Answers
The mean lifetime of a bulb is 149.37 hours.
What is the meaning of mean?
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined. Mean is equal to (Sum of All Observations/Total Observations).
The given table represents a continuous data.
The table attached in below. To get mean lifetime of a bulb, find the mean of the given table.
The formula for mean is = Σ fm/N
Where f is frequency and m is midpoint of the class.
N is total number of observation.
From the table, Σ fm = 53175
Total number of bulb is 356.
The mean lifetime is 53175/ 356 = 149.37 hours
To learn more about mean, click on below link:
https://brainly.com/question/28447535
#SPJ1
Related Questions
Determine if the table how a proportional relationhip. X 25. 6 72. 8 77. 2 y 6. 4 18. 2 19. 3 Ye, it i proportional becaue all y over x ratio are equivalent to one fourth. Ye, it i proportional becaue all y over x ratio are equivalent to one third. No, it i not proportional becaue 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8. No, it i not proportional becaue 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
Answers
Proportional relationship for the given table is true and is define as
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
As given in the question,
Value of x and y in the given table are :
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.
y / x for all the values of x and y:
First values:
y /x = 6.4 / 25.6
= 0.25
Second values:
y/x = 18.2/ 72.8
= 0.25
Third values :
y /x = 19.3/ 77.2
= 0.25
0.25 is equivalent to One fourth ( 1/4).
Constant of proportionality exist = 0.25 or One fourth.
Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.
The complete question is:
Determine if the table how a proportional relationship.
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
Yes, it is proportional because all y over x ratio are equivalent to one third.
No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.
No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
Learn more about table here
brainly.com/question/11533874
#SPJ4
a marketing class polled 270 people at a shopping center to determine how many read the daily news and how many read the weekly gazette. they found the following: 124 read the daily news. 33 read both. 19 read neither. How many read the Weekly Gazette?
Answers
128 were Daily News readers. 19 read neither while 35 read both. Weekly Gazette A marketing class conducted a survey of 270 shoppers at a mall to find out how many of them read the Weekly Gazette and how many the Daily News.
What is News readers?
150 attendees were surveyed by a marketing class to find out how many read the Weekly Journal and how many the National News. In this section, word problems will be solved using Venn diagrams. The areas of a Venn diagram that indicate quantities as opposed to will have numbers in them. Confidence interval for difference of two formula You may have read statements like the ones below in newspapers, for instance. law in numerous nations.
To learn more about newspapers from given link
brainly.com/question/21528399
#SPJ4
The diameter of a dime is 17.91 mm. The diameter of a strand of human hair is
6.0 x 10-2 mm. How many times greater is the diameter of a dime than the diameter of
the strand of human hair?
Answers
The diameter of a dime tells us the circumference of a dime is approximately 299 times larger than human hair.
What is DiameterThe diameter of an object is used to calculated the circumference or area of the object. This also helps us to know the width of a circular object.
In this problem, the diameter tells us about the length of the each quantity.
The diameter of a dime tells us how wide the coin is and the diameter if a hair tells us the width of the hair.
Comparing both values
Dime = 17.91mm
Hair = 6.0*10^-2
Divide both quantity together.
17.91 / 6.0*10^-2 = 298.5≅299
Learn more on diameter here;
https://brainly.com/question/13997576
#SPJ1
The monthly rents (in dollars) paid by 9 people are given below. (Note that these are already ordered from least to greatest.)
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210
Suppose that one of the people moves. Her rent changes from $1210 to $1480.
Answer the following.
What happens to the mean=____ it decreases by __$
____ it increases by __$
____ it stays the same
What happens to the median=____ it decreases by __$
____ it increases by __$
____ it stays the same
Answers
The mean of a data-set is given by the sum of the values of all observations in the data-set divided by the number of elements in the data-set.
In this problem, the data-set is given as follows:
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210.
Hence the mean is of:
M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1210)/9 = 1035.
After the change, the data-set is of:
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1480.
Hence the mean will be of:
M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1480)/9 = 1065.
Then the increase will be of:
1065 - 1035 = 30.
What is the median of a data-set?The median of a data-set is the middle element of the data-set, the value which:
50% of the data-set is lesser than.50% of the data-set is greater than.The median is not affected by the values at the bounds of the distribution, such as 1210 and 1480 are in this distribution, hence it remains constant.
