Answer:
A; ?; Line 3
Step-by-step explanation:
Question 1:
-30 divided by -6 is 5.
The negatives cancel each other out.
And 30 divided by 6 is simply 5.
Question 2:
[tex]62\div(3+9)[/tex]
Do the operation inside the parenthesis first:
[tex]62\div12[/tex]
Divide. 12 does not go into 62 evenly. 12 times 5 is 60, so the answer is 5 remainder 2:
[tex]62\div12=5\text { R}2[/tex]
Or in fractions:
[tex]31/6[/tex]
(Was there a typo? From what you've given me, the correct answer is not listed.)
Question 3:
So we have to following steps:
[tex]\text{Line 1: } 21+35\div7+6(2)\\\text{Line 2: }21+5+6(2)\\\text{Line 3: }21+11(2)\\\text{Line 4: }21+22\\\text{Line 5: }43[/tex]
The mistake is in Line 3. Danny cannot just combine 5+6(2) into 11(2). Instead, he should multiply 6(2) and then add. Thus, the correct solution is:
[tex]\text{Line 1: } 21+35\div7+6(2)\\\text{Line 2: }21+5+6(2)\\\text{Line 3: }21+5+12\\\text{Line 4: }26+12\\\text{Line 5: }38[/tex]
15 is 9 more than 5 j =
Answer:
15 = 9 + 5j
Step-by-step explanation:
When you want to make words become an equation, the word is usually means = and more usually means +.
In this case, we have 15 is 9 more than 5j.
We can rewrite this as 15 = 9 + 5j.
200 is 10 times as much as 20 true
Answer:
yes
Step-by-step explanation:
20x10= 200 therefor its 10times as much
This year's graduating class at Uniform University contains exactly 900 seniors. Each senior has a random number of parents (0, 1, or 2) who will attend the graduation ceremony, and it happens that each of those three possibilities is equally likely, with probability 1/3 each, and the numbers of parents attending the ceremony for different seniors are independent random variables The seating area for parents in the auditorium has 900 seats. Use a Normal approximation to approximate the probability that all of the parents who attend wil be able to be seated. What if the seating area has 925 seats? What is the minimum number of seats that can ensure that with probabty 0.95 of the parents who attend be able to be seated?
Answer:
941
Step-by-step explanation:
= 1, 2, 3...900 is the number of parents that are going to attend the ceremony.
we are given a random number of parents (0 1 2)
each of these random numbers have a probability of 1/3
so we multiply the numbers by their probability
E(X) = 0*1/3 + 1*1/3 +2*1/3
= 1
E(X²) = 0²*1/3 + 1²*1/3 + 2²*1/3
= 5/3
we calculate the variance
= E(X²)-[E(X)²
= 5/3 - 1²
= 2/3( got this by taking the lcm)
∑Xi with n = 900 will have to be the number of parents attending this ceremony for all seniors
E|S| = 900 * 1
= 900
var |S| = 900*2/3
=600
we are usng normal distribution to solve this
μ = E(S) = 900
σ² = var(S) = 600
for a seating area wth 900 seats now we are to find the probability that all the parents present will have seats
s-μ/√σ
900 -900/√600
= 0
p(z≤0)
= 0.5
for a seating area wth 925 seats we are to fnd probability that all parents will be seated
= s-μ/√σ
= 925-900/√600
= p(z≤1.0208)
= 0.84623
going to the table of standard normal distribution we have
p(z≤1.644845)= 0.95
s-μ/σ≤1.644845 = 0.95
we cross multply
s-μ≤1.644845σ
we make s subject of the formula
s ≤ μ+1.644845σ = 0.95
we now μ = 900 and
σ = √600
900+1.644845*√600
=900 +40.388
=940.388
= 941
we have that the minimum number of seat requred for all parents n attendance to be seat is 941 at a probability of 0.95
We have the minimum number of seats required for all parents' attendance to be seat is 941 at a probability of 0.95.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
1, 2, 3, .....900 is the number of parents that are going to attend the ceremony.
