Answers
Step-by-step explanation:
We have that
[tex](x + \frac{1}{x} ) {}^{2} = 3[/tex]
We are trying to find the number value so that we can apply in the later equation.
Qe first simplify.
Remeber that
[tex](a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} [/tex]
Also remeber that
[tex] \frac{1}{x} = {x}^{ - 1} [/tex]
so
[tex](x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3[/tex]
We then simply remeber that x^0=1 so
[tex] {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3[/tex]
Multiply both sides by x^2.
[tex] {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} [/tex]
Subtract both sides by 3x^2
[tex] {x}^{4} - {x}^{2} + 1 = 0[/tex]
Notice that x^4= (x^2)^2.
So our reformed equation is
[tex]( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0[/tex]
Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.
[tex]w {}^{2} - w + 1 = 0[/tex]
Now we use the quadratic formula
[tex] w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
and
[tex]w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
Let a=1 b=-1 and c=1.
[tex]w = \frac{1 + \sqrt{1 - 4(1)} }{2} [/tex]
[tex]w = \frac{1 - \sqrt{1 - 4} }{2} [/tex]
Now, we get
[tex]w = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]
and
[tex]w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} [/tex]
Now since we set both of these to the x^2 we solve for x.
and
[tex] {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]
and
[tex] {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} [/tex]
We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is
[tex] {x}^{2} = 1( \cos(60) + i \: \sin(60) [/tex]
and
[tex] {x}^{2} = 1( \cos(300) + i \: sin(300))[/tex]
Next we take the sqr root of 1 which is 1, and divide the degree by two.
[tex] {x} = 1( \cos(30) + i \: sin \: 30)[/tex]
and
[tex]x = 1( \cos(150) + i \: sin(150)[/tex]
We are asked for the 2nd root so just add 180 degrees to this and we have
[tex]x = 1 \cos(210) + i \: sin \: 210)[/tex]
and
[tex]x = 1( \cos(330) + i \: sin(330)[/tex]
which both simplified to
[tex]x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]
and
[tex]x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]
Now we must find
x^18+x^12+x^6+1.
We just use demovire Theorem. Which is a complex number raised to the nth root is
[tex] {r}^{n} (cos(nx) + i \: sin(nx)[/tex]
So let plug in our first root.
[tex]1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1[/tex]
To save time we multiply the angle and use rules of terminals angle and we get
[tex]1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1[/tex]
And we get
[tex] - 1 + 1 + - 1 + 1 = 0[/tex]
So one of the answer is x=0
And the other, let see
[tex]1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1[/tex]
[tex] \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1[/tex]
We get
[tex] - 1 + 1 + 1 + 1 = 2[/tex]
So our answer are 2.
So the answer to the second part is
0 and 2.
Related Questions
HELP!! I desperately need help!! I would appreciate if you could show work please!!!
Answers
Answer:
a) 137.9°
b) 12.2° (please refer to explanation because I didn't know what to round to)
Step-by-step explanation:
1a) A supplementary angle will equal 180°, so you must subtract 42.1 from 180
180-42.1 = 137.9
1b) A complementary angle will equal 90°, so you need to use the expression given and add an x for the other part of 90°
8x-20+x = 90
9x-20=90
9x=110
x=12.2
What is the slope of the line that passes through the points shown in the table?
X Y
-1 -5
0 -3
1 -1
2 1
Answers
hey guys , can you help me with this question please … i seriously don’t wanna fail this
Answers
Answer:
48
Step-by-step explanation:
You get the third length which is the hypotenuse then you add them all since its asking for the perimeter
What is the measure of the missing angle in this triangle
Yes
Answers
Answer:
The measure of the missing angle is 25 degrees.
Sum of angles in a triangle is 180.
To find the missing angle:
180 - total of other given angles = missing angle
Total of other given angles = 155
180 - 155 = 25
tim and sue share a small pizza. tim eats 2/3 o the pizza
Answers
Answer:
Sue eats 1/3 of the pizza
Step-by-step explanation:
Answer:
Sue eats 1/3 of the pizza
Step-by-step explanation:
3/3 - 2/3 = 1/3
Х
0
1
9
5
29
Y
4
What is the slope of the line?
