1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Arlecino [84]
3 years ago
12

Tom, Larry, Roberta, and John enjoy roller Coasters. Whenever a new roller Coaster opens near their town,

Mathematics
1 answer:
vazorg [7]3 years ago
5 0

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.

You might be interested in
Valentina has a tray where she keeps all of her important papers. The tray is in the shape of a rectangular prism with no top.
Alchen [17]
The answer is 300 as 2.5x10x12=300
6 0
3 years ago
Read 2 more answers
PLEASE HELP I BEG YOU I REALLY NEED HELP FEW QUESTIONS :(
pantera1 [17]
Number 2 for question 1 and number 4 for question 2
6 0
3 years ago
The virus is already 28% loaded. If it's loading at a rate of 12% every 10 minutes, how much time do we have before it is 100% l
KIM [24]
You will have 40 minutes before it it’s 100% loaded
4 0
2 years ago
Cos^2x+cos^2(120°+x)+cos^2(120°-x)<br>i need this asap. pls help me​
o-na [289]

Answer:

\frac{3}{2}

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

                   = - cos60cosx - sin60sinx

                   = - \frac{1}{2} cosx - \frac{\sqrt{3} }{2} sinx

squaring to obtain cos² (120 + x)

= \frac{1}{4}cos²x + \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

                   = -cos60cosx + sin60sinx

                   = - \frac{1}{2}cosx + \frac{\sqrt{3} }{2}sinx

squaring to obtain cos²(120 - x)

= \frac{1}{4}cos²x - \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + \frac{1}{4}cos²x + \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x + \frac{1}{4}cos²x - \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

= cos²x + \frac{1}{2}cos²x + \frac{3}{2}sin²x

= \frac{3}{2}cos²x + \frac{3}{2}sin²x

= \frac{3}{2}(cos²x + sin²x) = \frac{3}{2}

                 

5 0
3 years ago
How do I find 3/4 as a fraction
antiseptic1488 [7]
Divide 3 by for to get 0.75 but that is a fraction
5 0
3 years ago
Read 2 more answers
Other questions:
  • Use the distributive property to find the product mentally. Show the steps you used.
    10·1 answer
  • Which is better buy, 6 bagels for 3.29 or 8 bagels for 4.15?
    13·2 answers
  • Every month, a group of 46 students write essays in a class. Each student writes 2 essays, and each essay
    8·2 answers
  • What is 389/1000 converted into a decimal
    12·2 answers
  • A Playstation costs 500 dollars but I only want to pay 450 dollars. How much discount (percent) would I want?
    9·1 answer
  • I need help PLz what is 7/985 I will mark Brainlist to first person that answer.!!!!
    14·2 answers
  • What does the expression x ≤ 4 mean in word form?
    10·2 answers
  • Three numbers add up to 27. The third number is twice the second number. The first number minus the third number is equal to 2.
    8·1 answer
  • Simplify 5a×3×2b<br><br> Write down the answer, please.
    7·1 answer
  • Logan is trying to pick out an outfit for the first day of school. He can choose from 2
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!