A random number of parents (0, 1, 2)
The probability is 1/3.
[tex]\rm E(X) = 0 * \dfrac{1}{3} + 1*\dfrac{1}{3}+2*\dfrac{1}{3} = 1\\\\\\E(X^2) = 0^2*\dfrac{1}{3}+1^2*\dfrac{1}{3}+2^2*\dfrac{1}{3}= \dfrac{5}{3}[/tex]
Then the variance will be
[tex]\rm Var = E(X^2) -[E(X)]^2\\\\Var = \dfrac{5}{3} -1 \\\\Var = \dfrac{2}{3}[/tex]
∑Xi with n = 900 will have to be the number of parents attending this ceremony for all seniors
[tex]\rm E \left| S \right| = 900* 1 \\\\E \left| S \right| = 900[/tex]
And
[tex]\rm Var \left| S \right| = 900 * \dfrac{2}{3} \\\\Var \left| S \right| = 600[/tex]
Then by the normal distribution, we have
[tex]\rm \mu = E(S) = 900\\\\\sigma ^2 = Var (S) = 600[/tex]
For a seating area with 900 seats then the probability of the parents present will have seats.
[tex]\rightarrow \dfrac{S - \mu }{\sqrt{\sigma}}\\\\\\\rightarrow \dfrac{900-900}{\sqrt{600}}\\\\\\\rightarrow 0[/tex]
For a seating area with 925 seats then the probability of the parents present will have seats.
[tex]\rm \rightarrow \dfrac{S - \mu }{\sqrt{\sigma}}\\\\\\\rightarrow \dfrac{925-900}{\sqrt{600}}\\\\\\\rightarrow P(z \leq 1.0208) \\\\\rightarrow 0.84623[/tex]
From the standard normal distribution table, we have
[tex]\rm p(z\leq 1.644845) = 0.95\\\\\dfrac{S-\mu}{\sqrt{\sigma }} \leq 1.644845= 0.95\\\\S \leq \mu + 1.644845 \sqrt{\sigma }= 0.95\\\\S=900 + 1.644845*\sqrt{600}\\\\S= 941[/tex]
We have the minimum number of seats required for all parents' attendance to be seat is 941 at a probability of 0.95.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
A 120$ coat was on sale for 88$. What was the percent of change in the price of this coat.
Answer: about 73 %
Step-by-step explanation:
because 88 of 120 is about 73 %
The percent of change in the price of this coat is 26.66 %.
To find the percent of change in the price of this coat.
What is percentage?A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.
Given that:
Cost price of coat(C.P)= 120$
Selling price of coat(S.P)=88$
We know that ,
Percent change=change in price /C.P*100
Percent change=120$-88$/120$*100
Percent change=32/120*100
Percent change=26.66 %
Therefore, the percent of change in the price of this coat is 26.66 %.
Learn more about percentage here:
https://brainly.com/question/17198381
#SPJ2
Estimate the Value Of Each Expression to the nearest integer .
Answer:
see below
Step-by-step explanation:
14. We can represent 1 as √1 and 2 as √4 and because 1 < 3 < 4, we know that √3 is in between 1 and 2. However, 3 is closer to 4 than it is to 1 so √3 is about 2.
15. Again, 3 is √9 and 4 is √16. 9 < 10 < 16 so √10 is in between 3 and 4, however, since 10 is closer to 9 as it is to 16, we know that √10 is about 3.
16. -4 = -√16 and -5 = -√25, since 16 < 22 < 25, we know that -√22 is in between -4 and -5 but 22 is closer to 25 so the answer is -5.
17. -10 = -√100 and -11 = -√121 so -√120 is in between -10 and -11. Since 120 is closer to 121, the answer is -11.
If the length of JK is 3x and the length of LM is 12x and the length of the entire line JM is 25x , find the length of KL.
