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3 years ago

Solve the system: x' = (2 4 -1 6)x

Mathematics

1 answer:

sertanlavr [38]3 years ago

6 0

Answer:

$x=e^{8t}+c$

Step-by-step explanation:

we have given x'=(24-16)x=8x

x' denotes the differenation

$\frac{dx}{dt}=8x$ differentiation is performed with respect to t

by variable separable method we can write

$\frac{dx}{x}=8dt$

on integrating both side

$lnx=8t+c$

$x=e^{8t}+c$ (property of log )

so the solution for x will be $x=e^{8t}+c$

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Suppose there were m married couples, but that d of these 2m. people have died, Regard the d deaths as striking the 2m people at

iren2701 [21]

The function that represents surviving people are X = 2m - d

Given that there are m married couples and d of the 2m of these couples have died, the total people that remain is expressed as:

Total people remaining = Total married couple - those that died

Total married couple = 2m

Total people that died = d

Taking the difference to get the remaining people;

Total people remaining = 2m - d

Hence the function that represents surviving people are X = 2m - d

Learn more on difference here: brainly.com/question/2605546

6 0

2 years ago

I need help with 5-9

Goryan [66]

Answer:

5) x = 1, y = -3

6) x = -20, y = 2

7) infinite solutions

8) no solutions

Step-by-step explanation:

y = 5x - 8

y = -6x + 3

5x - 8 = -6x + 3

11x = 11

x = 1

y = 5 - 8

y = -3

2x + 10y = -20

-x + 4y = 28

2x = -20 - 10y

x = - 10 - 5y

-x = 28 - 4y

x = -28 + 4y

-10 - 5y = -28 + 4y

-10 + 28 = 4y + 5y

18 = 9y

2 = y

2x + 20 = -20

2x = -40

x = -20

this has infinite solutions because one equation is a simplified version of the other

this has no solutions because 5 does not equal -5

I can't graph on brainly, hope this helped though

3 0

2 years ago

M is proportional to the cube of r. when r=3m,m=216.when r=5 find the value of m

klio [65]

Answer:

The value of m is 1000 for r=5

Step-by-step explanation:

Given that m is proportional to the cube of r

It can be written as:

$m \propto\ r^3$

When the proportionality symbol is removed a proportionality constant is introduced in the equation.

Let k be the proportionality constant

$m = kr^3$

Given

r=3,m=216

Putting the values

$216 = k(3)^3\\216 = k * 27\\k = \frac{216}{27}\\k = 8$

The equation will now become

$m = 8r^3$

Putting r = 5

$m = 8(5)^3\\m = 8 * 125\\m = 1000$

Hence,

The value of m is 1000 for r=5

7 0

3 years ago

A film student wants to capture a shot of a satellite dish placed at the top of a building. The line of sight between the ground

ICE Princess25 [194]

The ground, the building and the line of sight between the ground camera and the top of the building form right triangle with hypotenuse equal to 45 feet and angle adjacent to this hypotenuse and ground - 50°. The building is an opposite leg to the given angle, then you should write sine function:

$\sin 50^{\circ}=\dfrac{height}{45} \\ \\ 0.766=\dfrac{height}{45}\\ \\ height=45\cdot 0.766=34.47$ .

The answer to the nearest tenth of a foot is 34.5 feet

6 0

3 years ago

If ax^3+9x^2+4x-10 when divided by x-3 leaves the reminder 5,then a=

FinnZ [79.3K]

Let f(x) = ax³ + 9x² + 4x – 10

g(x) = 0⇒x - 3 = 0

⇒ x = 0 + 3

⇒ x = 3

On dividing f(x) by x - 3, it leaves a remainder 5.

Now keeping, f(3) = 5

⇒a(3)³ + 9(3)² + 4(3) - 10 = 5

⇒ a × 27 + 9 × 9 + 4 × 3 - 10 = 5

⇒ 27a + 81 + 12 - 10 = 5

⇒ 81 + 12 - 10 - 5 = 27a

⇒ 81 + 12 - 15 = 27a

⇒ 93 - 15 = 27a

⇒ 78 = 27a

⇒ a = 27/78

⇒ a = 0.3461

7 0

3 years ago