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]
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The shape of the distribution of the time required to get an oil change at a 10 minute oil change facility is unknown. However, records indicate that the mean time is 11.2 minutes and the standard deviation is 4.8 minutes
(a) to compute probabilities regarding the sample mean using the normal model, what size sample would be required?
(b) What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 10 minutes?
Answer:
The answer is below
Step-by-step explanation:
a) For a normal model the sample size has to be equal or greater than 30 so that it can be a normal distribution.
b) Given that:
μ = 11.2 minutes, σ = 4.8 minutes, n = 45
The z score determines how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For x < 10 minutes
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.8/\sqrt{45} }= -1.68[/tex]
Therefore from the normal distribution table, P(x < 10) = P(z < -1.68) = 0.0465
Algebra question down below (screen shot of the question)
Hi there! :)
Answer:
[tex]\huge\boxed{18 units}[/tex]
Subtract point F from point G to solve for the distance:
12 - (-6) = 18 units.
3x=2x+50 solve for x
this is the answer to your question x=50
Step-by-step explanation:
3x-2x=50
1x=50
The value of x for the given equation is given as x = 50.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation is as below,
3x = 2x + 50
It can be solved as follows,
3x = 2x + 50
=> 3x - 2x = 50
=> x = 50
Hence, the solution of the given linear equation is x = 50.
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7 - 2x if x = -4 And show your work
Answer: 15
Step-by-step explanation: To evaluate an expression, we plug the value of the variable into the expression and simplify.
Since we have 7 - 2x and x is -4, we have 7 - 2(-4).
Simplifying from here, 2(-4) is -8 so we have 7 - (-8).
Now, remember that a a minus sign followed by a
negative sign turns the two signs into a plus sign.
So 7 - (-8) can be thought of as 7 + (+8) which is 15.
pls do this!! scientific method
Answer:
a. [tex]1\,\,\,10^4[/tex]
b. [tex]1.57\,\,\,10^{-4}[/tex]
c. [tex]1.2\,\,\,10^{10}[/tex]
d. [tex]1.72\,\,\,10^{-15}[/tex]
e. [tex]4.53\,\,\,10^5[/tex]
f. [tex]5.682\,\,\,10^{14}[/tex]
g. [tex]8.1\,\,\,10^{-8}[/tex]
h. [tex]9.04\,\,\,10^{-13}[/tex]
i. [tex]7.123\,\,\,10^3[/tex]
j. [tex]4\,\,\,10^{-3}[/tex]
Step-by-step explanation:
Start by recognizing the significant figures of the number in question. the first factor to include in the scientific notation should have a non-zero digit followed by a decimal point, and whatever other significant figures follow. Make sure you count how many places you need to move the decimal point to get to the first significant figure for the quantity. If you moved the decimal point to the left in order to get to the first significant figure, you have to include a positive exponent for the base ten, and that exponent is the number of places you counted. If you moved to the right when moving the decimal point to locate it after the first significant figure, you need to include the negative of the number of places you counted in the exponent of the accompanying base 10.
In how many ways can six people be assigned to three offices if there are two people located in each office
Answer: 504 ways
Step-by-step explanation:
given data:
no of people = 6
no of offices = 3
no of people in each office = 2
solution:
first we need to find the number of ways 6 people can be shared in 2 or pairs as this is a combination problem.
= 6C2
= 15 ways
ways to place a pair of 2 in 3 offices
= 15 * 3
= 45ways.
using the remaining 4 people we have 4C2 = 6 ways
in the remaining 2 offices
6 * 2 = 12ways
withour conditions
= 45 * 12
= 540ways
considering the constraint
= 4C2
= 6ways
shared in 3 offices
= 6 * 3
= 18 ways
remaining 2 offices
= 18 * 2
= 36 ways
Without constraints - With constraints
= 540 - 36
= 504ways
90 ways.
Given:
Six people are to be assigned in three offices, two people per office.
Thinking of this problem from the perspective of offices themselves picking persons, we get this:
Firstly out of 6 person, 2 person are chosen in [tex]^6C_2[/tex] ways.
