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3 years ago

Can some one help me.

Mathematics

2 answers:

Novay_Z [31]3 years ago

7 0

You have to collect the like terms and then solve the equation

alina1380 [7]3 years ago

3 0

Answer:

x = ± 2, x = 3

Step-by-step explanation:

note that x = 2 gives

2³ - 3(2)² - 4(2) + 12 = 8 - 12 - 8 + 12 = 0

Hence x = 2 is a root and (x - 2) is a factor

x³ - 3x² - 4x + 12 ÷ (x - 2)

= (x - 2)(x² - x - 6)

= (x - 2)(x + 2)(x - 3), hence

(x - 2)(x + 2)(x - 3) = 0

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x + 2 = 0 ⇒ x = - 2

x - 3 = 0 ⇒ x = 3

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Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsda

stich3 [128]

Answer:

The doomsday is 146 days

Step-by-step explanation:

Given

$\frac{dy}{dt} = ky^{1 +c}$

First, we calculate the solution that satisfies the initial solution

Multiply both sides by

$\frac{dt}{y^{1+c}}$

$\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}$

$\frac{dy}{y^{1+c}} = k\ dt$

Take integral of both sides

$\int \frac{dy}{y^{1+c}} = \int k\ dt$

$\int y^{-1-c}\ dy = \int k\ dt$

$\int y^{-1-c}\ dy = k\int\ dt$

Integrate

$\frac{y^{-1-c+1}}{-1-c+1} = kt+C$

$-\frac{y^{-c}}{c} = kt+C$

To find c; let t= 0

$-\frac{y_0^{-c}}{c} = k*0+C$

$-\frac{y_0^{-c}}{c} = C$

$C =-\frac{y_0^{-c}}{c}$

Substitute $C =-\frac{y_0^{-c}}{c}$ in $-\frac{y^{-c}}{c} = kt+C$

$-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}$

Multiply through by -c

$y^{-c} = -ckt+y_0^{-c}$

Take exponents of $-c^{-1$

$y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}$

$y = [-ckt+y_0^{-c}]^{-c^{-1}$

$y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}$

i.e.

$y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}$

Next:

$t= 3$ i.e. 3 months

$y_0 = 2$ --- initial number of breeds

So, we have:

$y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}$

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

We have the growth term to be: $ky^{1.01}$

This implies that:

$ky^{1.01} = ky^{1+c}$

By comparison:

$1.01 = 1 + c$

$c = 1.01 - 1 = 0.01$

$y(3) = 16$ --- 16 rabbits after 3 months:

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

$y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}$

$16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}$

$16 = [-0.03 * k + 2^{-0.01}]^{-100}$

$16 = [-0.03 k + 0.9931]^{-100}$

Take -1/100th root of both sides

$16^{-1/100} = -0.03k + 0.9931$

$0.9727 = -0.03k + 0.9931$

$0.03k= - 0.9727 + 0.9931$

$0.03k= 0.0204$

$k= \frac{0.0204}{0.03}$

$k= 0.68$

Recall that:

$-\frac{y^{-c}}{c} = kt+C$

This implies that:

$\frac{y_0^{-c}}{c} = kT$

Make T the subject

$T = \frac{y_0^{-c}}{kc}$

Substitute: $k= 0.68$ , $c = 0.01$ and $y_0 = 2$

$T = \frac{2^{-0.01}}{0.68 * 0.01}$

$T = \frac{2^{-0.01}}{0.0068}$

$T = \frac{0.9931}{0.0068}$

$T = 146.04$

<em>The doomsday is 146 days</em>

4 0

3 years ago

Write the 5th term in the expansion of (5x-y/2)^7

Nezavi [6.7K]

Answer:

65625/4(x^5)(y²)

Step-by-step explanation:

Using binomial expansion

Formula: (n k) (a^k)(b ^(n-k))

Where (n k) represents n combination of k (nCk)

From the question k = 5 (i.e. 5th term)

n = 7 (power of expression)

a = 5x

b = -y/2

....................

Solving nCk

n = 7

k = 5

nCk = 7C5

= 7!/(5!2!) ------ Expand Expression

=7 * 6 * 5! /(5! * 2*1)

= 7*6/2

= 21 ------

.........................

Solving (a^k) (b^(n-k))

a = 5x

b = -y/2

k = 5

n = 7

Substituting these values in the expression

(5x)^5 * (-y/2)^(7-5)

= (3125x^5) * (-y/2)²

= 3125x^5 * y²/4

= (3125x^5)(y²)/4

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

Multiplying the two expression above

21 * (3125x^5)(y²)/4

= 65625/4(x^5)(y²)

5 0

3 years ago

?/21 =6/7 what is the numerator

defon

18 is the numerator..

3 0

3 years ago

Read 2 more answers

(9c – 8d) + (2c – 6) + (–d + 3)=

Feliz [49]

Explanation: Just addition and subtraction which is easy, I'd remove the brackets first so it won't be too confusing.

$9c-8d+2c-6-d+3=???$

Here, just remember that:

Plus/Positive multiply Minus/Negative = Minus/Negative
Plus/Positive multiply Plus/Positive = Positive/Plus
Minus/Negative multiply Minus/Negative = Positive/Plus

Notice the +(-d+3), (+)(-) = - so it's -d+3

Now just addition and subtraction, for better looking and non-confusing.

$9c+2c-8d-d-6+3=???\\9c+2c-8d-d-6+3=11c-9d-3$

9c+2c = 11c

-8d-d = -9d

-6+3 = -3

Therefore, the answer is $11c-9d-3$

If you are confused, you can reply to this explanation (If it's wrong, let me know.)

3 0

4 years ago

GUYS! LISTEN!! There’s people answering with links! Don’t open the link it’s a virus!!! Also, can somebody check out my question

katrin2010 [14]

Answer:

Did they get rickrolled or something

Step-by-step explanation:

5 0

3 years ago