A 3
B 2
C 5
U UN W
D
Answers
Answer:
C
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (5, 29) ← 2 ordered pairs from the table
m = [tex]\frac{29-4}{5-0}[/tex] = [tex]\frac{25}{5}[/tex] = 5 → C
At a point on the ground 50 feet from the foot of a tree, the angle of elevation to the top of the tree is
53. What is the height of the tree rounded up to the nearest hundredth.
Answers
Answer:
At a point on the ground 50 feet from the foot of a tree, the angle of elevation to the top of the tree is 53°. Find the height of the tree to the nearest foot.
I got 50xtan53 = 66.35 nearest foot ? would I use tan or sin since I'm finding the foot of the tree
Step-by-step explanation:
.
Find 3 other points for this equation for both x and y ( bots don’t answer pls )
Answers
Answers:
Row one: x = -10 and y = -4Row two: x = 0 and y = 6Row three: x = 2 and y = 8There are infinitely many other possible answers.
===================================================
Explanation:
The [tex]\frac{3}{3}[/tex] simplifies to 1. Dividing any nonzero number over itself always leads to 1.
So the equation [tex]y = \frac{3}{3}x+6[/tex] simplifies to [tex]y = x+6[/tex]
To determine y, we add 6 to x.
Pick 3 random values you want for x.
Let's say we picked x = 0
y = x+6
y = 0+6
y = 6
So x = 0 leads to y = 6
-----------
If you tried something like x = 2, then,
y = x+6
y = 2+6
y = 8
So (2,8) is another point on the line
-----------
Lastly, let's try a negative number. Let's go for x = -10
y = x+6
y = -10+6
y = -4
The input x = -10 gives the output y = -4
There isn't any restriction on x, so you can use any number you want. Therefore, there are infinitely many possible answers.
help please anybody hmm
Answers
Answer:
94.6-18.8=75.8
75.8 is the answer
Step-by-step explanation:
Hope this helps
May i get braineist pls?
I need 3 more brainiest can anyone help a girl out plz
Answers
Answer:
:/
Step-by-step explanation:
Answer:
Sure
Step-by-step explanation:
What is the slope
A. 2
B. 4
C. 5
Answers
We know the slope formula.
=> [tex]\frac{y_{2} -y_{1} }_{x_{2}-x_{1} } }[/tex]=> [tex]\frac{16-12}{7-5}[/tex]=> [tex]\frac{4}{2}[/tex]=> [tex]2[/tex]Conclusion:Therefore, the slope is 2.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Determine whether it is possible to form a triangle
with side lengths 4.2, 4.2, and 8.4.
O yes
no
Answers
Answer:it is possible to have a triangle with the given side lengths. 7,9,13. Add any two sides and see if it is greater than the other side.
Step-by-step explanation:
What is the volume of this container?
Answers
∠HOA appears to be a right angle.
true or false
Answers
Answer:
False!
Step-by-step explanation:
Right angles are 90 degrees, for example EOA appears to be closer to a right angle but not HOA
what expressions are equivalent to 7 ^ 8 x 7 ^ -4
Answers
Answer:
7^4
Step-by-step explanation:
The equivalent expression 7^8 x 7^-4 using a single exponent is 7^4
How to write the expression using a single exponent.From the question, we have the following parameters that can be used in our computation:
7 ^ 8 x 7 ^ -4
This means that
7^8 x 7^-4
Apply the law of indices
So, we have
7^8 x 7^-4 = 7^(8 - 4)
This gives
7^8 x 7^-4 = 7^4
Hence, the solution is 7^8 x 7^-4 = 7^4
Read more about expressions at
brainly.com/question/30492964
#SPJ3
I'll mark you brainlest if you answer this correctly please help
Answers
Answer:
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Here is a balanced Hanger. Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and x represents the weight of each square. Select all equations that represent the hanger
Answers
Answer:
c if am wrong please correct me
ANSWER ASAP WILL MARK BRAINLIEST
Answers
Answer:
how many
Step-by-step explanation:
Helpp with number 23 pls
Answers
Answer : Susan is correct
Susan is correct because if you get that chart and turn all the numbers to decimals and divide the chart in half you will get the answer to 1.4/0.2 because the chart has 14 slots and if you divide that by 2 you will get 7 just think of 1.4/0.2 as 14/2.
Which ordered pair is the solution set
for 3x + 5y < 10?
Answers
Answer:
Slope is -3/5
Slope intercept form: y<-3/5x+2
Step-by-step explanation:
Your going to have a shaded region, with a dashed line
the y intercept will be (2)
the x intercept will be (3.333,0)
1 4/8 in a improper fraction?
Answers
Step-by-step explanation:
Step 1: Multiply the whole number part (1) by the denominator (8).
