Answer:
δw/δr = 4π
δw/δθ = -8π
Step-by-step explanation:
Given the following functions
w = xy + yz + zx, x = r cosθ y = r sinθ, z = rθ where r = 4 and θ = π/2
We are to find δw/δr and δw/δθ
δw/δr = δw/δx•δx/δr + δw/δy•δy/δr + δw/δz•δz/δr
δw/δx = y+z
δx/δr = cosθ
δw/δy = x+z
δy/δr = sinθ
δw/δz = y+x
δz/δr = θ
Substitute the given values into the formula
δw/δr = (y+z)cosθ+(x+z)sinθ+(y+x)θ
Substitute the value of x, y and z in terms of theta into the resulting function
δw/δr = (y+z)cosθ+(x+z)sinθ+(y+x)θ
δw/δr = (rsinθ+rθ)cosθ+(rcosθ+rθ)sinθ+(rsinθ+rcosθ)θ
Substitute r = 4 and θ = π/2
δw/δr = (4sinπ/2+4π/2)cosπ/2+(4cosπ/2+4π/2)sinπ/2+(4sinπ/2+4cosπ/2)π/2
Note that cos π/2 = 0 and sinπ/2 = 1
δw/δr = (4+2π)(0)+(0+2π)(1)+(4(1)+4(0))π/2
δw/δr = 0+2π+4π/2
δw/δr = 2π+2π
δw/δr = 4π
For δw/δθ
δw/δθ = δw/δx•δx/δθ + δw/δy•δy/δθ + δw/δz•δz/δθ
δw/δx = y+z
δx/δθ = -rsinθ
δw/δy = x+z
δy/δθ =rcosθ
δw/δz = y+x
δz/δθ = r
Substitute the given values into the formula
δw/δθ = (y+z)-rsinθ+(x+z)rcosθ+(y+x)r
Substitute the value of x, y and z in terms of theta into the resulting function
δw/δθ = (y+z)-rsinθ+(x+z)rcosθ+(y+x)r
δw/δθ = (rsinθ+rθ)-rsinθ+(rcosθ+rθ)rcosθ+(rsinθ+rcosθ)r
Substitute r = 4 and θ = π/2
δw/δθ = (4sinπ/2+4π/2)-4sinπ/2+(4cosπ/2+4π/2)4cosπ/2+(4sinπ/2+4cosπ/2)(4)
Note that cos π/2 = 0 and sinπ/2 = 1
δw/δθ = (4+2π)(-4)+(0+2π)(0)+(4(1)+4(0))(4)
δw/δθ = -16-8π+0+4(4)
δw/δθ = -16+16-8π
δw/δθ = -8π
PLEASE HELP WILL GIVE BRAINLIST
Answer:
greater than or equal to
Step-by-step explanation:
Point E is located at (-5,2). Point M is the reflection of point E across the y-axis. What is the distance between E and M?
Answer:
The distance is Ten
Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 7 years. Assume that money is worth 6.2%, compounded quarterly. If $90,000 is invested in an annuity that earns 5.4%, compounded quarterly, what payments will it provide at the end of each quarter for the next 7 1/2 years?
Answer:
Step-by-step explanation:
From the first question:
We are to find PV of the annuity.
Using the formula:
Present value of Annuity = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)
Where , Annuity Amount = $4,000
n = No. of periods = 7 years × 4 quarters per year = 28 periods but since the first payment is at beginning of the quarter, Then, n = 27 when considered for PVAF
r = 6.2% / 4 quarters = 1.55%,
PVAF(n0,r) when first payment is at beginning of n i.e. n0 = 1 + { [1-(1+r)^ -n0 ]/r }
= 1 + { [1-(1+0.0155)^ {-27}]/0.0155 }
= 1 + [ (1 - 0.66015 ) ] / 0.0155]
= 1 + 21.926
= 22.926
PVAF(28,1.55%) = 22.926
Thus , Present Value of Annuity = $4,000 × 22.926 = $91704.00
2. Present value of Annuity due = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)
Present Value of Annuity = $90,000
n = No. of periods = 7.5 years × 4 quarters per year = 30 periods
r = 5.4% / 4 quarters = 1.35%,
PVAF(n,r) = [1-(1+r)^-n]/r
PVAF(n,r) = [1-(1+0.0135)^ -30]/0.0135
PVAF(30,1.35%) = (1 - 0.6688)/0.0135
PVAF(30,1.35%) = 0.3312/0.0135
PVAF(30,1.35%) = 24.53
Hence ;
$90,000 = Annuity Amount × 24.53
Annuity amount = $90,000/24.53 = $3,668.48
Three friends each have some ribbon. Carol has 90 inches of ribbon, Tino has 7.5 feet of ribbon, and Baxter has 3.5 yards of ribbon. Express the total length of ribbon the three friends have in inches, feet, and yards.