More can be learned about the mean and the median of a distribution at https://brainly.com/question/17631693
#SPJ1
Suppose K⊆Rn is compact, f:K→R is continuous, and ϵ>0. Show that there is a number A>0 such that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
Answers
By using the concept of compact set, it can be proved that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
What is compact set?
A set K is said to be compact if every open cover of K has a finite subcover.
Let K⊆Rn is compact f:K→R is continuous, and ϵ>0
Let there exist [tex]x_n, y_n[/tex] ∈ K such that |f([tex]x_n[/tex])−f([tex]y_n[/tex])| > n∥[tex]x_n[/tex]−[tex]y_n[/tex]∥+ϵ,
Since K is compact there is a subsequence [tex]x_{nk}[/tex] and [tex]y_{nk}[/tex] of [tex]x_n, y_n[/tex] respectively such that [tex]x_{nk}[/tex] converges to x and [tex]y_{nk}[/tex] converges to y.
So, |f([tex]x_{nk}[/tex])−f([tex]y_{nk}[/tex])| > [tex]n_k[/tex]∥[tex]x_{nk}[/tex]−[tex]y_{nk}[/tex]∥+ϵ,
Since f is continuous,
We can write
|f(x)−f(y)| > [tex]n_k[/tex]∥x - y∥+ϵ,
This is true for infinite many [tex]n_k[/tex]
So ||x - y|| = 0
|f(x) - f(y)| > ϵ, a contradiction since f is continuous
So, there is a number A>0 such that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
To learn more about compact set, refer to the link-
https://brainly.com/question/17175854
#SPJ4
Which polygon appears to be regular?
Answers
Answer:
Figure b
Step-by-step explanation:
the sides are equal
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 402402 gram setting. is there sufficient evidence at the 0.020.02 level that the bags are overfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.
Answers
Yes there is sufficient evidence that the alternative hypothesis is;
bag filling machine works incorrectly at the 402 gram setting which is;
H_o ; μ ≠ 402
Null hypothesis; H_o ; μ = 402
Alternative hypothesis; H_o ; μ ≠ 402
The null hypothesis states that there is no difference in the test which is denoted by H_o. However, the sign of null hypothesis is denoted by the signs of = or ≥ or ≤.
Meanwhile, the alternative hypothesis is one that defers from the null hypothesis. This therefore implies a significant difference in the test. Thus, the signs of alternative hypothesis is denoted by; < or > or ≠.
Now, the question we have is a two tailed test. Thus;
The null hypothesis is;
bag filling machine works correctly at the 402 gram setting which is;
H_o ; μ = 402
The alternative hypothesis is;
bag filling machine works incorrectly at the 402 gram setting which is;
H_o ; μ ≠ 402
learn more about of hypothesis here
https://brainly.com/question/15720073
#SPJ4
Simplify -1(15+4-27) over 16
Answers
Answer:
1/2
Step-by-step explanation:
-1(15+4-27)/16
Add 15 and 4 to get 19.
Now you have -1(19-27)/16
Subtract 27 from 19 to get −8.
-1(-8)/16
Reduce the fraction 16/−8 to lowest terms by extracting and canceling out 8.
-(-1/2)
Simplify
1/2
Answer:
1/2
Step-by-step explanation:
⁻¹⁽¹⁵⁺⁴⁻²⁷⁾⁄₁₆
Calculate:
-(15 + 4 - 27) / 16
-(19-27)/16
-(-8) / 16
= 8/16
Simplify:
= 1/2
Given f(x)=3x+4f(x)=3x+4, find f(4)f(4).
Answers
Because:
f(4)= 3(4) + 4
f(4) = 12 +4
f(4) = 16
Answer:
f(x) = 3x + 4
f(4) = 3(4) + 4 = 12 + 4 = 16
prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
Answers
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
Learn more about Isosceles Triangle here
https://brainly.com/question/21475560
#SPJ4
Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
Answers
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
#SPJ1
if i have a b and then i get a 72% on a test that is 30% of my grade, what will my grade be?
