Find the common ratio for the geometric sequence defined by the formula: an=40(2

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

netineya [11]

Answer:

x = -7 ±√5 /2

That is;

x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction

Step-by-step explanation:

To find the solutions to the equation, we will follow the steps below

(2x + 3)² + 8(2x + 3) + 11 = 0 --------------------------------------------------------------(1)

let u = 2x + 3

we will replace 2x+ 3 by u in equation (1)

u² + 8u + 11 = 0 -----------------------------------------------------------------------------(2)

we will solve equation (2) using the formula method

a=1 b=8 and c=11

u = -b ± √b² - 4ac /2a

u = -8 ±√(-8)² - 4(1)(11) /2(1)

u = -8 ±√64 - 44 /2

u = -8 ±√20 /2

u = -8/2 ± √20/2

u= -4 ± √20/2

u= -4 ± √5×4 /2

u= -4 ± 2√5 /2

u= -4 ± √5 ---------------------------------------------------------------------------(30

but u = 2x + 3

Substitute u =2x+3 in equation (3)

2x + 3 = -4 ± √5

subtract 3 from both-side of the equation

2x + 3-3 = -4 -3 ± √5

2x = -7±√5

Divide both-side of the equation by 2

2x/2 = -7 ±√5 /2

x = -7 ±√5 /2

6 0

3 years ago

Factor completely if the polynomial is not factorable write prime also state the methods used to factor the polynomial.

weqwewe [10]

For question 1
x²-12x+36

An easy and efficient way to remember how to factor is to see the different parts of the polynomial.

If the last number (in this case 36) has the multiples which add up to the middle number (12), then the polynomial is factorable. 36 has the multiples (6,6) which add up to 12.

Now check the symbols, if the symbol before the last number is a +, that means the two factors have the same symbol. Now see the symbol before the middle number. If its a negative, the factors would be minus as well.

x²-12x+36
(x )(x )
(x- )(x- ) Same symbol as (-)12x
(x-6)(x-6) Multiples of the last number (36)

x²-12x+36 = (x-6)(x-6)

4 0

4 years ago

A large tank is filled to capacity with 300 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into t

Gwar [14]

Answer:

(a) $A = 1500(1 - e^{-0.01t})$

(b) $t = 0$

Step-by-step explanation:

Given

$V= 300gal$ --- Volume of tank

$B = 5lb/gal$ --- Brine solution

$R_1 = 3gal/min$ --- Rate in, in gallon/min

$R_2 = 6gal/min$ --- Rate out, in gallon/min

Required

Determine A(t)

First, calculate the rate in (R in) and (R out) in lb/min

$R_{in} = B * R_1$

$R_{in} = 5lb/gal * 3gal/min$

$R_{in} = 15lb/min$

R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2

So, we have:

$R_{out} = \frac{A(t)}{300} lb/gal * 3gal/min$

$R_{out} = \frac{3*A(t)}{300} lb/min$

$R_{out} = \frac{A(t)}{100} lb/min$

The change in the amount of brin e in the tank at time t is given as:

$A'(t) = R_{in} - R_{out}$

$A'(t) = 15 - \frac{A(t)}{100}$

Rewrite:

$\frac{dA}{dt} = 15 - \frac{A}{100}$

Multiply through by dt

$dA = [15 - \frac{A}{100}]* dt$

Make dt stand alone

$\frac{dA}{15 - \frac{A}{100}} = dt$

$ln|15 - \frac{A}{100}| = -0.01t + ln\ c$

Express as exponents

$15 - \frac{A}{100} = ce^{-\frac{t}{100}}$

Multiply through by 100

$1500 - A = 100ce^{-\frac{t}{100}}$

$A = 1500 - 100ce^{-\frac{t}{100}}$

$A = 1500 - 100ce^{-0.01t}$

Apply initial conditions

$A(0) = 0$

Substitute 0 for t in: $A = 1500 - 100ce^{-0.01t}$

$0 = 1500 - 100ce^{-0.01*0}$

$0 = 1500 - 100ce^{0}$

$0 = 1500 - 100c$

$100c = 1500$

$c = 15$

Substitute 15 for c in $A = 1500 - 100ce^{-0.01t}$

$A = 1500 - 100*15e^{-0.01t}$

$A = 1500 - 1500e^{-0.01t}$

Factorize:

$A = 1500(1 - e^{-0.01t})$

How long to empty the tank

Set A to 0

$1500(1 - e^{-0.01t}) = 0$

Divide through by 1500

$1 - e^{-0.01t} = 0$

Collect Like Terms

$e^{-0.01t} = 1$

Take ln of both sides

$ln\ (e^{-0.01t}) = ln\ 1$

$-0.0t = 0$

$t = 0$

8 0

3 years ago

a rectangle is 5cm longer than its breadth, its perimeter is 26 find the length and breadth of the rectangle

xxTIMURxx [149]

If the perimeter is 26 and the length of one side of the rectangle is 5cm longer than its breadth,

26 - 5 - 5 = 16
16 / 4 = 4 ( rectangle has 4 sides. )

the breadth is 4cm.
so the length must be 4+5=9cm.

5 0

3 years ago

Remember, adjectives in Spanish agree with the gender of the noun they describe.

Zanzabum

Answer:

1) A serious girl - Una chica seria/Una joven seria

2) The talented boy - El chico talentoso/El joven talentoso

3) An outgoing girl - Una chica extrovertida/Una joven extrovertida

4) The tasty ice cream - El helado delicioso/El helado sabroso

5) A funny book - Un libro divertido/Un libro entretenido

Step-by-step explanation:

Now, we present a possible set of solution, as there are solutions as many synonyms exist in Spanish. Then:

1) A serious girl - Una chica seria/Una joven seria

2) The talented boy - El chico talentoso/El joven talentoso

3) An outgoing girl - Una chica extrovertida/Una joven extrovertida

4) The tasty ice cream - El helado delicioso/El helado sabroso

5) A funny book - Un libro divertido/Un libro entretenido

4 0

3 years ago

Find the common ratio for the geometric sequence defined by the formula: an=40(2–√)n−1