Answer:
10x.
Step-by-step explanation:
It is given that,
JK = 3x
LM = 12x
JM = 25x
Let as consider the line as shown in the below figure.
From the figure it is clear that,
[tex]JK+KL+LM=JM[/tex]
[tex]3x+KL+12x=25x[/tex]
[tex]KL+15x=25x[/tex]
[tex]KL=25x-15x[/tex]
[tex]KL=10x[/tex]
Therefore, the length of KL is 10x.
55 liters = ______ microliters
When we transform the big quantity to the small one, we always have to multiply something. So micro refers x 10 to the power of 6
55 x 10^6 = 55,000,000 microliters.
Which are correct statements regarding proofs? Select three options.
In a paragraph proof, statements and their justifications are written in sentences in a logical order.
A two-column proof consists of a list statements and the reasons the statements are true.
A flowchart proof gives a visual representation of the sequence of steps without justifications.
A paragraph proof is a two-column proof in sentence form.
A two-column proof lists only the given information and what is to be proven.
Answer:
A, B, and D
Step-by-step explanation:
Just took the test :)
Answer:
a b d edge
Step-by-step explanation:
what is the volume of the cubic figure? enter the answer in the box below
use the figure to answer the question
9m, 5m, 18m, 10m, 9m, 24m,9m (look at picture)
Answer:
[see below]
Step-by-step explanation:
The figure is made out of two rectangular prisms.
V = w * l * h
Volume for the left prism:
V = 9 * 5 * 24
V = 1080 m³
Volume for the right prism:
V = 9 * 18 * 10
V = 1620 m³
Combine both volumes:
1620 + 1080 = 2700
2700 cubic meters should be your answer.
Hope this helps.
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
5, 8, 11, ...
A rectangle has an area of 35 square millimeters. The length of the rectangle is 7 millimeters. What is the width of the rectangle?
Answer:
5 millimetres
Step-by-step explanation:
Area of rectangle = lenght x width
35 = 7 x width
Width = 35/7
Width = 5 mm
The width of rectangle is 5 millimeters, whole length is 7 millimeters and area is 35 square millimeters.
What is rectangle?A rectangle is a part of a quadrilateral, whose corresponding sides are parallel to each other and equal, and makes right angle to each others.
Given that,
The area of rectangle = 35 square millimeters.
Also,
The length of the rectangle l = 7 millimeters.
Let the width of the rectangle is x millimeters.
To find the width of rectangle,
Use formula,
Area of rectangle = 35
length × width = 35
7 × x = 35
x = 5 millimeters.
The required width of rectangle is 5 millimeters.
To know more about Rectangle on:
https://brainly.com/question/15019502
#SPJ2
Line L containing points M, N and Q. Draw and label. Will give 5 stars & brainliest!
Answer: see image below
Step-by-step explanation:
Draw a line and label it L
Plot three points on the line and label them, M, N, and Q.
I am using o to represent each point.
<---------o-------------o---------------o-----------> L
M N Q
Linear regression describes the extent to which _______ predicts ________. X; Y the predictor variable; the criterion variable the known variable; the to-be-predicted variable all of the above
Answer: the known variable; the to-be-predicted variable
Step-by-step explanation:
In statistics, linear regression is a technique to model the relationship between two variables ( one independent and other dependent).
It requires some previous data to plot a best fit line.
It is used to predict the values for dependent variable for each independent variable.
Here, independent variable = known variable and dependent variable = is to be predicted
Hence, Linear regression describes the extent to which the known variable predicts the to-be-predicted variable.
A researcher conducts an experiment examining the effects of alcohol on college students' emotion. 120 participants are recruited from a large northeastern university to complete the study. Half of the participants are randomly assigned to an experimental condition in which they consume 3 alcoholic beverages and then complete a measure of emotion. Participants in the control condition consumed 3 non-alcoholic beverages before completing the same measure of emotion.
