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snow_lady [41]
3 years ago
15

Find the zeros (roots) of the following equations. f(x) = 2x5 - 9x4 + 12x3 - 12x2 + 10x - 3 = 0

Mathematics
1 answer:
Talja [164]3 years ago
8 0
Hi,
f(1)=2*1^5-9*1^4+12*1^3-12*1^2+10*1-3\\
=2-9+12-12+10-3\\
=0\\

f(x)=(x-1)(2x^4-7x^3+5x^2-7x+3)\\


g(x)=2x^4-7x^3+5x^2-7x+3\\

g(3)=2*3^4-7*3^3+5*3^2-7*3+3\\
=162-189+45-21+3\\
=0\\

g(x)=(x-3)(2x^3-x^2+2x-1)\\

h(x)=2x^3-x^2+2x-1\\

h( \dfrac{1}{2} )=2* \dfrac{1}{8} - \dfrac{1} {4}+1-1\\
=0\\

h(x)=(2x-1)(x^2+1)\\


f(x)=(x-1)(x-3)(2x-1)(x+i)(x-i)\\



Roots are 1,3,0.5,i,-i.

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Compute the magnitude and direction of the sum of the two vectors: 170N of force at 87° and 100N of force at 46°.
krok68 [10]

Answer:

F = 254.08N Θ = 72.03°

Step-by-step explanation:

First of all we find the resolution in both x and y axis

∑Fx = 170cos87 + 100cos46 = 78.36N

∑Fy = 170sin87 + 100sin46 = 241.70N

To find the resultant vector we use pythagorean theorem

F = √(∑Fx)² + ∑(Fy)²

F = √(78.36² + 241.70²)

F = √(64559.1796)

F = 254.08N

the angle between both force can be obtained using

tanθ = ∑Fy / ∑Fx

tanθ = 241.70 / 78.36

tanθ = 3.084

Θ = tan⁻ 3.084

Θ = 72.03°

5 0
3 years ago
A telephone pole has a wire attached to its top that is anchored to the ground. the distance from the bottom of the pole to the
kirza4 [7]

The height of the pole is 96 feet

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]

a^{2}+b^{2}=c^{2},

Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.

Set up the equation h^2 + (h - 68)^2 = (h + 4)^2 using the Pythagorean theorem (a^2 + b^2 = c^2).

h^2 + (h - 68)^2 = (h + 4)^2

On simplifying we get

h^2+h^2-136h+4624 = h^2+8h+16

2h^2-136h+4624=h^2+8h+16

h^2-144h+4608=0

Solving using quadratic formula

h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}  

h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}

h1 = 96 feet , h2 = 48 feet

If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .

Hence the height of the pole is 96 feet

Learn more about Pythagoras theorem here :

brainly.com/question/343682

#SPJ4

7 0
2 years ago
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