1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
n200080 [17]
2 years ago
6

If \: x + y + z = 0 \: then \: show \: that \: {x}^{3} + {y}^{3 } + {z}^{3} =3xy​

Mathematics
1 answer:
tankabanditka [31]2 years ago
8 0

Answer:

Given

x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y) 3 =(−z) 3

⟹x 3 +y 3 +3x 2y+3xy 2 =−z 3

⟹x 3 +y 3 +3xy(x+y)=−z 3

⟹x 3+y 3+3xy(−z)=−z 3

⟹x 3 +y 3−3xyz=−z 3

⟹x 3 +y 3 +z 3 =3xyz

Step-by-step explanation:

Hope it is helpful.....

You might be interested in
Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 8. If 100 people are
Sergeu [11.5K]

Answer:

D. 0.9938.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 115 and a standard deviation of 8.

This means that \mu = 115, \sigma = 8

100 people are randomly selected

This means that n = 100, s = \frac{8}{\sqrt{100}} = 0.8

Find the probability that their mean blood pressure will be less than 117.

This is the p-value of Z when X = 117, so:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{117 - 115}{0.8}

Z = 2.5

Z = 2.5 has a p-value of 0.9938, and thus, the correct answer is given by option D.

8 0
3 years ago
Triangle PQR has vertices at the following coordinates : P(0,1) Q(3,2) R(5,-4) . Determine wether or not triangle PQR is a right
lord [1]
Here is my answer. Hope this help.

8 0
3 years ago
A table is on sale for 464 , which is 36% less than the regular price.
viva [34]
The original price was 725.
Explanation:
"36% less than" means taking 36% away from 100%. 100-36 is 64, so 64% remains when 36% is taken away. So, 64% of the original table's price is 464.
So, if the original price was x, 464=0.64x
Solve this by dividing both sides by 0,64:
725=x
So, the original price was 725.
3 0
3 years ago
The volume of air inside a rubber ball with radius r can be found using the function vn What doerepresent? The volume of air ins
vekshin1

I would say it represents the volume function evaluated at r=5/7, or

V(5/7)=(4/3)π(5/7)² = 2.13714

8 0
3 years ago
this week Jada bought a 3 1/2 pound of cat food. her cat eats 5/8 of a pound each day. show your work and remember to include un
MakcuM [25]

Answer:

5 days.

Step-by-step explanation:

The food will last her 5 days.
3\frac{1}{2}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}
=1\frac{5}{8}-\frac{5}{8}-\frac{5}{8}
=1-\frac{5}{8}=\frac{3}{8}

5 0
1 year ago
Other questions:
  • I've never even seen a box and whiskers plot before!! Should be pretty straight forward though. Thanks!
    14·2 answers
  • Do you agree with Mark’s reasoning? Is he correct that 2 is a rational number? Explain your answer.
    8·1 answer
  • How do you solve 2.75+.003+.158=
    13·2 answers
  • Explain how you would estimate to subtract 189 from 643
    10·1 answer
  • Linda spent 3/4 of her saving on furniture and the rest on a tv.If the tv cost her $200,what were her original savings .
    12·1 answer
  • Which sum or difference identity would you use to verify that cos (180° - q) = -cos q?
    6·1 answer
  • Saidhari bought a toaster oven for $45. This price was 1/4 off the list price. What was the list price?
    8·1 answer
  • PLEASE HELP!!! This was due today
    15·2 answers
  • 18x-6y= 54<br> 12y=6x-18<br> Solve this system of equations using the substitution method.
    12·1 answer
  • A planet has a circular orbit around a star. It is a distance of 65,000,000 km from the centre of the star. It orbits at an aver
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!