Answer:
As this is a quartic equation, we should expect four roots (although some may end being repeated). Notice also that the equation is symmetrical, which suggests that there might be an element of symmetry in the answer.
First, as this equation is a quadratic in terms of z2 , we can use our formula for finding the roots of a quadratic equation to give the value(s) of z2 . [If you have a problem seeing this, use the substitution y=z2 , and you get a quadratic in y .]
z2=−4±42−4×1×16√2×1=−4±16−64√2
=−4±−48√2=−2±12−−√i=−2±23–√i
=4(−12±3√2)i
=4(cos(2kπ3)+isin(2kπ3)) , where k∈1,2
=4e2kiπ3
As this is the value of z2 , whereas we want z , we need to take the square roots of both sides
z=4–√ekiπ3+nπ , where n∈0,1
=2e(k+3n)iπ3
=2cis((k+3n)iπ3)
As we have two values of k and two values of n , this gives us four solutions.
Writing these angles in terms of degrees, we have: 60, 120, 240 and 300
Evaluating, we end up with the four solutions
z=1±3–√i∪z=−1±3–√i
You can substitute z^2 = x,
Then you get x^2+4x+16=0
Step-by-step explanation:
z=1±3–√i∪z=−1±3–√i
You can substitute z^2 = x,
Then you get x^2+4x+16=0
Then you can use classical x1,2 = (-b +- √[b^2–4ac])/2a
X1,2=(-4+-√[16–16*4])/2
After you solve that you substitute back z^2 = x
Find the area of a triangle with a base of 6 m and a height of 3 m.
Is 0.875 irrational or rational and why?
A small fly weighs approximately 2.2 • 10^-3 gram and an average sized gnat weighs approximately 9•10^-4
1. find the sum of the weights of the two insects
2. How much heavier is the fly than the gnat?
What inequality does this number line show?
find slope that is perpendicular to the line 4−2=12 ?
Answer:
m = -1/2
Step-by-step explanation:
4 − 2 = 12
= −2 = 12 − 4
= = (12 − 4) ÷ (−2)
= = 2−6
So, the slope is 2.
Now, keep this rule in mind: the product of a slope of two perpendicular lines will be -1.
Thus, the slope of the line that is perpendicular to this line is -1/2
Study the pattern of numbers given below and write the rule that describes the pattern 1,3,9,27,81
Can someone please help me please?
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Answer:
D. G(x) = (x+3)² -2
Step-by-step explanation:
G(x) is translated left 3 and down 2 from F(x). The transformation ...
G(x) = F(x -h) +k
is a translation right h units and up k units. We have h=-3 and k=-2, so the function of interest is ...
G(x) = F(x +3) -2
G(x) = (x +3)² -2
Plz help, I give Brainliest :-)
Answer:
8.754592 km
Step-by-step explanation:
5.44 × 1.6093 = 8.754592
Is 5 5/6 + 1 3/4=5 1/12 reasonable
Answer:
No, it is unreasonable.
Step-by-step explanation:
5/5/6+1/3/4=35/6+7/4
=70/12+21/12
=91/12
=7 7/12
HELP MEEEEE PLEASEEEEEE!!!
Write an expression for "the product of 5 and z.”
+
y
Stuck? Review related articles/videos or use a hint.
Answer:
5z
Step-by-step explanation:
Product means multiply
5z
A. Your friend says that the solutions to the inequality 9x-18x ≥ - 18 are x ≥ 2 Solve the inequality correctly. B. What error did your friend make?
Answer:
A. x≤2; B. wrong unequality after dividing by negative number.
Step-by-step explanation:
9x-18x≥ -18;
-9x≥ -18;
0≥ -18+9x;
18≥9x;
9x≤18;
x≤2.
The triangle shown below has an area of 20 units.
Find the missing side.
8.
2
2
units
Plz help 57.3 - 4.32 =
Answer:
52.98
Step-by-step explanation:
Share £360 into the ratio 3:2:1
Answer:
£180, £120 and £60.
Step-by-step explanation:
The number of parts = 3 + 2 + 1 = 6.
360 / 6 = 60, so the shares are:
3*60 = 180
2*60 = 120
1 * 60 = 60.
The distribution of £360 in the ratio of 3:2:1 will be £180, £120 and £60.
What is a ratio?
In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
The number of parts = 3 + 2 + 1 = 6.