Secondly, from rest of the 4 persons, 2 people are chosen in [tex]^4C_2[/tex] ways.
Then rest of the 2 persons are chosen from rest persons in [tex]^2C_2[/tex] ways.
Applying law of multiplication for number of ways:
Total number of ways = [tex]^6C_2 \times ^4C_2 \times ^2C_2 = 15 \times 6 \times 1 = 90[/tex]
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There are 1,639 students in attendance at Auburn High School. Approximately what percentage does one student count towards the total number of students?
Answer:
0.6%
Step-by-step explanation:
1/1639 is 0.0006, and to get the percent from that just move the decimal point twice to the right.
The 10,000-meter long-distance running event in the summer Olympics is approximately 6.2 miles. Which equation could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute?
Answer:
[tex]\bold{t = f(s) = \dfrac{6.2}{s}}[/tex]
Step-by-step explanation:
Given that distance is 10,000 meter or 6.2 miles.
Time taken is [tex]t[/tex] minutes.
Average speed is [tex]s[/tex] miles/minutes
To find:
Equation to determine time 't' as a function of average speed 's' = ?
t is in minutes and
s is in miles/minute
Solution:
First of all, let us have a look at the formula for Average Speed:
[tex]\text{Average Speed} = \dfrac{\text{Total Distance Traveled}}{\text{Total Time Taken}}\\\Rightarrow \text{Total Time Taken} = \dfrac{\text{Total Distance Traveled}}{\text{Average Speed}}\\[/tex]
Now, we are given that Time, [tex]t[/tex] should be in minutes and
Average speed, [tex]s[/tex] must be in miles per minute
That means, we must have distance in miles.
Putting all the values in above formula.
So, the formula or equation becomes:
[tex]t = \dfrac{6.2}{s}[/tex]
Therefore the equation to find time, [tex]t[/tex] in minutes as a function of Average Speed, [tex]s[/tex] is given as:
[tex]\bold{t = f(s) = \dfrac{6.2}{s}}[/tex]
A farmer has a field in the shape of a triangle. The farmer has asked the manufacturing class at your school to build a metal fence for his farm. From one vertex, it is 435m to the second vertex and 656m to the third vertex. The angle between the lines of sight to the second and third vertices is 49 degrees. Calculate how much fencing he would need to enclose his entire field.
Answer:
The amount required is [tex]l_t = 1586 \ m[/tex]
Step-by-step explanation:
From the question we are told that
The length of one side is [tex]l_1 = 435 \ m[/tex]
The length of the second side is [tex]l_2 = 656 \ m[/tex]
The angle between the line of sight of second and third side is [tex]\theta = 49^o \\[/tex]
Generally using cosine rule the third side is evaluated as
[tex]l_3^2 = l_1 ^2 + l_2^2 - 2 * l_1 * l_2 cos (\theta )[/tex]
=> [tex]l_3^2 = 435 ^2 + 656^2 - 2 * 453* 656 cos (49)[/tex]
=> [tex]l_3 = 495 \ m[/tex]
The total amount of face required is mathematically evaluated as
[tex]l_t = l_1 + l_2 + l_3[/tex]
[tex]l_t = 435 + 656 + 495[/tex]
[tex]l_t = 1586 \ m[/tex]
Give the values of Xmin, Xmax, Ymin, and Ymax for the screen, given the values for Xscl and Yscl.
Xscl = 10, Yscl = 10
Answer: Option C.
Step-by-step explanation:
Xmin, Xmax, Ymin, and Ymax represent the minimum/maximum values that X and Y can take.
We know that the scale in Y and X is 10.
This means that each mark in each axis represents 10 units.
Now, let's go to the vertical axis (y-axis)
Counting from the (0, 0) we can count:
4 marks up
4 marks down.
So if each mark represents 10 units, 4 marks are 40 units.
Then the range for Y is {-40, 40}
Now for the horizontal axis.
