Given that 1/(3^x) = 0.2 Find the value of (3^4)^x

Gekata [30.6K]

Answer:

$\large\boxed{\dfrac{\boxed{8}}{81}}$

Step-by-step explanation:

$\text{If}\ a_1,\ a_2,\ a_3,\ a_4,\ ...,\ a_n\ \text{is the geometric sequence, then}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=constant=r-\text{common ration}.\\\\\text{We have}\ \dfrac{1}{2},\ \dfrac{1}{3},\ \dfrac{2}{9},\ \dfrac{4}{27},\ ...\\\\\dfrac{\frac{1}{3}}{\frac{1}{2}}=\dfrac{1}{3}\cdot\dfrac{2}{1}=\dfrac{2}{3}\\\\\dfrac{\frac{2}{9}}{\frac{1}{3}}=\dfrac{2}{9}\cdot\dfrac{3}{1}=\dfrac{2}{3}\\\\\dfrac{\frac{4}{27}}{\frac{2}{9}}=\dfrac{4}{27}\cdot\dfrac{9}{2}=\dfrac{2}{3}$

$\bold{CORRECT}\\\\\dfrac{x}{\frac{4}{27}}=\dfrac{2}{3}\qquad\text{multiply both sides by}\ \dfrac{4}{27}\\\\x=\dfrac{2}{3}\cdot\dfrac{4}{27}\\\\x=\dfrac{8}{81}$

8 0

3 years ago

Eight and one-half years ago, steven was 7 years old.how old is he now?

shusha [124]

14 or 15 either of these

5 0

3 years ago

Read 2 more answers

A bag contains 7 red marbles, 8 blue marbles and 4 green marbles. If three marbles

dybincka [34]

Answer:

Step-by-step explanation:

A bag contains 8 red marbles, 3 blue marbles and 7 green marbles.

Total = 18 marbles.

Probability of drawing three red marbles = probability of drawing one red without replacement + probab of drawing another without reeplacement + probab of drawing a third without replacement.

Probability of drawing three red marbles = 8/18 + 7/17 + 6/16 = 0.4444 + 0.4118 + 0.3750 = 1.2312.

6 0

3 years ago

What is the solution to the equation P = 2L + 2w when solved for w?

ira [324]

Answer: w=(P - 2L)/2

Step-by-step explanation:

P=2L+2W

P - 2L=2W

Divide both sides by 2

(P - 2L)/2=2W/2

(P - 2L)/2=W

W=(P - 2L)/2

8 0

3 years ago

Find product of :(2x-y)(2x+3y).

Ierofanga [76]

Answer: 4x² + 4xy - 3y²

Concept:

When encountering questions that ask for simplifying algebraic expressions, using the FOIL method would be easier:

First, which means multiplying the first terms together;
Outer, which means that we multiply the outermost terms when the binomials are placed side by side;
Inner, which means multiply the innermost terms together;
Last, which means that we multiply the last term in each binomial together.

Solve:

Given

(2x - y) (2x + 3y)

Expand parentheses and apply the FOIL method

=4x² + 6xy - 2xy - 3y²

Combine like terms

=4x² + (6xy - 2xy) - 3y²

= $\boxed{4x^2+4xy-3y^2}$

Hope this helps!! :)

Please let me know if you have any questions

7 0

3 years ago