$1689 invested for 4 years at 3% compounded annually ?

The solution to the differential equation will be expressed as [tex]y_c=Ce^{2x}[/tex]

Given the differential equation;

[tex]\frac{d^2y}{dx^2}+2y \frac{dy}{dx} =0[/tex]

Since the right-hand side of the homogenous equation is zero, the differential equation is a homogenous equation

Let [tex]D=\frac{dy}{dx}[/tex]

The differential equation becomes;

[tex]D^2y-2Dy=0\\(D^2-2D)y=0[/tex]

Factorizing the auxiliary equation m² - 2m = 0

m² = 2m

m = 2

Since the auxiliary solution is real and distinct, the solution to the differential equation will be expressed as  [tex]y_c=C_1e^{m_1x} + C_1e^{m_2x} \\[/tex]

Given that m =2, the solution will be expressed as [tex]y_c=Ce^{2x}[/tex]

b) Most linear differential equations have a constant coefficient because they are mostly solved using the quadratic method which is also called the method of quadrature. This means that the solution maybe expressed in integral form.

Learn more here: https://brainly.com/question/13512633

Answer:

  8. x=6; supplementary consecutive interior angles

  10. x = 4; no applicable theorem

Step-by-step explanation:

The marked angles are "consecutive interior" angles. When their sum is 180°, the lines l and m will be parallel.

  (7x -15) +(24x +9) = 180

  31x = 186

  x = 6

Consecutive interior angles being supplementary will make the lines parallel.

__

The sum of the remote interior angles of a triangle is equal to the exterior angle:

  28x = 48 +16x

  12x = 48

  x = 4

The above relation holds regardless of whether line l is parallel to line m. There is no applicable theorem or converse.

_____

Additional comment

Adding the marking shown in the attachment would make the converse of the alternate interior angles theorem applicable to problem 10.

[tex]2v - 3u\\\\=2<3,7> - 3<-5,4>\\\\=<6,14>-<-15,12>\\\\=<6+15, 14-12>\\\\=<21,2>[/tex]

Answer:

Step-by-step explanation:

Answer:

Lower bound: 78.5

Upper bound: 79.5

Step-by-step explanation:

Since it is rounded to the nearest unit, we will subtract 1/2 to get the lower bound, and add 1/2 to get the higher bound.

If it were rounded for example to the nearest first decimal place, the number we will use is going to be 0.1 / 2

Explanation:

Start at the point (3,4) which is the tail of the vector. We move 2 units to the right and 4 units up to arrive at (5,8) due to the vector a = <2,4>. Effectively, we're using the translation rule [tex](x,y) \to (x+2,y+4)[/tex]

In other words, we add 2 to the x coordinate and add 4 to the y coordinate of the point (3,4) to move to (5,8)

Using angle sum property

[tex]\\ \sf\longmapsto 4x+20+3x+10+2x+30=180[/tex]

[tex]\\ \sf\longmapsto 9x+60=180[/tex]

[tex]\\ \sf\longmapsto 9x=120[/tex]

[tex]\\ \sf\longmapsto x=13.2[/tex]

Answer:

3:4 itself.

3:4 itself.

Step-by-step explanation:

3:4 itself.

Answer:

x = 7

Step-by-step explanation:

The difference between the length and width is 3 , then length = x - 3

area (A) of rectangle = length × width

A = x(x - 3) = 28 , distribute parenthesis

x² - 3x = 28 ( subtract 28 from both sides )

x² - 3x - 28 = 0 ← in standard form

(x - 7)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 4 = 0 ⇒ x = - 4

However, x > 0 , then x = 7

Answer:

(a.)

Step-by-step explanation:

(we talked abt it in the comment haah)

(f o h)(-1) = ...

= f(h(-1))

= f(-1 + 2)

= -2(-1 + 2) - 1

= 2 - 4 - 1

= -2 - 1

= -3

Answer:

$2.81

Step-by-step explanation:

8 feet = 2.44 meters

2.44 · $1.15 = $2.81

I hope that this helps!!!

Answer:

c. 2.81

Step-by-step explanation:

Answer:

what you men

Step-by-step explanation:

Answer:

This may not be right, but I tried! I believe its 6.

