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3 years ago

For what value of x does 3^2x=9^3x-4

Mathematics

2 answers:

AVprozaik [17]3 years ago

8 0

ANSWER

The value of x for which
${3}^{2x} = {9}^{3x - 4}$
is
$x = 2$

EXPLANATION

The given equation is
${3}^{2x} = {9}^{3x - 4} .$
This is an indicial equation or an exponential equation in x.

We can see that, this time, the variable is in the numerator.

So we need to express both sides of the equation to the same base to obtain,

${3}^{2x} = { 3 }^{2(3x - 4)}$

Since the base are the same, we can now equate the exponents to get,

$2x = 2(3x - 4)$

When we divide both sides of the equation by 2, we obtain,

$x = 3x - 4$

We now group like terms to obtain,

$x - 3x = - 4$

We simplify the left hand side to get,

$- 2x = - 4$

We finally divide through by negative 2 to obtain,

$x = 2$
Therefore the correct answer is B.

jek_recluse [69]3 years ago

4 0

The answer is x=2. Hope this helps!!!

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A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For ex

avanturin [10]

Answer:

Check Explanation

Step-by-step explanation:

The days of the week include

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

a) So, the possible letters to be taught include

A, D, E, F, H, I, M, N, O, R, S, T, U, W, Y

There are indeed 15 possible letters.

These are the letters from which all the days of the week are formed from.

b) There are more than 4 letters that can't be taught using this method.

All the letters that cannot be taught using this method because no day of the week contains them include

B, C, G, J, K, L, P, Q, V, X, Z

c) In Tuesday, there are 7 distinct letters.

So, the sample space consist of 7 letters.

n(sample space) = 7

n(Y) = 1

Probability of picking a Y = (1/7)

The reasoning is simple, picking a Y on a Tuesday is one out of 7 possible outcomes, so, the probability of picking a Y on a Tuesday to teach the kid about = (1/7) = 0.143

Hope this Helps!!!

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3 years ago

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Alex777 [14]

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4 years ago

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Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1,

sweet [91]

Answer:

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

$f'' = x - \frac{3}{2}$

$f' = \int {\left(x-\frac{3}{2}\right) } \, dx$

$f' = \int {x} \, dx -\frac{3}{2}\int \, dx$

$f' = \frac{1}{2}\cdot x^{2} - \frac{3}{2}\cdot x + C$ , where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative ( $f'(4) = 1$ ):

$1 = \frac{1}{2}\cdot 4^{2} - \frac{3}{2}\cdot (4) + C$

$C = 1 - \frac{1}{2}\cdot 4^{2} + \frac{3}{2}\cdot (4)$

$C = -1$

The first derivative is $y' = \frac{1}{2}\cdot x^{2}- \frac{3}{2}\cdot x - 1$ , and the particular solution is found by integrating one more time and using the initial condition ( $f(0) = 0$ ):