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kaheart [24]
2 years ago
5

Find all zeros of the polynomial function b(x)=x3-4x2-3x+12

Mathematics
1 answer:
Nadya [2.5K]2 years ago
8 0
x^3-4x^2-3x+12=0\\\\x^2\big(x-4\big)-3\big(x-4\big)=0\\\\\big(x^2-3\big)\big(x-4\big)=0\\\\\big(x-\sqrt{3}\big)\big(x+\sqrt{3}\big)\big(x-4\big)=0\\\\\\\boxed{x=\sqrt{3}\qquad\vee\qquad x=-\sqrt{3}\qquad\vee\qquad x=4}
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For questions 3 – 5, an airplane is heading south at an airspeed of 540 km/hr, but there is a wind blowing from the northeast at
GuDViN [60]

First, let's calculate the horizontal and vertical components of the wind speed (W) and the airplane speed (A), knowing that south is a bearing of 270° and northeast is a bearing of 45°:

\begin{gathered} W_x=W\cos45°\\ \\ W_x=50\cdot0.707\\ \\ W_x=35.35\\ \\ \\ \\ W_y=W\sin45°\\ \\ W_y=50\cdot0.707\\ \\ W_y=35.35 \end{gathered}\begin{gathered} A_x=A\cos270°\\ \\ A_x=540\cdot0\\ \\ A_x=0\\ \\ \\ \\ A_y=A\sin270°\\ \\ A_y=540\cdot(-1)\\ \\ A_y=-540 \end{gathered}

Now, let's add the components of the same direction:

\begin{gathered} V_x=W_x+A_x=35.35+0=35.35\\ \\ V_y=W_y+A_y=35.35-540=-504.65 \end{gathered}

To find the resultant bearing (theta), we can use the formula below:

\begin{gathered} \theta=\tan^{-1}(\frac{V_y}{V_x})\\ \\ \theta=\tan^{-1}(\frac{-504.65}{35.35})\\ \\ \theta=-86° \end{gathered}

The angle -86° is equivalent to -86 + 360 = 274°.

Therefore the correct option is b.

8 0
1 year ago
Which is an ordered pair on the line 2.5,14 2.25,12 1.25,5 1.5,9
Savatey [412]
I would think that all but one point would be on the line.  One way to approach this problem is to find the equation of the line based upon any two points chosen at random, and then determine whether or not the other points satisfy this equation.  Next time, would you please enclose the coordinates of each point inside parentheses:  (2.5,14), (2.25,12), and so on, to avoid confusion.
                                                               14-12
slope of line thru 1st 2 points is   m = ----------------  =  2/0.25 = 8
                                                              2.50-2.25

What is the eqn of the line:     y = mx + b becomes

                                               14 = (8)(2.5) + b; find b:

14-20 = b = -6.  Then,   y = 8x - 6.

Now determine whether (12,1.25) lies on this line.  

Is 1.25 = 8(12) - 6?  Is 1.25 = 90?  No.  So, unless I've made arithmetic mistakes, (1.25, 5) does not lie on the line thru (2.5,14) and (2.25,12).

Why not work this problem out yourself using my approach as a guide? 



5 0
3 years ago
2 Describe the solution set of y=8
Vedmedyk [2.9K]

Answer:

what is your question there is no equation

7 0
2 years ago
What is the y-intercept for the below inequality?
san4es73 [151]

Answer:

The correct answer is C

Step-by-step explanation:

In order to find the y-intercept, you need to first solve the inequality for y.

5x - 3y ≤ 15

-3y ≤ -5x + 15

y ≥ 5/3x - 5

Now we look at the constant at the end. Since that constant is -5, we know C to be the answer.

8 0
3 years ago
Problem 1.1.A basket of fruit is arranged out of apples, bananas, and oranges.What is the smallest number of fruit that should b
Vedmedyk [2.9K]

Answer:

21

Step-by-step explanation:

The question is based in pigeonhole principle that says If n or  more  pigeons  are  distributed  among k >0 pigeonholes,then at least one pigeonhole contains at least \frac{n}{k} pigeons.

8 + 6 + 9−3 + 1 = 21

3 0
2 years ago
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