Given z²+1/z² =14
using above equation,
z²+1/z² = 14
add 2 on both side,
z² + 1/z² + 2 = 14 + 2
the LHS is whole square of z + 1/z
so we can write it
(z + 1/z)² = 16z + 1/z = 4
Now we know,
(a + b)³ = a³ + b³ + 3ab(a+b)
here, a = z and b = 1/z,
substituting a and b in equation we will get,
(z + 1/z)³ = z³ + 1/z³ + 3z/z( z+ 1/z)
4³ = z³ + 1/z³ + 3×4
z³+ 1/z³ = 64-12
z³ + 1/z³ = 52
Answer:
52.
Step-by-step explanation:
Using the identity a^3 + b^3 = (a + b)(a^2 - ab + b^3):
z^3 + 1/z^3 = (z + 1/z)(z^2 - z *1/z + 1/z^2)
= (z + 1/z) (z^2 - 1 + 1/z^2)
= (z + 1/z) (14 - 1 )
= 13(z + 1/z).
Now using the identity a^2 + b^2 = (a + b)^2 - 2ab:
z^2 + 1/z^2 = ( z + 1/z)^2 - 2(z * 1/z) = 14 So:
( z + 1/z)^2 - 2 = 14
( z + 1/z)^2 = 16
Taking z + 1/z = 4 we therefore have:
z^3 + 1/z^3 = 13 * 4 = 52.
Find the perimeter of the right triangle. If necessary, round to the nearest tenth.
a. 13 in.
b. 169 in.
C. 60 in.
d. 30 in.
The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if necessary.
leg: 20 m; hypotenuse: 25 m
10.5 m
8.9 m
15 m
32 m
Answer:
the answer is third option
because, 20²+x²=25²
x²=625-400
x²=225
X=15mWhat common fraction is halfway between 1/8 and 1/10 on a number line?
Answer:
9/80
Step-by-step explanation:
1/8 = 10/80
1/10 = 8/80
9/80 is fraction between 1/8 and 1/10
The common fraction which is halfway between 1/8 and 1/10 on a number line is 9/80.
We are given that;
The two numbers 1/8 and 1/10
Now,
A fraction represents a part of a number or any number of equal parts.
To find the common fraction that is halfway between 1/8 and 1/10 on a number line, we need to find the average of the two fractions. To do this, we need to add the fractions and divide the sum by 2. To add the fractions, we need to find a common denominator for them. The least common multiple of 8 and 10 is 40, so we can multiply the first fraction by 5/5 and the second fraction by 4/4 to get equivalent fractions with the same denominator:
1/8 + 1/10 = (1/8)(5/5) + (1/10)(4/4) = 5/40 + 4/40
Now we can add the fractions by adding the numerators and keeping the denominator:
5/40 + 4/40 = (5 + 4)/40 = 9/40
To divide this fraction by 2, we can multiply it by the reciprocal of 2, which is 1/2:
(9/40) / 2 = (9/40) x (1/2) = (9 x 1)/(40 x 2) = 9/80
Therefore, by fraction the answer will be 9/80.
Learn more about fraction;
https://brainly.com/question/729654?referrer=searchResults
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Which name accurately describes the figure shown below and why?
A 4-sided figure with 2 parallel sides, 2 right angles, and 2 non-congruent sides.
parallelogram, because the figure has two pairs of parallel sides
parallelogram, because the figure has exactly one pair of parallel sides
trapezoid, because the figure has two pairs of parallel sides
trapezoid, because the figure has exactly one pair of parallel sides
Answer:
trapezoid, because the figure has exactly one pair of parallel sides.
Step-by-step explanation:
Answer:
trapazoid
Step-by-step explanation:
Daryl can jump 2 1/2 yards. Sarah can jump 8 feet and Michelle can jump 72 inches.Which statement is true?
Find g(x)) when f(x) = 3x2 + x - 8, and g(x) = 4x + 5
I have no idea what she’s talking about please help me out
Answer:
A
Step-by-step explanation:
Option A is the correct answer of this question.
PLEASE HELP ILL MARK BRAINLIEST 5O POINTS PLEASE
The data shows the ages of people in a restaurant.
20, 25, 5, 28, 66, 62, 21, 28, 34, 38, 40, 10, 12, 15, 45, 50, 28
Create a histogram of this data.
To create a histogram, hover over each age range on the x-axis. Then click and drag up to plot the data.
Answer:
Ok i will help
Step-by-step explanation:
The x axis numbers are the ages the y axis numbers are how many people with that age then record the data.
The measure of angle 5x/6 is . The equivalent measurement in degrees is
Answer:
17
Step-by-step explanation:
do only 4 for brainiest:):):)
Answer:
Step-by-step explanation:
1. 1/6
2. 3/6
3. 2/6
4. 1/6
5. 3/6
6. 3/6
btw you need to charge your computer... :)please help!!!