1. What is the population for the current study?
2. What is the sample for the current study?
3. What would be the null hypothesis for the current study?
4. What would be the alternative hypothesis for the current study?
5. In order to analyze the results of the current study, the experimenter would use a which is a(n):_________ statistical test.
a. F-test; Descriptive
b. F-test; Inferential
c. t-test; Descriptive
d. t-test; Inferential
Answer:
the answers are below
Step-by-step explanation:
1. the populaton of ths study are the college students that are beng tested on the effect of alcohol on their emotions. college students are the main focus of this experiment.
2. The sample for this study is the 120 students from the University. the sample of a study is actually the number of participants in that study. this queston says that they are 120
3. the null hyothesis:
h₀ : alcohol has no effect on college students emotions
4. the alternate hypothesis:
h₁: there is effect of alcohol on college students emotions
5. The researcher would have to use a t test which is an inferential statistical test. A t test is used to test for the existence of statistical difference between two means that may have similar features
If 4x+7=18 what is the value of 12x+21
show step by step work please
Answer:
54
Step-by-step explanation:
4x+7=18
subtracting 7 from both side of the equation
4x+7- 7=18 - 7
4x = 11
to find value of x , we divide both side of the equation by 4
4x/4 = 11/4 = 2.75
x = 2.75
now we plug in the found value of x = 2.75 in place of x in equation 12x+21
12*2.75 + 21 = 33 + 21 = 54
Thus, answer is 54
What type of graph would you use if you wanted to show the grade point averages of 10 individual students? Why?
Answer:
Histogram
Step-by-step explanation:
A histogram is a representation of approximate numerical data distribution. It was first introduced by Karl Pearson. Constructing a histogram, requires one to "bin" (or "bucket") the range of values, or say, divide the entire range of values into a series of Intervals, thereafter, count how many values fall into each interval. The bins well be specified as consecutive, and or non-overlapping intervals of a variable. The bins (intervals) is best left to be adjacent, and are often (but not required to be) of equal size.
An example of where a histogram would be used, is that of the distribution of grades on a school exam or the sizes of pumpkins, divided by size group, in a pumpkin festival.
Answer:
Bar graph
Step-by-step explanation:
It compares the data
Calculate the rate of change for the table of values.
X
у
2
50
3
75
4.
100
5
125
rate of change =
Answer:
25
Step-by-step explanation:
50:2=25
75:3=25
100:4=25
125:5=25
The rate of change of the given data in the table will be 25.
What is the rate of change?The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time.
The formula for the rate of change is straightforward: it simply divides the current value of a stock or index by the value from a previous time period.
The rate of change will be calculated by using the following formula:-
rate of change = ( y₂ - y₁ ) / ( x₂ - x₁ )
The rate of change will be calculated as below:-
50:2=25
75:3=25
100:4=25
125:5=25
Therefore, the rate of change of the given data in the table will be 25.
To know more about the rate of change follow
https://brainly.com/question/8728504
#SPJ2
use the figure and the Pythagorean theorem to write the equation relating e, b and (w-x)
Answer:
C) e²+(w-x)²=b²
Step-by-step explanation:
C) e²+(w-x)²=b²
B is the hypotenuse and takes the place of c in the Pythagorean Theorem. The second answer (x²+e²=b²) is also true, but isn’t what the question is asking for.
Orden the Numbers 0.78, 3/4, and 0.8 from last to greaters
Answer:
3/4, 0.78, 0.8
Step-by-step explanation:
3/4= 0.75.
0.78 is greater and 0.8 is greater again.
