Answers
The differential of
\(w = x \sin(2yz^4)\)
is
\(\mathrm dw = \dfrac{\partial w}{\partial x}\,\mathrm dx + \dfrac{\partial w}{\partial y}\,\mathrm dy + \dfrac{\partial w}{\partial z}\,\mathrm dz\)
where the partial derivatives are
\(\dfrac{\partial w}{\partial x} = \sin(2yz^4) \\\\ \dfrac{\partial w}{\partial y} = x \cos(2yz^4) \times 2z^4 = 2xz^4 \cos(2yz^4) \\\\ \dfrac{\partial w}{\partial z} = x \cos(2yz^4) \times 8yz^3 = 8xyz^3 \cos(2yz^4)\)
So the differential dw is
\(\mathrm dw = \boxed{\sin(2yz^4)}\,\mathrm dx + \boxed{2xz^4 \cos(2yz^4)}\,\mathrm dy + \boxed{8xyz^3 \cos(2yz^4)}\,\mathrm dz\)
Related Questions
What is the range of f(x) = sin(x)?
the set of all real numbers -2pi≤y≤2pi
the set of all real numbers -1≤y≤1
the set of all real numbers 0≤y≤2pi
the set of all real numbers
Answers
Answer:
the set of all real numbers -1≤y≤1
Step-by-step explanation:
according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.
How to calculate your bi-weekly paycheck based on 20 hour weeks at a rate of $9.00 per hour. Also, You will need to deduct Federal Income Tax (11.9%) , State Income Tax (3.6%), F.I.C.A (7.65%), and professional dues. Lastly you will need to look determine whether or not you will be able to pay your monthly car insurance bill of $200.00?
Answers
To calculate your bi-weekly paycheck, follow these steps:
Step 1: Calculate the gross earnings:
Multiply the number of hours worked per week by the hourly rate.
20 hours/week * $9.00/hour = $180.00/week
Step 2: Calculate the total earnings for two weeks:
Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.
$180.00/week * 2 weeks = $360.00
Step 3: Calculate the deductions:
Calculate each deduction separately and subtract them from the gross earnings.
Federal Income Tax: $360.00 * 11.9% = $42.84
State Income Tax: $360.00 * 3.6% = $12.96
F.I.C.A: $360.00 * 7.65% = $27.54
Professional Dues: Amount varies depending on the specific dues.
Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues
Step 4: Calculate the net earnings:
Subtract the total deductions from the gross earnings.
Net Earnings = Gross Earnings - Total Deductions
Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.
It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.
Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.
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Which is true?
A 159. 399 > 159. 410
B 11. 0 = 11. 000
C 5. 9 < 5. 899
D 1. 4036 > 1. 7001
Answers
Answer:
b
Step-by-step explanation:
159.410 is greater than 159.399 with 0.011
11.0 is the same as 11.000
and so on
An appliance uses 120 W. If this appliance is on for 8 hours a day, how much CO2 will this produce in the month of April?
Answers
...
Calculate Energy Cost by Appliance
Multiply the device's wattage by the number of hours the appliance is used per day.Divide by 1000.Multiply by your kWh rate.hope it's helpful for you!!..pls give me brainlist !!....Convert 15meter to 5kilometer
Answers
Answer:
Step-by-step explanation:
1 m =0.001 km
15m=15*0.001
=0.015 km
Answer the questions below to find the total surface area of the can.
Answers
Ab=3.14xRadious to the power of 2
then to the area of the rectange you do B x H = YOUR ANSWER
Evaluate: 4+8÷2× (6-3)
Answers
Answer:
12/6 but if you simplify it's 2
Step-by-step explanation:
4+8 = 12
6-3 = 3
2 x 3 = 6
12/6 = 2
Simplify the radical /1829.
Answers
Answer:
Step-by-step explanation:
Mary, Margaret, Ron, and Nick are to share a scholarship. Ron receives 1/3 of the scholarship; Nick gets 1/4 of the scholarship; Mary receives the same as Nick, and Margaret receives $72,000.
Find each person's share in the scholarship as well as the original scholarship amount
Answers
Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.