We can count 3 marks on each side, and with the same reasoning as before, we can find that the range for X is: {-30, 30}
Then we have that:
Xmin = -30
Xmax = 30
Ymin = -40
Ymax = 40
Now, as a point is defined as (X, Y)
This region can be written as:
{Xmin, Xmax} by {Ymin, Ymax}
or, replacing the values:
{-30, 30} by {-40, 40)
So the correct option is C.
C] X min and X max = (-300, 300) and Y min and Y max = (-400, 400)
Xmin, Xmax, Ymin and Ymax denote minimum and maximum values of X and Y respectively.
As x and Y scale are 10 each, the minimum and maximum values can be found by multiplying the units with respective scales.
On X (Horizontal Axis), there are 3 units of line segments each on both left & right sides of origin.
Hence X min & X max = (0 - 300, 0 + 300) = (-300, +300) respectively.
On Y (Vertical Axis), there are 4 units of line segments each on both upwards & downwards sides of origin.
Hence Y min & Y max = (0 - 400, 0 + 400) = ( -400, + 400) respectively.
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The equation 9 x 2 − 12 x + 4 = 0 9 x 2 − 12 x + 4 = 0 has how many different solutions?
We have the equation:
[tex]9x^2-12x+4=0[/tex]
so:
[tex]a=9\qquad b=-12\qquad c=4[/tex]
and:
[tex]\Delta=b^2-4ac=(-12)^2-4\cdot9\cdot4=144-144=\boxed{0}[/tex]
This equation has one solution.
A survey is being conducted in a city with 1 million residents. It would be far too
expensive to survey all of the residents, so a random sample of size 1000 is chosen
(in practice, there are many challenges with sampling, such as obtaining a complete
list of everyone in the city, and dealing with people who refuse to participate). The
survey is conducted by choosing people one at a time, with replacement and with equal
probabilities.
(a) Explain how sampling with vs. without replacement here relates to the birthday
problem.
(b) Find the probability that at least one person will get chosen more than once.
Answer: Find answers in the attached documents
Step-by-step explanation:
In this case, we have to use the knowledge of probability and calculate the chance of the event to occur, so we have to:
A) No have problem, because every person can be chosen once or not be chosen at all.
B) The event that everybody has been chosen maximally once is equal to the event that we have chosen the sample without replacement.
So that way, we have to analyze to know how the event will occur, so:
A)In this case we choose the sample with replacement, so the probability that there will be birthday match.
B) Using the formula, we have:
[tex]P=1-P\\=1-\frac{(10^6/10^3)}{(10^6)^{(10^3)}}[/tex]
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Two angles are supplementary. The measure of angle 1 is equal to 12x+4 and the measure of angle 2 is equal to 4(2x+5).what is the measure of angle 2?
Answer:
82.4
Step-by-step explanation:
12x+4+8x+20=180
20x+24=180
-24 -24
20x= 156
x= 7.8
Angle 2
4(2*7.8 +5)
4(15.6+5)
4(20.6)
82.4
AB= 10 & AC=25 find the length of BC.
Answer:
15
Step-by-step explanation:
We can imagine this like a number line.
A------------B--------------------C
The distance from A to B is 10.
The distance from A to C is 25.
This means that the distance from B to C will be [tex]25-10=15[/tex].
Hope this helped!
the ratio of girls to boys in the grade is 9 to 10. If there are 225 girls, how many boys are there?
Answer:
250 boys
Step-by-step explanation:
We know that the ratio is 9:10 from girls to boys
Take 225 and divide it by 9
225 ÷ 9 = 25
So we know that 25 is a factor of 225
We can the number of boys and multiply it by 25 to get 250
If we put it in the ratio form:
225:250 = 9/10
Check work:
25 x 9 = 225
25 x 10 = 250
Girls :Boys = 9:10
Total girls= 225
9=225
10=10/9×225
=250
NB: It will 250 because 9 is going to cancel 225
only number 7 please, and the expression
Answer:
8n, 40 miles in 5 weeks.
Step-by-step explanation:
given that nate runs 8 miles each week.
Hence in n weeks, he will run
8 miles per week x n weeks
= 8n miles
in 5 weeks, n = 5.
Substituting this into the expression,
8(5) = 40 miles
could i have some help? day 4 of online school and im already so confused lol..
