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steposvetlana [31]
2 years ago
14

Explain the special pattern for sketching a parabola

Mathematics
1 answer:
Lady bird [3.3K]2 years ago
8 0

Answer:

the parabola can be written as:

f(x) = y = a*x^2 + b*x + c

first step.

find the vertex at:

x  = -b/2a

the vertex will be the point (-b/2a, f(-b/2a))

now, if a is positive, then the arms of the parabola go up, if a is negative, the arms of the parabola go down.

The next step is to see if we have real roots by using the Bhaskara's equation:

x =  \frac{-b +-\sqrt{b^2 -4ac} }{2a}

Now, draw the vertex, after that draw the values of the roots in the x-axis, and now conect the points with the general draw of the parabola.

If you do not have any real roots, you can feed into the parabola some different values of x around the vertex

for example at:

x =  (-b/2a) + 1 and x =  (-b/2a) - 1

those two values should give the same value of y, and now you can connect the vertex with those two points.

If you want a more exact drawing, you can add more points (like x =  (-b/2a) + 3 and x =  (-b/2a) - 3) and connect them, as more points you add, the best sketch you will have.

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22. Use your model to determine when the volume of oil will get down to 500 gallons.
Helen [10]

Answer:

  21.  y = 75000·0.935^t

  22.  after 74.6 days

  23.  y = 27.8112·1.18832^t

  24.  18.8% per month

  25.  1748

Step-by-step explanation:

22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)

__

23. y = 27.8112·1.18832^t (see the second attachment)

__

24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.

  (1.18832 -1) × 100% ≈ 18.8% . . . . per month

__

25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.

_____

<em>Comment on graphing calculator</em>

A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.

8 0
3 years ago
I WILL MARK BRAINLIST!!
Soloha48 [4]

Answer:

For (2x^2 + 8x - 8), the group is CLOSED as it a polynomial.

Step-by-step explanation:

Here, the given polynomials are:

P(x)=(5x^2+2x-6)\\Q(x)=(3x^2-6x+2)

Now, a group G is said to be <u>CLOSED UNDER SUBTRACTION</u> if,

a and b are he elements of G ⇒ (a-b) is ALSO AN ELEMENT of G

Now, here:

R(x)  = P(x) - Q(x) = (5x^2+2x-6) - (3x^2-6x+2) = (2x^2 + 8x - 8)

or, R(x)  = (2x^2 + 8x - 8)

Also, R(x) is a POLYNOMIAL.

So, R(x) is an Element of group G.

So, the set G of polynomials.

Hence, for the polynomial  (2x^2 + 8x - 8), it will be a polynomial the group is CLOSED.

3 0
3 years ago
Read 2 more answers
What are the answers?
sattari [20]

Answer:

1. yes

2. yes

3. no

4. no

Step-by-step explanation:

Replace x by each value of x.

x+32>44

1. yes

14+32>44\\46>44

2. yes

17+32>44\\49>44

3. no

7+32>44\\39>44

4. no (this is not a solution because the value must be greater than 44 not equal to)

12+32>44\\44>44

5 0
3 years ago
Read 2 more answers
A cylindrical tank with a radius of 12 inches and a height of 20 inches is full of water. Does the tank have enough water to fil
Reptile [31]

Answer:

Yes, it can.

Step-by-step explanation:

To know if you can fill all the water balloons with the tank, the first thing is to calculate the volume of each one.

Volume of the tank, is a cylinder, whose volume is given as follows:

Vc = Pi * Rc ^ 2 * h

 

The radius of the cylinder has a value of 12 inches and the height of 20 inches. Thus:

Vc = 3.14 * (12) ^ 2 * 20 = 9043.2 inches ^ 3

Now, the volume of each globe that is a sphere is given by the following equation:

Ve = (4/3) * Pi * Re ^ 3

Being the radius of the sphere of 2, we have to:

Ve = (4/3) * 3.14 * 2 ^ 3 = 33.5 inches ^ 3

Now to know if you can fill all the balloons, we calculate the volume ratio of the tank and a balloon.

Vc / Ve = 9043.2 /33.5 = 269.95

Therefore, it can fill the 250 balloons because it has the capacity to carry approximately 269 balloons.

8 0
2 years ago
Read 2 more answers
How do you find the remaining side of a 45°-45°-90° triangle if the longest side is 28?
Irina-Kira [14]

Here you go! Hope this helps

3 0
2 years ago
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