PLEASE HELP! A) 2.9 B) 9.2 C) 3.3 D) 5
Answer:
9.2 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 57 = x/6
6 tan 57 = x
9.239189783 = x
9.2 =x
Answer:
x = 9.2
Step-by-step explanation:
Step 1: Find out what primary trigonometry ratio is needed
The give us the adjacent and the angle. We need to find the opposite value so we will use tangent
Step 2: Plug in information and solve
[tex]tan(57)=\frac{x}{6} \\x=6tan(57)\\x=9.239[/tex]
Therefore x= 9.2
If AC = 24, find the value of x. Then find AB and BC
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, the correct question is:
If B is between A and C, and AB=3x+1, BC=2x-7, and AC=24, then find the value of x and the value of AB
Answer: The line segment addition postulate states that if a point B is placed between a line segment with end points A and C, then the distance between the points can be expressed by the equation:
AB + BC = AC
But AB=3x+1, BC=2x-7, and AC=24, Hence:
3x + 1 + 2x - 7 = 24
3x + 2x + 1 - 7 = 24
5x - 6 = 24
5x = 24 + 6
5x = 30
x = 6
AB = 3x + 1 = 3(6) + 1 = 18 + 1 = 19
BC = 2x - 7 = 2(6) - 7 = 12 - 7 = 5
0.525 c. Han Solo is shooting at the imperial fighters with his newly installed proton cannon purchased at the MSU Surplus Store for $20.00 plus 6.00% TAX. The cannon emits protons at a speed of 0.741 c with respect to the ship.
What is the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction?
0.911 ANS
What is the velocity of the protons in the resting frame when the cannon is shot in the backward direction? (Use positive sign for the forward direction, and negative for the backward direction.)
This question is incomplete, the complete question is;
The Millennium Falcon is chased by the Imperial Forces. The ship is moving at a speed of 0.525 c. Han Solo is shooting at the imperial fighters with his newly installed proton cannon purchased at the MSU Surplus Store for $20.00 plus 6.00% TAX. The cannon emits protons at a speed of 0.741 c with respect to the ship.
What is the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction? 0.911 ANS .
What is the velocity of the protons in the resting frame when the cannon is shot in the backward direction?
(Use positive sign for the forward direction, and negative for the backward direction.)
Answer:
A)
the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction is 0.911c
B)
the velocity of the protons in the resting frame when the cannon is shot in the backward direction -0.3535c.
The negative sign indicates that the proton is moving in the opposite direction of the ship. (backward)
Step-by-step explanation:
Given that;
speed of ship u = 0.525C
speed of proton emission v = 0.741C
Now When Cannon is shot in Forward Direction
Relativistic speed S is Calculated as;
S = (u+v) / ((1 + (uv))/c²)
we substitute (0.525 + 0.741 )C / ((1 + (0.525 × 0.741) C)/c²)
the C² cancel each other
so we have
S = 1.266 / 1.389925
S = 0.9108 ≈ 0.911c
Therefore the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction is 0.911c
When Cannon is shot in Backward Direction
Relativistic speed S is Calculated as;
S = ( u – v ) / ( 1 – uv / c ²)
S = (0.525 - 0.741) C / ((1 - (0.525 × 0.741) C)/c²)
the C² cancel each other
so S = -0.216 / 0.610975
S = -0.3535c
The negative sign indicates that the proton is moving in the opposite direction of the ship. (backward)
Therefore the velocity of the protons in the resting frame when the cannon is shot in the backward direction -0.3535c.
A one batch recipe of muffins makes a dozen muffins. it requires 2 eggs, two
cups of flour, and a 1\4 pound of sugar. There are 454 grams of sugar in a pound.
How many grams of sugar are in a muffin? **
Answer: 9.46 grams
Step-by-step explanation:
Given: Number of muffins made in one batch = 1 dozen =12 ]
[ as 1 dozen = 12]
Also, in one batch the quantity of sugar = [tex]\dfrac14[/tex] pound
As there are 454 grams of sugar in a pound.
So, in one batch the quantity of sugar = [tex]\dfrac14\times454=113.5\ grams[/tex]
i.e. in 12 muffins , there is 113.5 grams of sugar.