Answer:
$2416
Step-by-step explanation:
plug in 5 in the place of t
1500(1.1)⁵
(1.1)⁵ = 1.61051
1.61051 x 1500 = 2415.765
If the mean of: 2x,x,(2x−11),(x−3) is equal 4, then the value of x is:
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 5}}}}}[/tex]Step-by-step explanation:
Given data : 2x , x , 2x - 11 , x - 3
Mean = 4
N ( number of items ) = 4
Σx = 2x + x + 2x - 11 + x - 3
To find : value of x
Finding the value of x
We know that ,
Mean = [tex] \sf{ \frac{Σx}{n} }[/tex]
plug the values
⇒[tex] \sf{4 = \frac{2x + x + 2x - 11 + x - 3}{4} }[/tex]
Collect like terms
⇒[tex] \sf{4 = \frac{6x - 14}{4 }}[/tex]
Apply cross product property
⇒[tex] \sf{6x - 14 = 16}[/tex]
Move 14 to right hand side and change it's sign
⇒[tex] \sf{6x = 16 + 14}[/tex]
Add the numbers
⇒[tex] \sf{6x = 30}[/tex]
Divide both sides of the equation by 6
⇒[tex] \sf{ \frac{6x}{6} = \frac{30}{6} }[/tex]
Calculate
⇒[tex] \sf{x = 5}[/tex]
Hope I helped!!
Best regards!!!
Write in standard form 9x + 3x^2-4x^8+x^4+2x^4 in standard form
Answer:
- 4x^8 + 3x^4 + 3x^2 + 9x
Step-by-step explanation:
Standard form means that the terms are ordered from biggest exponent to lowest exponentFirst simplify
9x + 3x^2-4x^8+x^4+2x^4 = 9x + 3x^2 - 4x^8 + 3x^4Put in standard form
- 4x^8 + 3x^4 + 3x^2 + 9xSmaller p-values indicate more evidence in support of the: A. the reduction of variance B. null hypothesis C. quality of the researcher D. alternative hypothesis
Answer:
A. the reduction of variance
Step-by-step explanation:
If the p bakue gets smaller, the smaller the p- value the stronger the evidence that we can or we should totally reject and not accept the null hypothesis.
Id the p value is lower, the result is trumpeted as significant, but if higher,it is not significant.
So Smaller p-values indicate more evidence in support of the the reduction of variance
which of the following is equivalent to 2/5 x 3/8
Answer:
[tex]\frac{3}{20}[/tex] or [tex]0.15[/tex] (they're the same thing)
Step-by-step explanation:
Find a common denominator between the fractions. Both denominator have an LGM of 40Increase the denominators, so they both are now 40. To make it even, increase the nominators by however much you increase the denominators: 5 × 8 = 40 and 8 × 5 = 40. 2 × 8 = 16 and 3 × 5 = 15.You fractions should now look like this: [tex]\frac{16}{40} and \frac{15}{40}[/tex] Now, you can multiply them together. So, 16/40 times 15/40 is 3/20 or 0.15 (they're the same)I hope this helps!
A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal-demand function Upper D prime (x )equals negative StartFraction 4000 Over x squared EndFraction where x is the price per unit, in dollars. Find the demand function if it is known that 1002 units of the product are demanded by consumers when the price is $4 per unit.
Answer: the demand function is D(x) = 4000/x + 2
Step-by-step explanation:
Given that
D'(x) = - 4000 / x²
Now d(D(x)/dx = - 4000/x²
so we integrate with respect to x
∫ d(D(x)) = - ∫ (4000/x²) dx = -4000 x⁻¹/-1 + C
⇒ D(x) = 4000/x + C
where C is a constant
Given that; x = 4 and D(x) = 1002
so we substitute
1002 = 4000 / 4 + C
1002 = 1000 + C
C = 1002 - 1000
C = 2
so D(x) = 4000/x + C ⇒ D(x) = 4000/x + 2
Therefore the demand function is D(x) = 4000/x + 2
Find a geometric power series for the function, centered at 0, by the following methods. f(x) = 7/8 + x by the technique shown in Examples 1 and 2 f (x) = sigma^infinity_ n = 0 by long division (Give the first three terms.) f (x) =
Answer:
f(x) = 7/8 + n=0 = 7/8 so the answer you looking for would be: n=0
What is the horizontal distance from the origin to the point (1, 4)
The horizontal distance from the origin to the point (1, 4) is 1 unit.