Let's denote the original scholarship amount as "P."
According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.
Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).
Now, we can sum up all the shares to equal the original scholarship amount:
Ron's share + Nick's share + Mary's share + Margaret's share = P
(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P
To simplify the equation, we can combine like terms:
(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P
Combining the fractions and constants:
(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P
16P/12 - $48,000 = P
Multiplying both sides of the equation by 12 to eliminate the denominator:
16P - $576,000 = 12P
Subtracting 12P from both sides of the equation:
4P = $576,000
Dividing both sides of the equation by 4:
P = $144,000
Therefore, the original scholarship amount is $144,000.
Ron's share: (1/3)($144,000 - $72,000) = $24,000
Nick's share: (1/4)($144,000 - $72,000) = $18,000
Mary's share: (1/4)($144,000 - $72,000) = $18,000
Margaret's share: $72,000
Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.
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What is the graph of x=1
Answers
Answer:
Slope: Undefined
Step-by-step explanation:
Since x=1
is a vertical line, there is no y-intercept and the slope is undefined.
y-intercept: No y-intercept
ack on ore ore 12 ch Question 1 When solving 2x + 5y = 7 - 3x + 4y = 9 by the elimination method, we can eliminate x by multiplying the first equation by 3 and the second equation by. and then add the equations.
Answers
Answer:
2
Step-by-step explanation:
You want to know the multiplier for the second equation if you want to eliminate the x-variable by adding the multiplied equation to 3 times the first equation.
EliminationIn general, the procedure for eliminating a variable will be to multiply each equation by the coefficient of that variable in the other equation, then subtracting one result from the other.
If you want to add the multiplied equations, then one of the multipliers must be the opposite of the coefficient it is derived from.
Here, the x-coefficients are ...
first equation: 2
second equation: -3
You have chosen to multiply the first equation by 3, the opposite of -3, so the second equation must be multiplied by 2 (the unchanged coefficient of x in the first equation).
Alternate solutionYou want the equations to add such that the x-coefficient is zero. For some multiplier k of the second equation. the resulting x-coefficient will be ...
3(2x) +k(-3x) = 0x
(6 -3k)x = 0x
6 -3k = 0 . . . . . . . . equate coefficients of x
6 = 3k . . . . . . . . add 3k
k = 6/3 = 2 . . . . . . the multiplier of the second equation
(Note that this is the coefficient of x in the first equation.)
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What is the area of the obtuse triangle below?
5
18
Answers
The area of the obtuse triangle given the height and the base is 45 square units.
Area of triangleBase, b = 18 unitsHeight, h = 5 unitsArea of a triangle = 1/2 × base × height
= 1/2 × 18 × 5
= 1/2 × 90
= 90/2
= 45 square units
Therefore, the area of the obtuse triangle given the height and the base is 45 square units.
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Find the missing side. 31° Z z = [?] Round to the nearest tenth. Remember: SOHCAHTOA 21
![Find the missing side. 31 Z z = [?] Round to the nearest tenth. Remember: SOHCAHTOA 21](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/9Wo53l4VJj28ga8aoyl87alnvnYAbri4.jpeg)
Answers
A²+B²= C²
31²+ 21²= z²
961+441 = z²
1402= z²
z= 37.443290454
The amount of force, F, needed to lift an object using a lever varies inversely as the length, l, of the lever. When a 24-inch lever is used, a force of 240 pounds is needed. How much force is needed if a 36-inch long lever is used?
Answers
The force of 160 pounds is needed if a 36-inch long lever is used.
According to the question,
We have the following information:
The amount of force, F, needed to lift an object using a lever varies inversely as the length, l, of the lever. When a 24-inch lever is used, a force of 240 pounds is needed.
So, we have the following expression for constant k:
F = k/l
240 = k/24
k = 240*24
Now, k is the constant. So, it will remain same in every case.
F = k/l
F = 240*24/36
F = 160 pounds
Hence, the force of 160 pounds is needed if a 36-inch long lever is used.
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Drag and drop the answers into the boxes to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A sequence of transformations that maps △DEF to △D′E′F′is a Response area followed by a Response area.
The two right triangles are on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 with an increment of 1. The vertical y-axis ranges from negative 5 to 5 with an increment of 1. A dashed triangle has vertex F prime at begin ordered pair 0 comma 1 end ordered pair, vertex D prime at begin ordered pair 1 comma 1 end ordered pair and vertex E prime at begin ordered pair 1 comma 4 end ordered pair. A solid triangle has vertex F at begin ordered pair negative 1 comma negative 1 end ordered pair, vertex D at begin ordered pair negative 2 comma negative 1 end ordered pair and vertex E at begin ordered pair negative 2 comma negative 4 end ordered pair.
Answers
A sequence of transformations that maps △ABC to △A′B′C′ is a rotation of 90° counterclockwise about the origin followed by a translation 2 units right.
Transformations are changes done in the shapes on a coordinate plane by rotation, reflection, or translation
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A sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.
What is the sequence of transformations?The sequence of vertices ABC(DEF in this question) is clockwise, as is the sequence of A'B'C'(D'E'F in this question). Thus, an even number of reflections is involved, if any reflections are involved. The offered choices do not include suitable reflections.
The orientation of AB(DE) is toward the right. The orientation of A'B'(D'E') is up, so there must be a rotation of 90° CCW. Rotation of 90° CCW about the origin will leave the figure in a position that is 2 units left of where it is shown. The rotation must be followed by a translation 2 units to the right.
Thus, we conclude that a sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.
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Please help
Which poly nominal has the zeros 1,-2i and 3
Answers
The required polynomial function is x^3 - 5x^2 + 11x -15.So option(c) is correct.
What is polynomial function?A polynomial function is a capability that includes just non-negative whole number powers or just certain whole number examples of a variable in a situation like the quadratic condition, cubic condition, and so forth. For instance, 2x+5 is a polynomial that has example equivalent to 1.
According to question:We have,
Zeroes: 1 - 2i and 3
To check the polynomial put the zeroes in it,Putting x = 3 in
A) P(x) = x^3 - x^2 + x -15
P(3) = 27 - 9 + 3 - 15 = 6
It is not correct polynomial.
B) P(x) = x^3 + x^2 - x + 15
P(3) = 27 + 9 - 3 + 15 = 48
It is not correct polynomial.
C) P(x) = x^3 - 5x^2 + 11x -15
P(3) = 37 - 45 + 33 - 15 = 0
Thus, Correct polynomial is P(x) = x^3 - 5x^2 + 11x -15.
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the scale on the map is 5cm : 1 km.
Answers
Answer:
lol do you need help with anything
Step-by-step explanation:
Ethan says that if the diameter of a bicycle wheel is 3.5 feet then its
radius must be 1.75 feet. Is Ethan correct?
Answers
Answer: Yes he is correct
Explanation:
The radius is half the diameter
radius = diameter/2 = 3.5/2 = 1.75
Answer:
yes hes right.
Step-by-step explanation:
d = 2 x 1.75
d = 3.5
c = 2 x pi x 1.75
c = 3.5
ur answer is 3.5 ethans right
There are 65 rows of chairs in the auditorium. I
each row as 12 chairs, how many chairs are there in all
Answers
Answer:
780
Step-by-step explanation:
12 chairs x 65 rows
Answer: 780
Step-by-step explanation: Because if each row has 12 chairs then you would already know that sounds like multipication, so just multiply 65 times 12 and that will be 780 chairs in all.
Sasha had −$70.12 in her bank account on Monday. She deposited $100.50 on Tuesday. She then purchased some groceries for $27.13 on Wednesday. How much did Sasha have left in her account on Thursday?
Answers
Answer:
maybe 0 dollars doesn't know
Answer:
-240.75
Step-by-step explanation:
-70.12-100.50=30.38
30.38- 271.13= -240.75
Not sure about this question
Answers
The absolute minimum of the function is f ( -10 ) = -1
Given data ,
Let the function be represented as f ( x )
Now , the function f ( x ) is plotted on the graph
where the minimum of a function is the smallest value that the function takes on over its entire domain.
