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3 years ago

Do 3/7and7/3 represent the same length on a number line?

1 answer:

8 0

Nope. 3/7 is less than 7/3. 7/3 in mixed numbers form is 2 1/3. Therefore, we will have different lengths where 3/7 will be smaller than 7/3.

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find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu

topjm [15]

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

$\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}$

Now, differentiate P with respect to x, and we get,

$\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}$

Solving the above equation to zero, we get,

$\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}$

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

$\begin{aligned}y&=108-36\\y&=72\end{aligned}$

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

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4 0

11 months ago

What is 1/5 of 11????????????

Helga [31]

Multiply 1/5 by 11 to get 2.2, to check, multiply 2.2 by 5. The answer though, is 2.2.

7 0

3 years ago

If i make 1.5 million dollars per day, plus an extra 250k interest every 31 hours, how much money do i make per day?

lidiya [134]

Answer: Alot

Step-by-step explanation:

4 0

3 years ago

A firm has a fixed cost of $500 in its first year of operation. When the firm produces 100 units of output, its total costs are

HACTEHA [7]

Answer:

option (a) $250

Step-by-step explanation:

Data provided in the question:

Fixed cost = $500

For 100 units produced Total cost = $3,500

For 101 units produced, Total cost = $3,750

Now,

Marginal cost is calculated as:

Marginal cost = $\frac{\textup{Total change in cost of producing more goods}}{\textup{Total change in produced goods}}$

thus,

Marginal cost = $\frac{\textup{Total cost of 101 units - Total cost of 100 units}}{\textup{101-100}}$

Marginal cost = $\frac{\textup{3,750-3,500}}{\textup{1}}$

Marginal cost = $250

Hence,

The correct answer is option (a) $250

7 0

2 years ago

Which of the following statements about diversification is correct

Luba_88 [7]

Diversification means wide variety of different investment options available in the portfolio so that it becomes lesser risky towards minimizing losses in down market.

It provides better protection towards common issues like inflation, market instability, war effects, hike in exchange rates, interest rates reduction etc. So, we can conclude that :-

Diversification is the method to make investments less vulnerable to a catastrophic loss.

Hence, option A is best answer from given choices.

7 0

3 years ago