What is Distance?The length along a line or line segment between two points on the line or line segment.
To find the horizontal distance from the origin to the point (1, 4)
we need to find the x-coordinate of the point.
The x-coordinate of the point (1, 4) is 1
1 represents the horizontal distance from the origin to the point.
Therefore, the horizontal distance from the origin to the point (1, 4) is 1 unit.
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An earthquake was felt throughout a circular area of 1808.64 Square miles what was the radius of the circular area
A.24 miles
B. 12 miles
c. 20 miles
d. 576 miles
Answer:
A
Step-by-step explanation:
The area of a circle is given by the formula:
[tex]A=\pi r^2[/tex]
Where A is the area and r is the radius.
Since we already know the area, we can plug it in and solve for r. Thus:
[tex]1808.64=\pi r^2\\[/tex]
Divide both sides by π. We can use 3.14 as an approximation. The πs on the right cancel out:
[tex]1808.64\div(3.14)=r^2\\r^2=576[/tex]
Take the square root of each side:
[tex]\sqrt{r^2}=\sqrt{576}[/tex]
The squares on the left cancel. The root of 576 is 24:
[tex]r=24[/tex]
Therefore, the radius is 24.
Answer:
I agree 24 miles
Step-by-step explanation:
the person above is correct
If f(x) = 5x2 – X + 2, then what is the remainder when f(x) is divided by x + 1?
Answer:
The answer is 8Step-by-step explanation:
f(x) = 5x² - x + 2
Using the remainder theorem
To find the reminder substitute the value of x into the above function and solve
That's
x + 1 = 0
x = - 1
So we have
f(-1) = 5(-1)² - ( - 1) + 2
f(-1) = 5 + 1 + 2
f(-1) = 6 + 2
We have the final answer as
8Hope this helps you
Please help me please?! ❤️❤️
Answer:
(4,3)
Step-by-step explanation:
Point V lies in the Ist quadrant . and the co-ordinates are (4,3)
find the distance between a point (6,9) and a horizontal line at y=5
Answer:
Distance = √52
Step-by-step explanation:
Given:
First point = (6,9)
And y = 5
So,
x = 0
Second point = (0,5)
Find:
Distance
Computation:
Distance = √(x1 - x2)² + (Y1 - Y2)²
Distance = √(6 - 0)² + (9 - 5)²
Distance = √ 36 + 16
Distance = √52
The new bookcase for your future dorm room has the dimensions of 24 in wide by 12 in deep by 36 in tall. if one average
textbook has the dimensions of 8.5 in wide by 11 in long by 1.5 in tall, how many books could you fit on your bookshelf with
no shelving?
O 73 books
140 books
10368 books
The correct answer is A. 73 books
Explanation:
The first step to find the answer is to know the total volume/space in the bookcase. This can be calculated by using the formula v (volume) = h (height) x l (length) x w (width) or multiplying the three sides given because this is the formula for a cuboid and most bookcases have this shape.
v (volume) h x l x w
v = 36 in x 24 in x 12 in
v = 10368 in
According to this, the total volume of the shelf is 10368 in. The next step is to calculate the volume of 1 book. This can be found using the same process and formula.
1.5 in x 11 in x 8.5 in = 140.25 in
Finally, to know how many books can fit in the bookshelf divide the total volume of the bookshelf into the volume of one book.
10368 ÷ 140.25 = 73.9
Thus, the total books that can be fit in the bookshelf is 73
There are four students, all of different heights, who are to be randomly arranged in a line. What is the probability that the tallest student will be first in line and the shortest student will be last in line?
Answer:
Hey there!
The answer is 1/12
1/4(1/3)=1/12
Let me know if this helps :)