Answers
Answer:
if you have about an 85 now than you shouldn’t go below a b
Step-by-step explanation:
Multiple (3x+y) by (4x+2y)
Answers
Answer:
12x² + 10xy + 2y²
Step-by-step explanation:
(3x + y)(4x + 2y) =
= 12x² + 6xy + 4xy + 2y²
= 12x² + 10xy + 2y²
In the context of hypothesis testing, what is a test statistic?
a. The confidence level that is to be used to except or reject the null hypothesis.
b. A parameter determine from a sample, such as mean or standard deviation, used to test a hypothesis.
c. A value, determined from sample information, used to test the null hypothesis.
Answers
In the context of hypothesis testing, a test statistic is; c. A value, determined from sample information, used to test the null hypothesis.
How to Interpret Hypothesis Testing?Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample. The null hypothesis is said to be a hypothesis where no important difference between the random variables
The test statistic is defined as a value that is computed from the sample data that is used when making a decision about whether or not to reject the null hypothesis.
Looking at the options and based on the definitions above, option C adequately describes the test statistic.
Read more about Hypothesis Testing at; https://brainly.com/question/15980493
#SPJ1
a military unit wants to pass through a forested arwa, but wants to check the area for possible enemy troops first. a team of speciaists will place 15 motion sensors throughout the area. each sensor has a probability of 0.95 of operating for a 24-hour period
Answers
By using Binomial distribution, it can be calculated that
a) Probability that the operation is successful = 0.8290
b) Number of sensors expected to operate during the 24 hour period = 14.25
What is Binomial Distribution?
Binomial Distribution is a discrete type probability distribution whose probability mass function is given by
P(X = x) = [tex]{n \choose x}p^xq^{n-x}[/tex]
p is the probability of success and q is the probability of failure.
a) This is a problem on Binomial Distribution
Probability that the operation is successful = P(X [tex]\geq[/tex] 14)
= P(X = 14) + P(X = 15)
P(X = 14) =
[tex]{15 \choose 14}(0.95)^{14}(1- 0.95)^{15 - 14}\\15 \times 0.95^{14}\times 0.05\\0.3657\\[/tex]
P(X = 15) =
[tex]{15 \choose 15} 0.95^{15}(1-0.95)^{15 - 15} = 0.4633[/tex]
Probability that the operation is successful = 0.3657+0.4633 = 0.8290
b) Number of sensors expected to operate during the 24 hour period = [tex]15 \times 0.95[/tex] = 14.25
To learn more about Binomial Distribution, refer to the link-
https://brainly.com/question/9325204
#SPJ4
What error did the student make? in line 2, the student forgot to multiply the right side of the equation by 2. in line 3, the student should have subtracted the equations instead of adding them. in line 3, the student added the two equations incorrectly. in line 5, the student used an incorrect equation when solving for x.
Answers
Answer: the student forgot to multiple by right side of equation 2 in line 2
Step-by-step explanation: your welcome :)
This graph shows the revenue, cost, and profit functions of a company. How can this company become profitable?
A graph shows the Price per Unit on the x-axis and dollars on the y-axis. A downward parabola revenue vertex at (25, 12,000) intercepts the origin and x-axis at (30, 0) linear function costs intercept the y axis at (0, 13,000).
A.
by increasing its production
B.
by increasing its prices
C.
by reducing its costs
D.
by reducing its prices
Answers
Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.
What is a profit?In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.
Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:
Profit = Revenue - Cost
In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.
Read more on profit here: https://brainly.com/question/13849511
#SPJ1
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
if the points below represent a direct variatin find the missing value (2, -6) and (5, y)
Answers
The missing value if the point is a direct variation is -15
How to determine the missing value?From the question, we have the following ordered pairs
(2, -6) and (5, y)
These ordered pairs are direct variation
A direct variation is represented as
k = y/x
This means that
y/5 = -6/2
Evaluate the quotient
y/5 = -3
Multiply both sides by 5
y = -15
Hence, the value of y is -15
Read more about direct variation at
https://brainly.com/question/6499629
#SPJ1
estimate using compatibl numbers.
241 divided by 34
Answers
240/30
240/30=8
Orr you could round to
240/35
Which equals 6.86 but it’s easier to do 240 divided by 30
alexis likes to go for boat rides along a river with her family. in still water, the boat travels about 7 kilometers per hour. in the river, it takes them the same amount of time t to go upstream 4 kilometers as it does to travel downstream 8 kilometers. if the speed of the river is r, which of the following expressions represents the time it takes to travel 4 kilometers upstream?
