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3 years ago

A liquid form of penicillin manufactured by a pharmaceutical firm is sold in bulk at a price of

1 answer:

7 0

The revenue is given by the unit price * number of units.
Profit = Revenue - Cost = 200x - 500,000 - 80x - 0.003x^2 = 120x - 500,000 - 0.003x^2
For profit to be maximum dP/dx = 0
120 - 0.006x = 0
x = 120/0.006 = 20,000

Therefore, to maximize profit, the firm should produce 20,000 penicillin.

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Which one of These is a rational number

Ainat [17]

Answer:

OPTION D: 0

Step-by-step explanation:

Rational numbers are subset of real numbers. These are the numbers that can be represented by a ratio of two integers i.e., of the form $\frac{p}{q}$ , where 'q' is non-zero. The numbers after the decimal forms a pattern. Since, 'q' can be equal to 1, we conclude all integers are rational numbers.

Irrational numbers are the numbers which cannot be represented as ratios. They can only be represented as an approximate value. The numbers after the decimal do not form a pattern.

Here, A is 11.761038... Clearly, the decimal is non-terminating and does not follow a pattern.

In Option B we have √20. √20 = √2 . √10. We know that √2 is an irrational number. So, √20 is also irrational.

In Option C, we have the famous $\pi$ . The value of $\pi$ is 3.14.... It is an irrational number. The approximate representation of $\pi$ is $\frac{22}{7}$ .

In Option D, we have 0. It is an integer. So, it is rational as well.

6 0

3 years ago

Write the equation of the line that contains the given point and has the given slope. (–1, 1), slope = –2

vichka [17]

We can write the equation in point-form in this case. The equation should be:

y-y1 = m(x-x1)

y and x can be any point in the line, so we leave them just like that in the equation, we don’t have to add any numbers to them. m is the slope of the line, and (x1, y1) is the given point in the line, which is (-1, 1) in this case.

Now, just substitute the number in,

y - 1 = -2 [x - (-1)]
y - 1 = -2 (x+1)
y - 1 = -2x - 2
2x + y + 1 = 0

So, 2x + y + 1 = 0 is your answer.

4 0

3 years ago

The original price of a skateboard was $85. The owner of the store

lora16 [44]

Answer:

$\$68$

Step-by-step explanation:

1. Approach

To solve this problem, one wants to find the price of a product after its discount has been applied. The discount is 20% off, so the new price of the item is 80% of its original price (percent is out of 100 so if a an item is 20% off, it is 100 - 20 = 80; 80% the original price). To calculate the percent cost, one would divide the percent value by 100, and then multiply it by the price of the item.

2. Solving

The price of the new item is 80% of the price of the original item. To calculate the percent cost, cent, one would divide the percent value by 100, and then multiply it by the price of the item.

Therefore, the equation that will be formed is,

$price * \frac{percent}{100}$

Substitute,

$85 * \frac{80}{100}$

Simplify,

$85 * 0.8\\\\= 68$

5 0

3 years ago

Simplify the expression: (4 + 3i)(2 – 8i).<br> 32 - 26<br> -16 + 26<br> 32 + 381<br> -16 + 38

alex41 [277]

Answer:

32-26i

Step-by-step explanation:

(4+3i)(2-8i)

8+6i-32i-24i^2

8-26i-24(-1)

8-26i+24

-26i+32

Remember that i^2=-1.

4 0

4 years ago

A 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the

ira [324]

Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.

Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.

Pythagoras theorem, $x^{2} + y^{2} = (12)^{2}$ --->(1)

Given, $\frac{dx}{dt}= 2feet/second$ at x=3

Put x=3 in Pythagoras theorem equation (1)

$(3)^{2} + y^{2} = 144$

$y^{2} = 144 - 9$

$y^{2}$ = 135

y = 11.61

Derive equation (1) w.r.t to 't'

$2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$ ---->(2)

substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

$2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0$

12 + 23.22 $\frac{dy}{dt}$ = 0

$\frac{dy}{dt}= \frac{-12}{23.22}$

$\frac{dy}{dt} = -0.518$

Hence, using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.

Learn more about Pythagoras theorem here

brainly.com/question/21511305

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5 0

2 years ago