1 × 8 = 8
Step 2: Add the product from Step 1 (8) to the numerator (4).
8 + 4 = 12
Step 3: Write that result (12) above the denominator. So,
[tex]\frac4{8}{1}[/tex]
Step 4: The fraction [tex]\frac{12}{8}[/tex]
Can be reduced by dividing both numerator and denominator by the GCD(12,8) = 4. Thus,
[tex]\frac1{4}{8} =\frac{3}{2}[/tex]
What is the number of Santa’s reindeer (without Rudolph!) times the number of
golden rings in the song, “The Twelve Days of Christmas”?
Answers
someone please help me with this question, pleaseeeee :/
tyyyyy!
Answers
Answer:
4x+9y-27=0
compare and fill em
hope it helps
Answer:
2
Step-by-step explanation:
y=1y
x=1x
so the answer will be 2.
may be
hope to help!!!
given a isotope with a 3 charge, a mass number of 28, and an atomic number of 13, what are:
Answers
Answer: The element described is aluminum.
y-2=-7/5(x--2). Please include explanation when giving your answer. I'm really struggling with this. 20 points for whoever can answer this.
Answers
Answer:
[tex]x=\frac{10y-27}{5\left(-2+y\right)};\quad \:y\ne \:2[/tex]
Step-by-step explanation:
First, you have to simplify [tex]\frac{-7}{5(x-2)}[/tex] to become [tex]-\frac{-7}{5(x-2)}[/tex]
Next, you multiply both sides by [tex]5(x-2)[/tex] to make [tex]y\cdot \:5\left(x-2\right)-2\cdot \:5\left(x-2\right)=-\frac{7}{5\left(x-2\right)}\cdot \:5\left(x-2\right)[/tex]
After that, you need to simplify again to become [tex]y\cdot \:5\left(x-2\right)-10\left(x-2\right)=-7[/tex]
Now, expand [tex]5(x-2)-10(x-2)[/tex] to become [tex]5xy-10y-10x+20=-7[/tex]
Then, add 10y to both sides [tex]5xy-10y-10x+20+10y=-7+10y[/tex]
Next, you simplify to create [tex]5xy-10x+20=-7+10y[/tex]
After that, subtract 20 from both sides to make [tex]5xy-10x+20-20=-7+10y-20[/tex]
Now, simplify again to get [tex]5xy-10x=10y-27[/tex]
Next, factor [tex]5xy-10x[/tex] to get [tex]5x(y-2)[/tex]
Finally, divide both sides by [tex]5(y-2)[/tex] to get [tex]\frac{5x\left(y-2\right)}{5\left(y-2\right)}=\frac{10y}{5\left(y-2\right)}-\frac{27}{5\left(y-2\right)};\quad \:y\ne \:2[/tex]
If you did it right your final answer should be [tex]x=\frac{10y-27}{5\left(-2+y\right)};\quad \:y\ne \:2[/tex]
Hope this helps explain it!
QUICK I NEED HELP….PLZ Hurry!! ;-;
Which equation represents a liner function
Equation 1: Y=2x+1
Equation 2: Y^2= 3x+1
Equation 3: y=5x^5-1
Equation 4: Y= 4x^4-1
Answers
Answer: Equation 1: Y=2x+1
Step-by-step explanation:
solve the following x2-2x-24=0
Answers
Answer:
[tex]x=6[/tex] and [tex]x=-4[/tex]
Step-by-step explanation:
[tex]x^2-2x-24=0[/tex]
[tex](x-6)(x+4)=0[/tex]
[tex]x=6[/tex] and [tex]x=-4[/tex]
can anyone help me pls
Answers
Answer:
88 degrees, 44 degrees
Step-by-step explanation:
The total of angles in a triangle is 180 degrees
so, 48+x+x-44=180
48-44+x+x=180
4+2x=180
-4 on both sides
2x=176
x=88
26=7(g−9)+1226, equals, 7, left parenthesis, g, minus, 9, right parenthesis, plus, 12
Answers
To find g, we expand the brackets first(multiplying every term in the bracket by the term outside it):
26=7g-63+1226
Add the terms on the right hand side:
26=7g+1163
Collect alike terms to left hand side:
26-1163=7g
-1137=7g
Divide equation by 7 to get g on its own:
g= -162.428 (3dp)
Hope this helps!
Please help, I will mark brainliest :)
Answers
Answer:
Its A $0.50 per mile
Step-by-step explanation: