All categories

3 years ago

The volume of a swimming pool is 4x^3 - 20x^2 + 3x - 15 . what is one of the dimensions of the pool

Mathematics

1 answer:

maxonik [38]3 years ago

5 0

Answer:

$Height = x - 5$ --- one of the dimension

Step-by-step explanation:

Given

$Volume = 4x^3 - 20x^2 + 3x - 15$

Required

The side dimension

Factorize the given expression

$Volume = 4x^2 (x- 5) + 3(x - 5)$

Factor out x - 5

$Volume = (4x^2 + 3)(x - 5)$

Volume is the product of base area and height'

Hence:

$Area = 4x^2 + 3$

$Height = x - 5$

You might be interested in

Please help me- thank you

Kruka [31]

Answer:

a) The profit will be: $Profit=y^2-99500$

b) Since the profit is -9500 (negative) so, company will not gain any profit if they produce 300 bicycles.

Step-by-step explanation:

Cost of Bicycles= $y^2+10y+100,000$

Revenue generated = $2y^2+10y+500$

Find a polynomial that represent profits

The formula used for finding profit is:

$Profit = Total \ Revenue - Total \ Cost\\Profit= 2y^2+10y+500 - (y^2+10y+100,000)\\Profit= 2y^2+10y+500 - y^2-10y-100,000\\Profit=2y^2-y^2+10y-10y+500-100,000\\Profit=y^2-99500$

So, the profit will be: $Profit=y^2-99500$

If the company can produce bicycles y= 300

The profit will be:

$Profit=y^2-99500\\Profit=(300)^2-99500\\Profit=90000-99500\\Profit=-9500$

Since the profit is -9500 (negative) so, company will not gain any profit if they produce 300 bicycles.

5 0

3 years ago

A pond has 150 fish and the population decreases by 8% each day. How many days before there are 30 fish

nlexa [21]

Answer:

19 days

Step-by-step explanation:

Given

$a = 150$ --- initial

$r = 8\%$ -- rate

Required

Days when the fish gets to 30

The function is exponential and as such it follows;

$y = ab^x$

Where x represents the number of days and y the number of fishes

Because the fishes decreases;

$b = 1 - r$

So, we have:

$b = 1 - 8\%$

Express as decimal

$b = 1 - 0.08$

$b = 0.92$

In $y = ab^x$

$a =150$

$y = 30$

$b = 0.92$

So, we have:

$30 = 150 * 0.92^x$

Divide both sides by 150

$0.2 = 0.92^x$

Take log of both sides

$log(0.2) = log(0.92^x)$

Apply law of logarithm

$log(0.2) = x\ log(0.92)$

Make x the subject

$x = \frac{log(0.2)}{log(0.92)}$

$x = \frac{-0.6990}{-0.0362}$

$x = 19.309$

$x \approx 19$

<em>Hence, it takes approximately 19 days</em>

3 0

3 years ago

Is 1\8 equivalent to 4\32

Klio2033 [76]

Yes it is, 8•3 is 32

4 0

3 years ago

Jose had 4 times as many trading cards as Philippe. After Jose gave away 50 cards to his little brother and Philippe gave 5 card

tensa zangetsu [6.8K]

Answer:

Jose had 60 cards

Phillipe had 15 cards

Step-by-step explanation:

Let the number of trading cards Phillipe had be x. Jose had 4 times, meaning he has 4x of these cards.

Jose gave away 50 cards while Phillipe gave away 5 cards to make their numbers equal.

Mathematically:

4x - 50 = x - 5

3x = 45

x = 45/3 = 15

Phillipe had 15 cards while Jose had 15(4) = 60 cards

5 0

3 years ago

Write a linear function f with f(−10)=4 and f(−2)=4.

Orlov [11]

f(-10) = 4

f(-2) = 4

Since y is constant while x isnt we just dont need to put x

f(x) = 4

6 0

4 years ago