Answer:
x = 4.17
Step-by-step explanation:
We can use a ratio to solve
4.2 k 2 k
---------------- = ---------------
8.76 x
Using cross products
4.2 * x = 2 * 8.76
4.2x =17.52
Divide by 4.2
x=4.17
Answer: 24.2° SouthWest
<u>Step-by-step explanation:</u>
First step: DRAW A PICTURE of the vectors from head to tail <em>(see image)</em>
I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.
<u>Perpendicular (x):</u>
cos 35° = adjacent/hypotenuse
cos 35° = x/160
→ x = 160 cos 35°
<u>Angle (θ):</u>
sin θ = opposite/hypotenuse
sin θ = x/320
sin θ = 160 cos 35°/320
θ = arcsin (160 cos 35°/320)
θ = 24.2°
Direction is down (south) and left (west)
Answer: x - 3y = -2
x = -2 + 3y
x - 3y = 16
x = 16 + 3y
Answer:
f(x) = x³ + x² - 5x + 3
Step-by-step explanation:
The cubic polynomial has zeros at 1, 1, - 3.
Therefore, x = 1, 1, - 3 are the roots of the polynomial and hence, (x - 1), (x - 1) and (x + 3) will be factors of the cubic polynomial.
Hence, we can write the polynomial as a function of x as
f(x) = (x - 1)(x - 1)(x + 3)
⇒ f(x) = (x² - 2x + 1)(x + 3)
⇒ f(x) = x³ - 2x² + 3x² + x - 6x + 3
⇒ f(x) = x³ + x² - 5x + 3
So, this is the cubic polynomial function in standard form. (Answer)