52

Now we need to get x to become a positive, so we just divide -x by -1 to get x.

And 52/-1 to get our final answer of -52.

Answer: -52

Step-by-step explanation:

-4(x + 10) - 6 = -3(x - 2)

Distribute the left side to get:

(-4x + -40) - 6

Now distribute the right side to get:

-3x + 6

Arrange the equation as the following:

-4x - 40 - 6 = -3x + 6

Add the like terms on each side:

-4x - 46 = -3x + 6

Do the inverse operation of each term:

-x = 52

Now we need to get x to become a positive, so we just divide -x by -1 to get x.

And 52/-1 to get our final answer of -52.

Answer:

n=39/5

Step-by-step explanation:

24=5(n-3)

24=5n-15

-5n= -15-24

-5n=39

n= 39/5

Answer:

y = -1/6x - 1.

Step-by-step explanation:

I  am assuming that the point id (6, -2).

The slope of the required line = -1/6.

y - y1 = m(x - x1) where m = slope and x1,y1 is a point on the line so we have

y - (-2) = -1/6( x- 6)

y + 2 = -1/6x + 1

y = -1/6x - 1.

Answer:

82.8

Step-by-step explanation:

mean = sum of all points, over the total given number of points

84 * 26 = 2184

2184 + 69 + 66 = 2319

Now the total number of tests is 26 + 2 or 28

So divide 2319 by 28

2319/28 = 82.82142

rounded to the nearest tenth is 82.8

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

1/64

Step-by-step explanation:

25% own a dog, so picking one person has a probability of 1/4 (0.25) for that person to own a dog.

picking 3 people means combining (multiplying) the probabilities of the non-overlapping and non-depending events.

picking the third person has 1/4 chance of owning a dog (as the population is "infinite") combined with the chance that also the second pick owned a dog, which has to be combined with the chance of the first pick owning a dog.

so,

1/4 × 1/4 × 1/4 = 1/4³ = 1/64 = 0.015625

A well formatted table of the distribution is attached below :

Answer:

0.124

0.733

0.408

Step-by-step explanation:

Using the table Given :

1.) P(AP Statistics) = 90 / 725 = 0.124

2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733

3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408

Answer:

I believe its  EG and NE but i might be wrong

Step-by-step explanation:

Answer:

4/27

Step-by-step explanation:

total number of marbles=9

probability of red=4/9

since you returned the first marble, the total number of marbles remains the same

prob(Blue)=(3/9)=1/3

P(red then blue)=(4/9)*(1/3)

=4/27

Answer:

The probability is 0.857

Step-by-step explanation:

We know that:

There is a total of 440 cars

There are 63 cars with defective turn signals

There are 39 with defective tires.

Now we want to find the probability that a randomly selected car does not have defective turn signals.

If all the cars have the same probability of being selected, this probability will be equal to the quotient between the number of cars that do not have defective turn signals and the total number of cars.

We know that the total number of cars is 440

And 63 of these have defective turn signals, then the rest don't.

440 - 63 = 377 cars do not have defective turn signals.

Then the probability is:

P = 377/440 = 0.857

Answer:

N=240;I%=5.6=-205000;PMT=;Fv=0;P/Y=12;C/Y=12;PMT:END

Step-by-step explanation:

A P E X

The group of values to be plugged into TVM solver is

N=240 ; I % = 19.2% , P = -205000 , PMT= -$510, Fv =0 , P/Y =12.

We have 20  year loan then the number of periods will be

N = 20 x 12

N= 240

and, the Monthly payment is $510 then

PMT = - 510

and, Interest = 19.2%

and, PV = - 205, 000

Thus, N=240 ; I % = 19.2% , P = -205000 , PMT= -$510, Fv =0 , P/Y =12.

Learn more about TVM here:

brainly.com/question/5566317

#SPJ7

Answer:

x = -3

Step-by-step explanation:

12 -4x-5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from each side

12-9x-12 = 39-12

-9x = 27

Divide by -9

-9x/-9 = 27/-9

x = -3

Answer:

x = -3

Step-by-step explanation:

12 - 4x - 5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from both sides

12 - 12 - 9x = 39 - 12

-9x = 27

Divide both sides by -9

-9x/-9 = 27/-9

x = -3

Answer:

$1000.00

Step-by-step explanation:

The supervisor is asking for an expense form of a total (?) when you return.

Given the charges given in the word problem, it is only logical to assume the supervisor wants a expense form of how much you spent (total) on the trip. Thus, you add!

Answer:

Inverses

Step-by-step explanation:

One things I could tell about the earth from this graph is that the northern and southern hemispheres are inverses because when the temp of one goes up over the months, the other goes down.

Answer:

..... surface area = 16 km^2.

Answer:

50√3 square units.

Step-by-step explanation:

Let the two sides of the triangle given be 'a' and 'b'.

Let the angle between them be θ

From the question given above, the following data were obtained:

Side a = 20 units

Side b = 10√3

Angle (θ) = 30°

Area (A) =?

A = ½ × ab × Sineθ

A = ½ × 20 × 10√3 × Sine 30

A = ½ × 20 × 10√3 × ½

A = 10 × 5√3

A = 50√3 square units

Therefore, the area of the triangle is 50√3 square units

Answer:

Scheme a 45000 is the answer

Answer:

None of these.

Step-by-step explanation:

8/x is the result when 8 is divided by x.

Answer:

D. 157

Step-by-step explanation:

4(x^2+3)-2y

4(6^2+3)-2(-1/2) add in given values

4(39)+1.     start with parentheses

156+1.        combine like terms

157.            answer

Answer:

D. 157

Step-by-step explanation:

Hi there!

We want to find the value of the expression 4(x²+3)-2y is when x=-6 and y=-1/2

Let's first simplify the expression, as that will likely make it easier

Distribute 4 to both x² and 3

4x²+12-2y

That's the expression

Substitute -6 as x into the expression

4(-6)²+12-2y

Raise (-6) to the second power

4*36+12-2y

Multiply 36 by 4

144+12-2y

Add 12 and 144 together

156-2y

Now the expression is 156-2y

But remember that we know that y=-1/2, and we haven't substituted it into the expression yet

Substitute -1/2  as y into the expression

156-2(-1/2)

Multiply

156+2/2

Simplify

156+1

Add

157

Hope this helps!

Answer:

The answer is D  

Step-by-step explanation:

there are 8 1/6 five and one sixth in 2/3