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Kamila [148]
3 years ago
5

16 gallons of water are used to completely fill 5 fish tanks. If each tank holds the same amount of water, how many gallons will

each tank hold?
Mathematics
1 answer:
____ [38]3 years ago
3 0
Each tank holds 3.2 gallons of water
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Tom, Larry, Roberta, and John enjoy roller Coasters. Whenever a new roller Coaster opens near their town,
vazorg [7]

Answer:

  • <u>a) degree 3</u>
  • <u>b) 3 times</u>
  • <u>c) cubic</u>

<u></u>

Explanation:

The function that represents the first drop of the roller coaster is:

       h(t)=t^3-12t^2+35t,

where t is the  time in seconds and h is the height in feet.

<u></u>

<u>a) What is the degree of the function?</u>

The degree of a polynomial is the highest power of the variable, t. Thus, the degree of the function is 3.

<u>b) According to the degree of the function, how many times should the roller coaster hit the ground?</u>

The number of complex roots of a polynomial is equal to the degree of the polynomial. Thus, in this case this polynomial has 3 roots. Each root represents the value of the polynomial that makes it equal to zero, this is:

     t^3-12t^2+35t=0

Thus, since the polynomial function represents the height of the, the value zero represents when the roller coaster hits the ground.

To learn if the three roots are real numbers you can solve the equation, which may be done by factoring the polynomial.

Take t out as common factor:

  • t(t² - 12t + 35)

Find two numbers that add up -12 and its product is 35. Those are -7 and -5. Hence, use the factors t - 12 and t - 5:

  • t ( t - 12) (t - 5) = 0  This is the factored form of the polynomial

Whose solutions are t =0, t = 12, and t = 5. Three real numbers.

Hence, the roller coaster hits the ground three times: first at start, then  at 5 seconds, and finally at 12 seconds.

<u>c) Will the roller coaster be in the form of a linear, quadratic, cubic or quartic graph?</u>

It will be in the form of a cubic graph, becasue a linear graph corresponds to a polynomial of degree 1, a quadratic graph corresponds to a polynomial of degree 2, a cubic graph corresponds to a polynomial of degree 3, and a quartic graph corresponds to a polynomial of degree 4.

5 0
3 years ago
Raymond is four times as old as christine plus 5 years.Write an algebraic expression for Raymonds age in terms of christine age
igor_vitrenko [27]

Answer:

4c + 5 = R

Step-by-step explanation:

This should help you

8 0
3 years ago
Which of the following is equivalent to sin theta csc(–theta) wherever sin theta csc(–theta) is defined?
Firlakuza [10]
sin\theta csc(-\theta)=sin\theta\cdot\frac{1}{sin(-\theta)}=sin\theta\cdot\frac{1}{-sin\theta}=\frac{1}{-1}=-1\\\\Answer:F
3 0
3 years ago
The perimeter of the polygon is 36 in. What is the length of side z?<br> any one for 20pt
Reil [10]

Answer:

brqnficojeuiyrjnxsoihgfyufhrbjenfrvbwejifwhbfuiwebf

Step-by-step explanation:

7 0
2 years ago
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
nlexa [21]

Answer:

190 ft^2

Step-by-step explanation:

So first we need to find which equation we're using and since it's a rectangular prism we're going to use:

2Lw + 2wh + 2Lh

Now what we need to do is plug in the values

2*9*2 + 2*2*7 + 2*9*7

Now just multiply everything and then add it together.

36 + 28 + 126

Once you add everything together you get:

190

The question says to include the correct unit. It says that its feet, but we need to know if its feet squared (^2) or cubed (^3)

If it were area of the whole object, it would be cubed because it is all the area that the object takes up but since it's just the area of the surface it's going to be squared. Therefore, the answer is:

190 ft^2

4 0
3 years ago
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