43+29= ? +60
Answer:
12
Step-by-step explanation:
43 + 29 = 72
? = 72 - 60 = 12
therefore, 43 + 29 = 12 + 60
WILL MAKR BRAINLIEST IF GOTTEN RIGHT
Answer:
[tex] V_{weights} =1,243 \: cm^3 [/tex]
Step-by-step explanation:
Radius of weight [tex] r_1=\frac{20}{2}= 10 \:cm[/tex]
Radius of hole [tex] r_2=\frac{2}{2}= 1 \:cm[/tex]
Height of weight as well as hole (h) = 2 cm
Volume of weights = (Volume of one weight - volume of hole)
[tex] \therefore V_{weights} = 2 (\pi r_1^2 h - \pi r_2^2 h)[/tex]
[tex]\therefore V_{weights} = 2 \pi (r_1^2 - r_2^2 )h[/tex]
[tex]\therefore V_{weights} = 2 (3.14)(10^2 - 1^2 )2[/tex]
[tex]\therefore V_{weights} =12.56(100 - 1 )[/tex]
[tex]\therefore V_{weights} = 12.56(99)[/tex]
[tex]\therefore V_{weights} =1,243.44[/tex]
[tex]\therefore V_{weights} \approx 1,243 \: cm^3 [/tex]
What are the solutions of this quadratic equation?
6x^2 + 6 = 12x + 18
A. x = 1 ± √3
B. x = 2 ± 2√3
C. x = 2 ± √6
D. x = -1 and x = 3
The Answer Is: A. x = 1 ± √3
Please help me. This is URGENT. I really need help,
Answer:
39 ovoid it e fifty from ff
Step-by-step explanation:
39
The table shows the number of practice problems completed in 30 minutes in three samples of 10 randomly selected math students. Number of practice problems completed In 30 minutes
Sample 1 18 15 17 17 18 | 13 | 17 16 | 16 | 14 | 18 Mean = 16.2
Sample 2 21 20 18 20 19 19 20 21 21 20 Mean = 19.9
Sample 3 | 14 16 18 13 | 18 | 16 | 16 | 17 | 19 | 19 Mean = 16.6
Which statement is most accurate based on the data?
A. A prediction based on the data is reliable, because the means of samples 1 and 3 are very close together.
B. A prediction based on the data is not completely reliable, because the means of samples 1 and 3 are too close together.
C. A prediction based on the data is reliable because there are no noticeable differences among the samples
D. A prediction based on the data is not completely reliable because the meaning of sample 2 is noticeably higher than the means of the other two samples. : ))
Answer:
D
Step-by-step explanation: please give me brainlist Thanks!
WHAT IS A RATIONAL NUMBER
Isa makes a goal to drink 56 cups of water this week. She drinks 9 cups of water on each of the first 4 days of the week
Answer:
I dont know what the question is but she drank 36 cups of water already so she needs to drink 20 more
Answer:20
Step-by-step explanation:
which property of polynomial multiplication says that the product of two polynomials is always polynomial
Answer:
Closure is the right answer.
Which of the following are roots of the polynomial function
Answer:
its a and b
Step-by-step explanation:
Johnny took a math quiz last week. He got 9 problems correct and 11 problems incorrect. What percentage did Johnny get correct?
Answer:
The answer is 45%
Step-by-step explanation:
9+11=20
9/20
=4.5/10
=45/100
=45%
4
The net below shows four equilateral
triangles.
8 ft
12 ft
+
What is the total surface area of the
triangular pyramid in square feet?
A 144
B
192 ft
C 258 ft
D 384 Ft
Answer:
B) 192 ft
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
is parallel to . and are perpendicular to and .
The ratio of the lengths of and is __:__
Answer:
1 : 1
Step-by-step explanation:
PQ parallel to RS
PR and PS ; perpendicular to PQ and RS
FOR parallel lines, the perpendicular line joining then are always the same ; here the 4 angles formed are all 90°
Answer:
1:1
Step-by-step explanation:
Will Give Brainliest,. Make Sure to Show your work.
Answer:
540
Step-by-step explanation:
All you have to do is multiply all of the numbers on the upside of the shape
Answer:
24 unit^2.
Step-by-step explanation:
Area = 1/2 * base * height
= 1/2 * 12 * 4
= 1/2 * 48
= 24 unit^2.
what a quadrilateral with four equal sides, four equal angles, and all angles are right angles.
Answer:a square
Step-by-step explanation:
Refer to the following data set: What is the median?
Answer:
8
Step-by-step explanation:
What is the midpoint
(-9,8) and (-4,-2)
give two examples of organism that has cell structure similar to cell of permanent alide
it is a polygon with 3 sides and 3 angles
Answer:
A triangle is that polygon with three side and three Angles
16 x 7 = (10x7) + (6 x p)
Please help me I'm not smart enough to figure this out LITERALLY
In a game, players roll a 6-sided dice. Each side has dots ranging from 1 dot to 6 dots. For the player to win the prize, a dice must show a side containing 5 dots. What is the probability of landing on 5 dots?
5/6
2/6
5/12
1/6
Answer:
1/6
Step-by-step explanation:
There are six sides, but only one side has 5 dots, meaning 1/6 has 5 dots. Therefore the probability is 1/6.
A cone has a height of 18 yards. Its base has a radius of 19 yards. Find its volume, in cubic yards, to the nearest tenth. Use 3.14 or the calculator value for pi.
Answer:
Solution given:
height [h]=18yards
radius [r]=19yards
π=3.14
we have
Volume of cone=⅓(πr²h)
=⅓(3.14*19²*18)6801.24 cubic yards6801.24 cubic yards is a required volume of cone.