can put $11 of his allowance and in his savings account every week call how much money will he have after 15 weeks

If 18√8 - 8 √18 = √n, what is n?

Yuliya22 [10]

Answer:

n=288

Step-by-step explanation:

Rewrite the equation as

√

n

=

18

√

8

−

8

√

18

.

√

n

=

18

√

8

−

8

√

18

To remove the radical on the left side of the equation, square both sides of the equation.

√n

2

=

(

18

√

8

−

8

√

18

)

2

Simplify each side of the equation.

Use

n

√

a

x

=

a

x

n

to rewrite

√

n as n

1

2

.

(

n

1

2

)

2

=

(

18

√

8

−

8

√

18

)

2

Simplify

(

n

1

2

)

2

.

Multiply the exponents in

(

n

1

2

)

2

.

Apply the power rule and multiply exponents,

(

a

m)n

=

a

m

n

.

n

1

2

⋅

2

=

(

18

√

8

−

8

√

18

)

2

Cancel the common factor of 2

Cancel the common factor.

n

1

2

⋅

2

=

(

18

√

8

−

8

√

18

)

2

Rewrite the expression.

n

1

=

(

18

√

8

−

8

√

18

)

2

Simplify.

n

=

(

18

√

8

−

8

√

18

)

2

Simplify

(

18

√

8

−

8

√

18

)

2

Simplify each term.

Rewrite

8 as 2

2

⋅

2

.

Factor

4 out of 8

n

=

(

18

√

4

(

2

)

−

8

√

18

)

2

Rewrite

4 as 2

2

n

=

(

18√

2

−

8

√

18

)

2

Pull terms out from under the radical.

n

=

(

18

(

2

√

2

)

−

8

√

18

)

2

Multiply

2 by 18

n

=

(

36

√

2

−

8

√

18

)

2

Rewrite

18

as

3

2

⋅

2

.

Factor

9

out of

18

.

n

=

(

36

√

2

−

8

√

9

(

2

)

2

Rewrite

9

as

3

2

.

n

=

(

36

√

2

−

8

√

3

2

⋅

2

)

2

Pull terms out from under the radical.

n

=

(

36

√

2

−

8

(

3

√

2

)

2

Multiply

3

by

−

8

.

n

=

(

36

√

2

−

24

√

2

)

2

Simplify terms.

Subtract

24

√

2

from

36

√

2

.

n

=

(

12

√

2

)

2

Simplify the expression.

Apply the product rule to

12

√

2

.

n

=

12

2

√

2

Raise

12

to the power of

2

.

n

=

144

√

2

Rewrite

√

2

as

2

.

Use

n

√

a

x

=

a

x

n

to rewrite

√

2

as

2

1

2

.

n

=

144

(

2

1

2

)

2

Apply the power rule and multiply exponents,

(

a

m

)

n

=

a

m

n

.

n

=

144

⋅

2

1

2

⋅

2

Combine

1

2

and

2

.

n

=

144

⋅

2

Cancel the common factor of

2

.

Cancel the common factor.

n

=

144

⋅

2

Rewrite the expression.

n

=

144

⋅

2

1

Evaluate the exponent.

n

=

144

⋅

2

Multiply

144

by

2

.

n

=

288

5 0

3 years ago

Please help math !!!!!!

Andrews [41]

I think it’s the second choice

3 0

3 years ago

Read 2 more answers

HELP PLEASE!

NeTakaya

Answer:5×4×9/9 +(9(4))

=180/9 + (36)

= 20+36

=56

Thank You

5 0

3 years ago

Read 2 more answers

D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$