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n200080 [17]
3 years ago
14

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

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A 2000-gallon metal tank to store hazardous materials was bought 15 years ago at cost of $100,000. What will a 5,000-gallon tank
harkovskaia [24]

Answer:

The value  is P_o = \$ 561958.9

Step-by-step explanation:

From the question we are told that

  The capacity of the metal  tank is  C =  2000 \  gallon

   The duration usage is  t = 15\ years \ ago

   The cost of 2000-gallon tank 15 years ago is P =  \$100,000

    The capacity of the second tank considered is C_1 = 5,000  

    The power sizing exponent is e = 0.57

     The initial construction cost index is  u_1 = 180

      The new construction after 15 years cost index is  u_2 =600

Equation for the power sizing exponent is mathematically represented as

      \frac{P_n}{P} = [\frac{C_1}{C} ]^{e}

=> Here P_n is the cost of 5,000-gallon tank as at 15 years ago  

So

     P_n  =  [\frac{5000}{2000} ] ^{0.57} * 100000

      P_n  =  \$168587.7

Equation for the cost index exponent is mathematically represented as

      \frac{P_o}{P_n}  =  \frac{u_2}{u_1}

HereP_o is the cost of 5,000-gallon tank today

So

       \frac{P_o}{168587.7}  =  \frac{600}{180}

=>    P_o = \frac{600}{180} * 168587.7

=>      P_o = \$ 561958.9

8 0
3 years ago
Need help understanding this please
castortr0y [4]

Answer:

G

Step-by-step explanation:

6 0
3 years ago
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