Step-by-step explanation:

Answer:

9 cherry, 6 blueberry

Step-by-step explanation:

lets do a table!

cherry | blueberry

----------------------------

   3             2

   6             4

   9             6

When there are 2 blueberry, there are 3 cherry. 3 is 1 more than 2. When there are 4 blueberry, there are 6 cherry. 6 is 2 more than 4. When there are 6 blueberry, there aare 9 cherry. 9 is 3 more than 6.

[tex] \: \: \: \: [/tex]

[tex] lim_{n→ \infty }( \frac{xe ^{x} }{x + ex} ) [/tex]

[tex] \frac{x {e}^{x} }{x + ex} [/tex]

[tex] = \frac{ {e}^{x} }{1 + e} [/tex]

[tex] \: \: \: [/tex]

Answer:

so what do i do

Step-by-step explanation:????????????

Answer:

14,17, 20

Step-by-step explanation:

Kindly see the picture I have solved it as required

Answer:

Well I assume 220ºC.

Step-by-step explanation:

That is the MAXIMUM temperature of the oven

Answer: He sold 1,800 merchandise

Step-by-step explanation: 426 - 300 = 126 ÷0.07 = 1,800

I dont know if im right though

Answer:

16.5 shirts were small.

Step-by-step explanation:

0.75 x 22 = 16.5

[tex]Hiya![/tex]

Sokka is here to help!!

Here's a explanation!

[tex]-8-(-6)[/tex]

[tex]=-8-(-6)[/tex]

[tex]=-8+6[/tex]

[tex]=-2[/tex]

The answer is B.

Here's a graph photo!

Hopefully, this helps you!!

[tex]Sokka[/tex]

Answer:

I can't see the file or I can't open the file

Step-by-step explanation:

The scenario could be modeled as a linear equation to produce the mathematical model written as : y = 10x + 7

Number of cards from previous card = 7

Number of cards per cardstock purchased = 10

Let :

Number of cardstocks purchased = x

Total Number cards made = y

The total number of cards made, y can be expressed thus :

(Number of cards per cardstock purchased × number of cardstocks purchased) + number of previous cards

This means :

y = 10x + 7

Therefore, the required equation is y = 10x + 7

Answer:

y = -8x + 2

Step-by-step explanation:

A slope-intercept form equation is y = mx + b where m is the slope and b is the y-intercept. Using this, we can plug in -8 and 2 to create our equation.

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

mean = 93

mode(s) = 90 and 94

median = 93

Step-by-step explanation:

[tex]\sf{mean = \frac{90 + 92 + 94 + 91 + 90 + 94 + 95 + 98}{8} }[/tex]

[tex]\sf{mean = \frac{744}{8} }[/tex]

[tex]\bf{mean = 93}[/tex]

.

mode(s) = 90 and 94

.

sort from smallest

90, 90, 91, 92, 94, 94, 95, 98

median :

[tex]\sf{median = \frac{92 + 94}{2} }[/tex]

[tex]\sf{median = \frac{186}{2} }[/tex]

[tex]\bf{median = 93}[/tex]

Step-by-step explanation:

check the attached file

Answer:

volume=300m3

length=5m

width=300cm=300/100=3m

To find: height of tank .

so,

volume=l×b×h

300=5×3×h

300/15=h

finally,h=20m

Answer:

Inverse:  (3, 2)

Step-by-step explanation:

Given the point, (2, 3), as an ordered pair of the function, f(x):

Since we know that for any functions, there is a one-to-one correspondence between each domain and range values.  Conversely, each range value also corresponds to one domain value.  

The inverse of a function, [tex]f^{-1}(x)[/tex], also has a one-to-one correspondence. Simply put, we are essentially switching the x and y values to determine the inverse of a function.

Therefore, given the ordered pair from f(x) = (2, 3), then the corresponding coordinates in the inverse function, [tex]f^{-1}(x)[/tex], must be (3, 2).

Answer:

1:3

Step-by-step explanation:

Since your scaling down you divide the smaller number by the larger number

7/21=1/3

=1:3

Hope this helps :)