Then, in one muffin the quantity of sugar = (113.5 grams) ÷ 12
≈9.46 grams
Hence, there are 9.46 grams of sugar in 1 muffin.
An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and _t_ statistic. Also determine if the null hypothesis would be rejected at $\alpha$
Answer:
(a) P-value = 0.044
(b) P-value = 0.0022
(c) P-value = 0.4402
(d) P-value = 0.022
Step-by-step explanation:
The complete question is: An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and t-test statistics. Also, determine if the null hypothesis would be rejected at α = 0.05.
a) HA : μ > μ0, n = 11, T = 1.91
b) HA : μ < μ0, n = 17, T = -3.45
c) HA : μ [tex]\neq[/tex] μ0, n = 7, T = 0.83
d) HA : μ > μ0, n = 28, T = 2.13
(a) We are given the right-tailed test with sample size (n) of 11 and the test statistics of 1.91.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_n_-_1[/tex] > 1.91)
= P([tex]t_1_0[/tex] > 1.91) = 0.044
Since the P-value of the test statistics is less than the level of significance as 0.044 < 0.05, so we have sufficient evidence to reject our null hypothesis.
(b) We are given the left-tailed test with sample size (n) of 17 and the test statistics of -3.45.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_n_-_1[/tex] < -3.45)
= P([tex]t_1_6[/tex] < -3.45) = 0.0022
Since the P-value of the test statistics is less than the level of significance as 0.0022 < 0.05, so we have sufficient evidence to reject our null hypothesis.
(c) We are given the two-tailed test with sample size (n) of 7 and the test statistics of 0.83.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_n_-_1[/tex] > 0.83)
= P([tex]t_6[/tex] > 0.83) = 0.2201
For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.2201 = 0.4402.
Since the P-value of the test statistics is less than the level of significance as 0.044 < 0.05, so we have sufficient evidence to reject our null hypothesis.
(d) We are given the right-tailed test with sample size (n) of 28 and the test statistics of 2.13.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_n_-_1[/tex] > 2.13)
= P([tex]t_2_7[/tex] > 2.13) = 0.022
Since the P-value of the test statistics is less than the level of significance as 0.022 < 0.05, so we have sufficient evidence to reject our null hypothesis.
Arrange the operations into the order they should be performed in.
(60 + 15) - 3-2
Subtract 2.
Add 60 and 15.
Divide by 3.
1: Add 60 and 15.
2: Divide by 3.
3: Subtract 2.
What is the sum of 87 and 234252464375675647
Answer:
234252464375675734
Step-by-step explanation:
addition...
Answer:
here 234252464375734
Graph 4y – 5x = 20
Please help
4y-5x=20
. Just give numbers for x or y . Then, find the x value or y value from the equation.
Remember that y-axis is the vertical and x-axis is the horizontal line.
For example, just give x = 0 . 4y=20 y = will be 5 .
Now, write these on your graph.
As you see, 0 means orijin point , but if y=5 , use vertical line for writing 5.
Then, find the values while x=1 , x=2 ,and also x= -1 , x= -2 .
Finally, find the points from the connection of x and y points.
Then, combine all of connected points as a curve .
Do have an example of how to write in chronological order ?
Just write it in the order it first was in for instance. Firstly she put flour in the bowl. Secondly she added water. And finally she put the sugar in. Like that.
Answer:
Firstly she put flour in the bowl. Secondly she added water. And finally she put the sugar in.
A machine can fill containers with 45 ounces of hazelnuts. The weight of a container is 2 ounces. After a container is filled, another machine weighs it. If a filled container’s weight differs from the desired weight by more than 2 ounces, the container is rejected. Create an equation that can be used to determine the minimum and maximum acceptable weights of the containers filled with hazelnuts. (Represent the total weight of the container and the nuts with x.)