Answer: 306 inches or 25.5 feet or 8.5 yards.
Step-by-step explanation:
Given: Carol has 90 inches of ribbon, Tino has 7.5 feet of ribbon, and Baxter has 3.5 yards of ribbon.
1 feet = 12 inches
length of ribbon Tino has = 12 x 7.5 = 90 inches
1 yard = 36 inches
length of ribbon Baxter has = 3.5 x 36 = 126 inches
Total ribbon they have = (length of ribbon Carol has) + (length of ribbon Tino has) + (length of ribbon Baxter has)
= (90+90+126) inches
= 306 inches
In feet , Total ribbon = [tex]\dfrac{306}{12}\text{ feet}[/tex] [tex][\text{ 1 inch}=\dfrac{1}{12}\text{ feet}][/tex]
[tex]=\text{25.5 feet}[/tex]
In yards, Total ribbon =[tex]\dfrac{25.5}{3}\text{ yards}[/tex] [tex][\text{1 feet}=\dfrac{1}{3}\text{ yard}][/tex]
[tex]=\text{ 8.5 yards}[/tex]
Hence, the total length of ribbon the three friends have is 306 inches or 25.5 feet or 8.5 yards.
If f(x) = 2x^2 +1, complete the following:
a. f(-4)
b. f(-2)
c. f(0)
d. f(2)
e. f(4)
This is a timed test please i need help!!
Answer:
Sub the values in the brackets of each question into the equation
Step-by-step explanation:
eg. c. f(0) = 2(0)^2 + 1 = 1
I Need Helpp PLZZ i will mark as brainliest
Answer:
9x+18Reasoning:
You multiply x by 9 and 2 by 9 and it expands out from 9(x+2) to 9x+18
I hope this helps and good luck!
Answer:
9x + 18
Step-by-step explanation:
9 times x = 9x
9 x 2 = 18
Can anyone help me with this question of m
Answer:
<DBC=31
Step-by-step explanation:
<ABC=<ABD+<DBC
125=94+<DBC
125-94=<DBC
31=<DBC
Help me pleaseeeeeee
The answer is the second one
Explanation above
Answer:
The correct answer is "y = 3/4x"
Step-by-step explanation:
Slope-intercept form is y2-y1/x2-x1. If you place the points into slope-intercept form you get 6-3/8-4. After reducing the fractions you will get 3/4. So the equation is y = 3/4x.
At a toy store, Colton can buy a package of 6 mini footballs for $7.50, or a package of 8 mini footballs for $9.60. Which option has the lesser price?
Answer:
The 8-pack is better value
Step-by-step explanation:
$7.50/6 = $1.25 per ball
$9.60/8 = $1.20 per ball
The 8-pack is a better value if the toy store, Colton can buy a package of 6 mini footballs for $7.50, or a package of 8 mini footballs for $9.60.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
At a toy store, Colton can buy a package of 6 mini footballs for $7.50, or a package of 8 mini footballs for $9.60.
For:
At a toy store, Colton can buy a package of 6 mini footballs for $7.50
Each ball price
$7.50/6 = $1.25 per ball
Each ball price
$9.60/8 = $1.20 per ball
The 8-pack is a better value
Thus, the 8-pack is a better value if the toy store, Colton can buy a package of 6 mini footballs for $7.50, or a package of 8 mini footballs for $9.60.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
determine if the relation is a function
(-1, 5), (0,3), (2,3), (3, -1)
Answer:
This relation IS a function
Answer:
This is a function
Step-by-step explanation:
Down below none of them overlap
There is no two points in the lines.