Answers
It takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?
it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.
speed of boat = 7 km/hr
speed of river = r km/hr
speed upstream = 7-r km/hr
speed downstream = 7+r km/hr
time taken to go upstream 4 km = 4/(7-r)
time taken to go downstream 8 km = 8/(7+r)
as time taken is equal in both scenario:
4/(7-r) = 8/(7+r)
on solving we get:
r = 7/3 km/hr
put this value in time taken for upstream
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
to learn more about relative speed:
https://brainly.com/question/29523095
#SPJ4
Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?Think about two trains that are traveling in the same direction and at the same pace.
Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.
The other train seems to be moving at a constant speed.
So, we know that:
Speed of boat = 7 km/hr
Speed of river = r km/hr
Now,
Speed upstream = 7-r km/hr
Speed downstream = 7+r km/hr
Time taken to go upstream 4 km = 4/(7-r)
Time taken to go downstream 8 km = 8/(7+r)
As the time taken is equal in both scenarios:
4/(7-r) = 8/(7+r)
On solving we get:
r = 7/3 km/hr
Put this value in time taken for upstream as follows:
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
Learn more about relative speed here:
https://brainly.com/question/29523095
#SPJ4
Write the equation of the line that passes through (4,2) and is parallel to y =3x + 1 in point-slope form
Answers
Answer:
y=3x-10
Step-by-step explanation:
y=mx+b
2=3(4)+b
2=12+b
b=-10
y=3x-10
Elephants sometimes damage trees in Africa. It turns out that elephants dislike bees. They recognize beehives and avoid them. Can this information be used to keep elephants away from trees? Will elephant damage be less in trees with hives? Will empty hives even keep elephants away? Researchers want to design an experiment to answer these questions using 72 acacia trees. Identify the experimental units, treatments, and the response variable.
Answers
a) The experimental units are the Acacia Trees.
b) The treatments carried used are; active beehives, empty beehives and no single beehive.
c) The response variable is the damage that the elephants caused to the trees.
How to interpret experimental research design?Experimental design is defined as the process of carrying out research in a manner that is objective and controlled such that precision is maximized and then specific conclusions can possibly be drawn regarding a hypothesis statement. Generally, the purpose of this is to establish the effect that a factor or independent variable has on a dependent variable.
From this question, it is very clear that the experimental units are the Acacia Trees. This is because they are the primary interest or objective of the research.
The treatments carried out here are the active beehives, empty beehives and no single beehive.
The response variable is defined as the result of the experiment where the explanatory variable is manipulated. In this case, the response variable is the damage that the elephants caused to the trees.
Read more about Experimental Research Design at; https://brainly.com/question/17009178
#SPJ1
The table below shows that the number of miles driven by Abigail is directly
proportional to the number of gallons she used.
Gallons Used Miles Driven
15
517.5
33
1138.5
36
1242
What is the constant of proportionality between the
number of miles driven and the number of gallons
used?
Answers
Answer: 34.5
Step-by-step explanation:
To find the constant of proportionality between miles driven and number of gallons used, we will divide the miles driven by the gallons used.
517.5 / 15 = 34.5
1138.5 / 33 = 34.5
1242 / 36 = 34.5
If 50% of a number is 120 and 80% of the same number is 192, find 30% of that
number.
Answers
Answer: the answer is 72
Step-by-step explanation:
if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240
Now we need to determine 30% of 240 and the procedure explaining it as such
Step 1: In the given case Output Value is 240.
Step 2: Let us consider the unknown value as x.
Step 3: Consider the output value of 240 = 100%.
Step 4: In the Same way, x = 30%.
Step 5: On dividing the pair of simple equations we got the equation as under
240 = 100% (1).
x = 30% (2).
(240%)/(x%) = 100/30
Step 6: Reciprocal of both the sides results in the following equation
x%/240% = 30/100
Step 7: Simplifying the above obtained equation further will tell what is 30% of 240
x = 72%
Therefore, 30% of 240 is 72
I hope this helps
Answer:
72
Step-by-step explanation:
You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.
SolutionThe 30% you want will be the difference between 80% and 50%:
80% -50% = 30%
192 -120 = 72
30% of the same number is 72.
