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lisabon 2012 [21]
3 years ago
12

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

Mathematics
2 answers:
luda_lava [24]3 years ago
6 0
It's D I took the test
9966 [12]3 years ago
5 0

For this case we have that the following function complies with the given conditions:

f (x) = 3x ^ 2 - 15x + 12

To prove it, let's find the roots of the polynomial:

3x ^ 2 - 15x + 12 = 0

By doing common factor 3 we have:

3 (x ^ 2 - 5x + 4) = 0

Factoring the second degree polynomial we have:

3 (x-1) (x-4) = 0

Then, the solutions are:

Solution 1:

x-1 = 0\\x = 1

Solution 2:

x-4 = 0\\x = 4

Answer:

A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is:

f (x) = 3x ^ 2 - 15x + 12

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This is a 3 part 1 question each part on how to locate the plane and a small explanation report working out the recovery details
sesenic [268]

Third leg.

The crew flies at a speed of 560 mi/h in direction N-20°-E.

The wind has a speed of 35 mi/h and a direction S-10°-E.

We then can draw this as:

We have to add the two vectors to find the actual speed and direction.

We will start by adding the x-coordinate (W-E axis):

\begin{gathered} x=560\cdot\sin (20\degree)+35\cdot\sin (10\degree) \\ x\approx560\cdot0.342+35\cdot0.174 \\ x\approx191.53+6.08 \\ x\approx197.61 \end{gathered}

and the y-coordinate (S-N axis) is:

\begin{gathered} y=560\cdot\cos (20\degree)-35\cdot\cos (10\degree) \\ y\approx560\cdot0.940-35\cdot0.985 \\ y\approx526.23-34.47 \\ y\approx491.76 \end{gathered}

Then, the actual speed vector is v3=(197.61, 491.76).

The starting location for the third leg is R2=(216.66, 167.67) [taken from the previous answer].

Then, we have to calculate the displacement in 20 minutes using the actual speed vector.

We can calculate the movement in each of the axis. For the x-axis:

\begin{gathered} R_{3x}=R_{2x}+v_{3x}\cdot t \\ R_{3x}=216.66+197.61\cdot\frac{1}{3} \\ R_{3x}=216.66+65.87 \\ R_{3x}=282.53 \end{gathered}

NOTE: 20 minutes represents 1/3 of an hour.

We can do the same with the y-coordinate:

\begin{gathered} R_{3y}=R_{2y}+v_{3y}\cdot t \\ R_{3y}=167.67+491.76\cdot\frac{1}{3} \\ R_{3y}=167.67+163.92 \\ R_{3y}=331.59 \end{gathered}

The final position is R3 = (282.53, 331.59).

To find the distance from the origin and direction, we transform the cartesian coordinates of R3 into polar coordinates:

The distance can be calculated as if it was a right triangle:

\begin{gathered} d^2=x^2+y^2_{} \\ d^2=282.53^2+331.59^2 \\ d^2=79823.20+109951.93 \\ d^2=189775.13 \\ d=\sqrt[]{189775.13} \\ d\approx435.63 \end{gathered}

The angle, from E to N, can be calculated as:

\begin{gathered} \tan (\alpha)=\frac{y}{x} \\ \tan (\alpha)=\frac{331.59}{282.53} \\ \tan (\alpha)\approx1.1736 \\ \alpha=\arctan (1.1736) \\ \alpha=49.56\degree \end{gathered}

If we want to express it from N to E, we substract the angle from 90°:

\beta=90\degree-\alpha=90-49.56=40.44\degree

Answer: the final location can be represented with the vector (282.53, 331.59).

1) The distance from the origin is 435.63 miles and

2) the direction is N-40°-E.

7 0
1 year ago
Mr. Gonzales is replacing a cylindrical air-conditioning duct. He estimates the radius of the duct by folding a ruler to form tw
GalinKa [24]

Answer:

  • <em><u>5.6875 in</u></em>

Explanation:

At the point of tangency, the <em>tangent </em>to a circle and the <em>radius</em> form a right triangle (the radius is perpendicular to the tangent).

Here you are given the length of the tangent (6in), and the distance from the bisected vertex to the circle (2.75 in)

I tried to upload the drawing but the tool is not allowing it now.

In the figure:

  • The length of the tangent (6 in) is one leg of the triangle
  • The distance from vertex and the circle (2.75in)  along with the radius forms the hypotenuse of the right triangle: 2.75 + r.
  • The other leg is the radius, r.

Then, you can use Pythagorean theorem:

  • (r)² + (6)² = (r +2.75)²

Solve:

  • r² + 36 =  r² + 5.5r + 7.5625
  • 5.5r = 36 - 7.5625
  • 5.5r = 28.4375
  • r = 5.6875

The solution is in inches: r = 5.6875 inches ← answer

4 0
3 years ago
PLEASE LED ME THE ANSWER<br> ILL GIVE YOU 20 POINTS
krok68 [10]

Answer:

DEC+DEF=180

DEC=180-116

DEC=64°

in triangle DCE

angle D+angle C+angle E=180

7y+6+4y+64=180

11y+70=180

11y=180-70

11y=110

y=110/11

y=10°

angle C=4y

=4(10)

=40°

3 0
3 years ago
67&gt; f - 15 is true when f
ANTONII [103]
When f is greater than 82.
6 0
3 years ago
Read 2 more answers
I need help with these this is due today
Oduvanchick [21]

Answer:

Yah no way man your gonna fail

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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