If AABC = ADEC,
ZB = 48° and ZE = x + 4
Answer:
[tex]x = 44^\circ[/tex]
Step-by-step explanation:
Triangle Congruence
Given triangle ABC is congruent to triangle DEC, then it's true that angle ABC is congruent to angle DEC.
The figure shows that:
[tex]m\angle B = 48^\circ[/tex]
[tex]m\angle E = x + 4^\circ[/tex]
Those angles are congruent, or have the same measure, thus:
[tex]x + 4^\circ = 48^\circ[/tex]
Subtracting 4°:
[tex]x = 48^\circ - 4^\circ[/tex]
[tex]\mathbf{x = 44^\circ}[/tex]
Roses need 14 times as much water as irises to bloom. if irises need 12 milliliters of water to bloom, how much water do roses needs
Answer:
168 milliliters
Step-by-step explanation:
Since roses need 14 times as much water as irises and we are given the water irises need, you multiply them together.
14•12=168What is 2052 divided by 76
Answer:
27
Step-by-step explanation:
Answer:
Yes, by 27 times
Step-by-step explanation:
I hope it helps you
if 3(2x-4)=-36 ,the value of x is
Answer:
x = -4
Step-by-step explanation:
Answer:-4
Step-by-step explanation:
2 + 36 ÷ 12 - 6 = 8. where does the parenthesis go to make 8 the answer
Answer:
The parenthesis go around the 12 and 6, just like this. (12 - 6)
Answer- 2 + 36 ÷ (12-6)
which of the following are properties of all rectangles? Select all that apply.
Answer:
see explanation
Step-by-step explanation:
The rectangle has the following properties
• Opposite sides are parallel and congruent
• All angles are right angles
• The diagonals are congruent
• The diagonals bisect each other
Thus
They are quadrilaterals
Opposite sides are equal in length
All angles are 90°
Opposite sides are parallel
Rectangles are not parallelograms ( the angles of a parallelogram are not necessarily right and diagonals are not congruent )
An auto mechanic earns $498.75 in 35 hours during the week. His pay is 2.50 more per hour on the weekends. If he works 6 hours on the weekend in addition to 35 hours during the week,hiw much does he earn
Answer:
Total pay= $599.25
Step-by-step explanation:
First, we need to calculate the unitary pay per hour:
Unitary pay= 498.75/35
Unitary pay= $14.25
Now, we can determine the total earn of 35 regular hours and 6 weekend hours:
Total pay= 498.75 + (14.25 + 2.5)*6
Total pay= 498.75 + 100.5
Total pay= $599.25
1. Adding decimals is very similar to adding___________.
2.Line up the number vertically so that all the decimal points are_______.
3. Add extra______to the right of the number so that each number has the same number of digits to the right of the decimal point.
4. Place the______________of the result in line with the other decimal points.
Answers:
1. Adding decimals is very similar to adding whole numbers.
2. Line up the number vertically so that all the decimal points are aligned.
3. Add extra zeros to the right of he number so that each number has the same number of digits the right of the decimal point.
4. Place the decimal point of the result in line with the other decimal points.
I hope this helped you. If it is please click the thanks button. Thank You, Bye! ;-D
1. Adding decimals is very similar to adding whole numbers.
2. Line up the number vertically so that all the decimal points are aligned.
3. Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal point.
4. Place the decimal point of the result in line with the other decimal points.
While adding two decimals.
First, the decimals numbers are written under each other so that decimal points are lined up.The numbers are converted to like decimals by attaching the zeros. The number of zeros attached depends on the number with the maximum digits after the decimal point. The digits of each numbers are lined up so that each column contains digits in the same place. Addition is carried out the normal way by starting from the right to the left. The decimal point is then placed in the place as the numbers above it.Learn more about decimal form here:
https://brainly.com/question/358789?referrer=searchResults
Learn more about decimal addition here:
https://brainly.com/question/13611222?referrer=searchResults
The entrance for the amusement park is $40, visitors purchase additional $2
tickets for rides, games and food. How many tickets can you buy if you
brought $100 to spend at the park?