360 / 6 = 60, so the shares are:
3 x 60 = 180
2 x 60 = 120
1 x 60 = 60.
Hence the distribution of £360 in the ratio of 3:2:1 will be £180, £120 and £60.
To know more about ratios follow
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what is answer to 5/6 x 2/3 x 8/5 =
Answer:
8/9
Step-by-step explanation:
5/6 x 2/3 = 10/18 (5/9 reduced)
5/9 x 8/5 = 40/45 ( 8/9 reduced)
please show work 7r + 21 = 49r
Answer:
1/2 = r
Step-by-step explanation:
7r + 21 = 49r
Subtract 7r from each side
7r-7r + 21 = 49r-7r
21 = 42r
Divide each side by 2
21/42 = 42r/42
1/2 = r
Answer:
r = 0.5
Step-by-step explanation:
First you need to isolate the r variable.
7r + 21 = 49r
-7r -7r
21 = 42r
Then Divide both sides by 42
0.5 = r
Now check your answer by inserting it back into the original equation.
7(0.5) + 21 = 49(0.5)
3.5 + 21 = 24.5
24.5 = 24.5
The equation is true so r = 0.5
How would this triangle be classified ..
Answer:
This given triangle is an equilateral triangle.
Look at image for question and answers
Answer:
d
Step-by-step explanation:
i did this last year
The temperature of the pool water was 83 degrees during the day and
dropped 7 degrees at night. What was the new temperature.
Answer:
76
Step-by-step explanation:
83-7=76
One of the legs of a right triangle measures 1 cm and the other leg measures 17 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
using phythagoras formula of right angles we can calculate the hypotenuse
1^2=x^2+17^2
x^2=17^2-1^2(transpose)
×^2=288 (introduce a square root)
x=15.01(round of to the nearest tenth)
Step-by-step explanation:
x=10
The measure of the hypotenuse is 17.029
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have Pythagoras theorem:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Given;
The legs of a right triangle measures 1 cm
The other leg measures 17 cm
Now,
|AC|^2 = |AB|^2 + |BC|^2
|AC|^2 = |1|^2 + |17|^2
|AC|^2 = 1 + 289
AC=17.029
Therefore, by pythagoras theorem answer will be 17.029.
Learn more about Pythagoras theorem here:
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determine the value of n and what property is represented.
3n = 1
What are the missing factors in the factor tree for 45?
45
5
A
B
С
Answer:
c
Step-by-step explanation:
the missing factors in the factor tree
please help that’s all i just need to make i’m correct it due tomorrow early so please
Gabriella goes for a power walk every three days, and Mona walks every fivedays. They both walked on Monday this week.a.After how many days will they both walk again on the same day?[3 pts]b.What day of the week will it be when they walk again on the same day?
Power Walking has been at the top of a natural range to walk with such a speed. A walk defines as a walking journey, and the further discussion can be defined as follows:
Given:
Power walking by the Gabriella by every 3 days
Walking by the Mona by every 5 days
Both walk on Monday then They both walked together,
after taking LCM of 5 and 3 that is = 15 days
For question a:
When both walk again after the same day is = 15 days
For question b:
"Tuesday" is the weekday that will it be when they walk again on the same day.
Learn more:
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I need the logistics models student guide answer key!!
Answer:
Ans
Step-by-step explanation:
if you get it, please share it with me.
If the side length of a square is 7.2 inches, what is the area of the square
Answer:
51,84
Step-by-step explanation:
The area of the square if side * side, so 7.2 * 7.2 = 51,84 square inches
Pls help it's due today It's DUE IN 8 MINUTES.
Answer:
84 pounds
Step-by-step explanation:
Use the map below. Find the distance between the cities Everett and Fairfield to the nearest tenth
What is -1 7/8 + -2 1/4? Please explain why and a step by step :).
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Answer:
-4 1/8
Step-by-step explanation:
Many people find it easier to factor out -1, then do the addition. The fractions need a common denominator before they can be added. A suitable denominator that is a multiple of both 4 and 8 is 8.
The fraction 1/4 = (1/4)(2/2) = (1·2)/(4·2) = 2/8.
__
So, the problem can be rewritten as ...
-(1 7/8 +2 2/8)
= -((1+2) +(7/8 +2/8))
= -(3 +9/8)
The fraction 9/8 is an improper fraction equal to 8/8 +1/8 = 1 1/8. Then the sum is ...
-(3 +1 1/8) = -4 1/8