Answer: 2 = |x − 47|
Step-by-step explanation:The total weight of the container and the nuts is x ounces. The desired weight of the container and the nuts is (45 + 2), or 47 ounces. The absolute error allowed is 2 ounces.
absolute error = |actual weight − desired weight|
Substituting the values, the equation obtained is 2 = |x − 47|.
Use the Chain Rule to find the indicated partial derivatives.
w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ;
r=4 theta=pi/2
dw/dr=
dw/dtheta=
By the chain rule,
[tex]\dfrac{\partial w}{\partial r}=\dfrac{\partial w}{\partial x}\dfrac{\partial x}{\partial r}+\dfrac{\partial w}{\partial y}\dfrac{\partial y}{\partial r}+\dfrac{\partial w}{\partial z}\dfrac{\partial z}{\partial r}[/tex]
and similarly, [tex]\frac{\partial w}{\partial\theta}[/tex] is the same with [tex]r[/tex] replaced with [tex]\theta[/tex].
We have
[tex]\dfrac{\partial w}{\partial x}=y+z[/tex]
[tex]\dfrac{\partial w}{\partial y}=x+z[/tex]
[tex]\dfrac{\partial w}{\partial z}=x+y[/tex]
[tex]\dfrac{\partial x}{\partial r}=\cos\theta[/tex]
[tex]\dfrac{\partial y}{\partial r}=\sin\theta[/tex]
[tex]\dfrac{\partial z}{\partial r}=\theta[/tex]
Putting everything together, we get
[tex]\dfrac{\partial w}{\partial r}=(y+z)\cos\theta+(x+z)\sin\theta+(x+y)\theta[/tex]
Replace [tex]x,y,z[/tex] with their equivalent expressions in terms of [tex]r,\theta[/tex]:
[tex]\dfrac{\partial w}{\partial r}=r(\sin\theta+\theta)\cos\theta+r(\cos\theta+\theta)\sin\theta+r(\cos\theta+\sin\theta)\theta[/tex]
[tex]\dfrac{\partial w}{\partial r}=2r\theta\sin\theta+2r\theta\cos\theta+r\sin(2\theta)[/tex]
When [tex]r=4[/tex] and [tex]\theta=\frac\pi2[/tex], the derivative has a value of
[tex]\dfrac{\partial w}{\partial r}\left(4,\dfrac\pi2\right)=\boxed{4\pi}[/tex]
The same process will yield
[tex]\dfrac{\partial w}{\partial\theta}\left(4,\dfrac\pi2\right)=\boxed{-8\pi}[/tex]
The value of partial derivative are,
[tex]\frac{\partial w }{\partial r}(4,\frac{\pi}{2} )=4\pi[/tex] and [tex]\frac{\partial w }{\partial \theta}(4,\frac{\pi}{2} )=-8\pi[/tex]
Partial derivative :It is given that,
[tex]w = xy + yz + zx, x = r cos(\theta), y = r sin(\theta), z = r\theta[/tex]
We have to find partial derivative.
[tex]\frac{\partial w }{\partial r}=\frac{\partial w }{\partial x}*\frac{\partial x }{\partial r}+\frac{\partial w }{\partial y}*\frac{\partial y }{\partial r}+\frac{\partial w }{\partial z}*\frac{\partial z }{\partial z}\\\\\frac{\partial w }{\partial r}=(y+z)cos\theta+(x+z)sin\theta+(x+y)\theta\\\\\frac{\partial w }{\partial r}=2r\thetasin\theta+2r\thetacos\theta+rsin(2\theta)[/tex]
When [tex]r=4,\theta=\frac{\pi}{2}[/tex]
[tex]\frac{\partial w }{\partial r}(4,\frac{\pi}{2} )=4\pi[/tex]
Similarly,
[tex]\frac{\partial w }{\partial \theta}(4,\frac{\pi}{2} )=-8\pi[/tex]
Learn more about the chain rule of derivative here:
https://brainly.com/question/11549233