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3 years ago

Can someone please show me the steps in finding the answers to these two problems ?

Mathematics

2 answers:

Leona [35]3 years ago

8 0

Answer:

$\displaystyle 24 = x \\ 8^{x - 1} = y$

Step-by-step explanation:

$\displaystyle [(\sqrt[3]{9})(\sqrt[3]{x})]^3 = 6^3 → 216 = 9x; 24 = x$

According to the Definition of Rational Exponents [part II], you can rewrite an exponents as radicals:

$\displaystyle \sqrt[n]{a}^m = a^{\frac{m}{n}} \\ \\ \sqrt[3]{x} = x^{\frac{1}{3}} \\ \sqrt[3]{9} = 9^{\frac{1}{3}}$

_______________________________________________

This table is in the form of a geometric sequence:

$\displaystyle a_n = a_1r^{n - 1}, where\:n\:is\:the\:common\:ratio \\ \\ y = 8^{x - 1}$

Since 8 is the common ratio, all you have to do is plug in each value from the table, into the function to confirm their authenticities.

I am joyous to assist you anytime.

ratelena [41]3 years ago

5 0

Answer:

y = 8^(x-1)
x = 24

Step-by-step explanation:

The first step is always to look at the question to see what you are given and what you are asked for. The next step is to identify the relevant relations between what you have and what you need to find.

1) You are given a sequence of (x, y) points where x increases by 1 from one point to the next, and y increases by a factor of 8. This tells you the value of y form a geometric sequence that is described by an exponential function.

The general form of the n-th term of a geometric sequence is ...

an = a1·r^(n-1)

where a1 is the value for n=1, and r is the common ratio.

If this were a geometric sequence, we could write the general term using a1=1 and r=8:

an = 1·8^(n-1)

Instead, this is a relation between x and y. It is the same relation as for the geometric sequence, but with different variable names. We have y instead of an, and we have x instead of n. So, the equation is ...

y = 8^(x -1) . . . . . . . or . . y = (1/8)8^x

2) This equation is of the form ...

k·∛x = 6

Since k is also a cube root, it is easiest to cube both sides of the equation:

9x = 6³ = 216

Now, you can divide by 9 to find x:

x = 216/9

x = 24

You might be interested in

Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame

lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678$

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{207.9 - 208}{0.1678}$

$Z = -0.6$

$Z = -0.6$ has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

6 0

3 years ago

2. A soccer field is bordered on three sides by a parking lot of width x. The total

notsponge [240]

Answer: 50m

Step-by-step explanation:

this is the logical way I solved it:

1. Find the area of the entire area thing

300*200=60000

2. Subtract the area of the field from the area of the entire place

60000-30000=30000

3. Divide the area of the parking by three because there are three sides

30000 ÷ 3 = 10000

4. Divide 10000 by 200, not 300 because we want to find the side with one x, not two x (there are two sides adding on to the side with 300, but only one side on the side with 200)

10000÷200= 50

I know the steps are weird, but I know this is the right answer because this was on the unit test (same misspelling and everything lol) and during tutoring my teacher showed me how to do it, but of course I had to forget the steps.

4 0

3 years ago

If the trapezoid on the grid below is translated by using the rule (x,y)-> (x-4,y-3) what will be the coordinates of B’?

vesna_86 [32]

Answer:

B'(3, 5)

Step-by-step explanation:

Rule for the translation of a point (x, y) by 'h' units left and 'k' units upwards,

(x, y) → (x - h, y + k)

If h = 4 and k = 3,

$(x, y)\rightarrow(x-4,y+3)$

Following this rule coordinates of the image point of B will be,

B(7, 2) → B'(7 - 4, 2 + 3)

→ B'(3, 5)

Therefore, coordinates of the image point B' will be,

B'(3, 5)

6 0

3 years ago

What is 12.496 rounded to a whole number. what is 2.90 rounded to a whole number

otez555 [7]

A whole number is a number that is whole as in 1,2,3,4,etc, they don’t have decimals. To find the whole number for these questions you must look at the places (hundreds, thousands, ten thousands.) I was always told a trick which is 4 or less let it rest, 5 or more let it sore. (Basically if it’s less than 4 then decrease it, if it’s higher than increase it.)

12.496 = 13
2.90 = 3

Your answers are 13 and 3.

7 0

3 years ago

Read 2 more answers

Y=[[x]] evaluate this function at x=3

dedylja [7]

Step-by-step explanation:

Solution

y=[[x]], at x=3,

therefore the function of y = 3

you can merge 3,3

7 0

3 years ago