Answer:
2 tickets because round
Step-by-step explanation:
make an equation: 100=40x+2 and solve
2.45 tickets so only two
40+40 =80
100-80=20
but 100-2=98 so there is only 18$ left so not enough for another ticket
Answer:
30 Tickets
Step-by-step explanation:
In the question, it said that $40 is the entrance fee. Then, it said that visitors purchase additional tickets for rides, games, and food. This means that EACH ticket is 2 dollars.
Hence, $40 (entrance fee) + $2 (each ticket price) x (the number of tickets spent) = 100 (total amount of money).
So, the equation should be 40 + 2x = 100, which means x = 30.
100 - 40 = 60
60/2 = 30
30 tickets can be purchased
Which is the net force acting on a 1.7-kg object that is accelerating at 5.0 m/s??
A. 8.5 N
B. 2.9 N
C. 0.34 N
D. 3.3 N
Answer:
A. 8.5 N
Step-by-step explanation: F = 8.5 N
For the following quadratic equation, find the discriminant.
5x^2– 10x – 255 = 0
please help meee
Answer:
5200
Step-by-step explanation:
STEP 1: The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
[tex]b^2-4(ac)[/tex]
STEP 2: Substitute in the values of a, b, and c.
[tex](-10)^2-4(5)(-255)[/tex]
STEP 3: Evaluate the result to find the discriminant.
[tex]5200[/tex]
Five of the 25 girls on Alden Middle School’s soccer team are seventh-grade students. Find the percentage of seventh graders on the team.
Answer:
20%
Step-by-step explanation:
5 divided by 25 multiplied by 100 will give you 20%.
I hope you understand
Linear equation: -1 (6x + (6x + 10) = 13
Step 1: -3x - 5 = 13
Step 2: -3x = 18
Step 3: x= -6
Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?
O the addition property of equality and then the division property of equality
O the addition property of equality and then the multiplication property of equality
O the subtraction property of equality and then the division property of equality
O the subtraction property of equality and then the multiplication property of equality
Answer:
the addition property of equality and then the division property of equality
Please help me with this
Answer is C, 138°
It's the answer that makes the most sense.
Find the unknown
*
7.8-2.15
What is one hundred times greater than 40?
1 point
6. Precipitation for the month of March was 4 inches less than average. In
April the precipitation was 14 inches less than average. How many inches
below average was the precipitation for both March and April?
Answer:
4 inches because March was 4 so april has to be 4 too
Step-by-step explanation:
Tall Mountain is 8,678.37 feet higher than Mt. Might. What is the elevation of Tall Mountain?
The elevation of Tall Mountain is
feet.
Answer:
i wont give u a direct answer but i will tell u this.. Look up Mt. Mights height and subtract 8,678.37 with a cauculator. The answer will tell you
Answer: 28,979.87
Step by step explanation: I GOT THE ANSWER CORRECT!!!!!! For any one wondering I am doing this question right no and what the other guy said about subtracting is wrong because i tried doing tat and it said it was wrong.
12
A study was done to investigate the population of bald eagle breeding pairs over time. The correlating regression model is shown
below where x represents the number of years after 1986, and y represents the number of bald eagle breeding pairs. Interpret the y-
intercept
y=1.772-334
A. There were approacimately 334 eagle breeding pairs in 1986.
B. There were approximately 1.772 eagle breeding pairs in 1986.
c. There were approximately 1.772 additional eagle breeding pairs each year after 1986.
D. There were approximately 334 additional eagle breeding pairs each year after 1986
Complete question :
A study was done to investigate the population of bald eagle breeding pairs over time. The correlating regression model is shown
below, wiere x represents the number of years after 1986, and y represents the number of bald eagle breeding pairs. Interpret the y-
intercept
y = 1.772 +334x
Answer:
B. There were approximately 1.772 eagle breeding pairs in 1986
Step-by-step explanation:
Given the regression equation : y = 1.772 +334x
Recall the general form of a linear regression equation :
y = mx + c
y = predicted variable ; x = predictor Variable ; c = intercept ; m = slope
x = number of years after 1986 ; y = number of bald eagle pairs.
The intercept is a constant value at time t = 0
For x to be 0, on a graph, this this the value on the y axis where the regression line crosses the y - axis. That is in 1986; the number of y when in 1986 when x = 0 is 1.772
Which rate is the lowest price?
$3.00/6 lb
$2.50/5 lb
$2.40/4 lb
$2.40/6 lb