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3 years ago

Find the 8th Term for the Geometric Sequence for which a1 - 3 and r = -2

Mathematics

1 answer:

Firdavs [7]3 years ago

4 0

Answer:

-384

Step-by-step explanation:

geometric sequence : every new element is generated by multiplying the previous element always with the same number r.

a(n) = a(n-1) * r

a(n) = a(1) * r^(n-1)

so, a(1) = 3, r = -2

a(8) = ?

a(8) = a(1) * r^7 = 3 * (-2)^7

a negative number to an uneven power is again a negative number.

so, (-2)^7 = -128

3 * -128 = -384 = a(8)

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Solve the Differential equation (x^2 + y^2) dx + (x^2 - xy) dy = 0

natita [175]

Answer:

$\frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C$

Step-by-step explanation:

Given differential equation,

$(x^2 + y^2) dx + (x^2 - xy) dy = 0$

$\implies \frac{dy}{dx}=-\frac{x^2 + y^2}{x^2 - xy}----(1)$

Let y = vx

Differentiating with respect to x,

$\frac{dy}{dx}=v+x\frac{dv}{dx}$

From equation (1),

$v+x\frac{dv}{dx}=-\frac{x^2 + (vx)^2}{x^2 - x(vx)}$

$v+x\frac{dv}{dx}=-\frac{x^2 + v^2x^2}{x^2 - vx^2}$

$v+x\frac{dv}{dx}=-\frac{1 + v^2}{1 - v}$

$v+x\frac{dv}{dx}=\frac{1 + v^2}{v-1}$

$x\frac{dv}{dx}=\frac{1 + v^2}{v-1}-v$

$x\frac{dv}{dx}=\frac{1 + v^2-v^2+v}{v-1}$

$x\frac{dv}{dx}=\frac{v+1}{v-1}$

$\frac{v-1}{v+1}dv=\frac{1}{x}dx$

Integrating both sides,

$\int{\frac{v-1}{v+1}}dv=\int{\frac{1}{x}}dx$

$\int{\frac{v-1+1-1}{v+1}}dv=lnx + C$

$\int{1-\frac{2}{v+1}}dv=lnx + C$

$v-2ln(v+1)=lnx+C$

Now, y = vx ⇒ v = y/x

$\implies \frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C$

5 0

3 years ago

-1/9+-5/9=<br> Simplest form<br> 24 points

Nataly [62]

-1/9+-5/9=

When you are adding a negative number, the operation turns into subtraction:

-1/9-5/9= $\frac{-1-5}{9}$ $=-\frac{6}{9}=-\frac{2}{3}$

Really, it's just subtraction. The simplest form is -2/3, which is equal to -0.66667.

I hope this helps :)

5 0

3 years ago

Read 2 more answers

Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x re

Veronika [31]

Answer:

The equations which represents the situation are

1) 2Y+X=5

2) 5X-Y=3

Step-by-step explanation:

<em>~Cornasha_Weeb</em>

3 0

3 years ago

A set of 3 pens costs $1.68. At that unit price, how much would one pen cost?

Tanzania [10]

Answer:

$.56

Step-by-step explanation:

To find the cost of one pen, take the total cost and divide by the number of pens

$1.68/ 3

$.56 per pen

8 0

2 years ago

It was found that an unknown solid had a density of 20 g/cm3 and a volume of 30 cm3. Determine the mass of the solid.

In-s [12.5K]

Answer:

Step-by-step explanation:

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3 years ago