The heights, in feet, of the trees for sale at two nurseries are shown below.
Yard Works: 7, 9, 7, 12, 5
The Grow Station: 9, 11, 6, 12, 7
Which statements are true regarding the measures of center and variability of these data sets? Select three choices.
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.
The median of the tree heights at Yard Works is greater than the median of the tree heights at The Grow Station.
The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is greater than the mean absolute deviation of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.
THIS IS URGENT NEED NOW
Answers
The correct option regarding the heights of the trees include:
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow StationHow to calculate the value?The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station. This was illustrated as:
(12 - 5) > (12 - 7)
7 > 5
The mean of tree heights at Yard Works is 8 feet.
The mean of tree height at The Grow Station is 9 feet.
The mean absolute deviation of the tree heights at both yards is 2.
Learn more about mean on:
https://brainly.com/question/10002748
#SPJ1
the rectangular coordinates of a point are s2, 2, 21d. find the cylindrical and spherical coordinates of the point
Answers
The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.
Rectangular coordinates of a point is written like (x, y, z)
Cylindrical coordinates of a point is written like (r, θ, z)
Spherical coordinates of a point is written like (p, θ, φ)
First talk about Rectangular vs Cylindrical.
x = rcosθ
y = rsinθ.
z = z
x^2 + y^2 = r^2
given rectangular coordinates as (2,2,-1)
x=2, y=2, z=-1.
r^2 = 4+4 = 8.
r = [tex]\sqrt{8}[/tex]
r = 2[tex]\sqrt{2}[/tex]
θ = [tex]tan \inv-1[/tex](y/x) = [tex]tan \inv-1[/tex](2/2) = [tex]tan -1[/tex](1) = 45° = 0.78rad .
z = -1.
So Cylindrical coordinates is (r,θ,z) = ([tex]\sqrt{8}[/tex],0.78,-1).
Now let's us talk about Rectangular vs Spherical Coordinates.
x = pcosθsinφ.
y= psinθsinφ.
z = pcosφ.
p^2 = x^2+y^2+z^2.
tanθ = y/x
cosφ = z/p = z/[tex]\sqrt{x^2+y^2+z^2}[/tex].
given rectangular coordinates as (2,2,-1)
x=2, y=2, z=-1.
p = [tex]\sqrt{x^2+y^2+z^2}[/tex] = [tex]\sqrt{2^2+2^2+(-1)^2}[/tex] = [tex]\sqrt{9}[/tex] = 3
θ = [tex]tan -1[/tex](y/x) = 0.78rad .
φ = [tex]cos -1[/tex](z/p) = [tex]cos -1[/tex](-1/3) = 1.91rad
So Spherical coordinates is (3, 0.78rad, 1.91rad).
The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.
Given Question is incomplete, Complete Question here
The Rectangular Coordinates Of A Point Are (2,2,-1) Find The Cylindrical And Spherical Coordinates Of the Point,
To know more about cylindrical and spherical coordinates here.
https://brainly.com/question/4465072
#SPJ4
Find the equation of a line that passes through the point (0,-1) and has a gradient of 2.
Leave your answer in the form
y=mx+c
Answers
Answer:
Step-by-step explanation:
y = 2x - 1
when you sub in 0 in x and -1 in y, the y-intercept is -1.
f(x) =
2/9x2+18x-216
Answers
Answer:
Domain: all real numbers
Step-by-step explanation:
The function is:
[tex] f(x) = \dfrac{2}{9}x^2 + 18x - 216 [/tex]
The domain of a function is the set of values of the x-coordinates of the points of the function.
In this function, there is no restriction on x, so the domain is all real numbers.
simplify (8^(5))/(8^(-9))
1.8^-45
2.8^-4
3.8^14
4.8^45
Answers
The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3
What are index forms?Index form of a number can simply be described as that number written in the form of an exponential expression.
The number can also be written as a single number which is raised to another number.
Some rules of indices to note;
Multiplying index form results in addition of their powersDivision results in subtraction of their powersGiven that;
(8^(5))/(8^(-9))
Then, we have;
8^5-(-9)
8^5+9
Add the powers
8^14
Hence, the value is 8^14
Learn more about index forms here:
https://brainly.com/question/15361818
#SPJ1
