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1 year ago

Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Mathematics

2 answers:

Elden [556K]1 year ago

7 0

Answer:

( 6(x)² + 12(x) - 90 ) ft³

Explanation:

deep end water: 2(x)² + 12(x) + 10

shallow end water: 4(x)² - 100

addition problem: 2(x)² + 12(x) + 10 + 4(x)² - 100

total volume of water:

2(x)² + 12(x) + 10 + 4(x)² - 100

2(x)² + 4(x)² + 12(x) + 10 - 100

6(x)² + 12(x) - 90

ValentinkaMS [17]1 year ago

5 0

Answer:

a) $\sf total \ volume \ of \ pool= (2x^2+12x+10)+(4x^2-100) \ ft^3$

b) $\sf total \ volume \ of \ pool =(6x^2+12x-90) \ ft^3$

Step-by-step explanation:

Given:

volume of water in the deep end: $\sf (2x^2+12x+10) \ ft^3$
volume of water in the shallow end: $\sf (4x^2-100) \ ft^3$

a) Total volume of water = deep end volume + shallow end volume

$\implies \sf total= (2x^2+12x+10)+(4x^2-100)$

b) Simplify:

$\sf \implies 2x^2+12x+10+4x^2-100$

Collect like terms:

$\sf \implies 2x^2+4x^2+12x+10-100$

Combine like terms:

$\sf \implies 6x^2+12x-90$

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tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

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lapo4ka [179]

Answer:

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