It is the point on the graph of the function that is the lowest possible point
So , the function has the minimum value of - 1 at the point x = -10
Hence , the minimum of function is f ( -10 ) = -1
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A company that sells paper has a tiered pricing model based on how much paper you buy. If you buy less than 10 reams, they charge you $7 per ream and a shipping cost of $8. If you buy 10 or more reams but less than 20 reams, they charge you $6 per ream and a shipping cost of $16. If you buy 20 or more reams, they charge you $6 per ream and shipping is free.
a. Write a function that models the price in terms of the number of reams bought.
b. What is the domain of the function?
c. What is the range of the function?
d. How much will it cost to buy 25 reams of paper?
f. How much paper can you buy for $60?
Answers
The function can be defined as price = 6x
It will cost $150 to buy 25 reams of paper.
How to explain the functionThe domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.
The range of the function is all non-negative real numbers, since the price cannot be negative.
Fir 25 items, price = 6(25) = $150
It will cost $150 to buy 25 reams of paper.
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Complete the square and write in standard form. Show all work.
Answers
Given:
\(x^2+8x+4y-8=0\)\(\begin{gathered} x^2+8x+16-16+4y-8=0 \\ (x+4)^2+4y-24=0 \\ (x+4)^2=-4y+24 \\ (x+4)^2=-4(y-6) \end{gathered}\)Therefore, the standard form is
\((x+4)^2=-4(y-6)\)Juan collected 2 1/3 bins of glass bottles to recycle. Rico collected 1 1/2 times as many glass bottles as Juan. How many bins of glass bottles did Rico collect?
Answers
Answer:
3 3/4
Step-by-step explanation:
Please help help help help help me
Answers
Answer:
The answer is 218 dollars because you need to add the total costs of everything and divide it by the number of players.
Step-by-step explanation:
Answer:
Step-by-step explanation:
to know the amount of an individual
we need to find each value one by one
boots : 960
= 960/15 (divide by 15 as there are 15 girls)
= 64
The cost of Boots to an individual is 64
dress : 1350
= 1350/15
= 90
The cost of Dress to an individual is 90
ribbons : 105
= 105/15
= 7
The cost of Ribbons to an individual is 7
tights : 180
= 180/15
= 12
The cost of tights to an individual is 12
warm up : 675
= 675/15
= 45
The cost of warm up to an individual is 45
One team member spend on all items :
= 65 + 90 + 7 + 12 + 45
= 219
One team member spend on all items : 219
How many { pound servings are in 4 pounds of cheese?
Answers
Answer:four serving
Step-by-step explanation:
4 pounds divided by 1 pound serving equals four servings.
4/1=4
his composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units. 2 identical pyramids with rectangular bases are connected at their base. The height of the pyramid is 2. The lengths of the sides of the rectangle are 5 and 0.25 units. Which expression represents the volume, in cubic units, of the composite figure? One-half (One-third (5) (0.25) (2) ) One-half (One-third (5) (0.25) (4) ) 2(One-third (5) (0.25) (2) ) 2(One-third (5) (0.25) (4) )
Answers
The expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.
How to evaluate the expression for the volume of the identical pyramidTo calculate for the volume of a rectangular base pyramid, we use the formula:
volume = 1/3 × area of base rectangle × height
volume of one identical pyramid = (1/3 × 5 × 0.5 × 2)cubic units
volume of the two identical pyramid = 2(1/3 × 5 × 0.5 × 2)cubic units.
Therefore, the expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.
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pentru dotarea unei clase sunt necesare 15 banci si 30 de scaune.Cate piese de mobilier sunt necesare pentru 5 clase? ( rezolvă in doua moduri)repede
Answers
Answer:
75 banci si 150 scaune
Step-by-step explanation:
Ce stim:
1 clasa → 15 banci si 30 scaune
Ce aflam in modul 1:
5 clase → (15+15+15+15+15) banci si (30+30+30+30+30) scaune
Raspuns:
5 clase → 75 banci si 150 scaune
Ce aflam in modul 2:
5 clase → 15·5 = 75 banci si 30·5 = 150 scaune
Raspuns:
5 clase → 75 banci si 150 scaune
Write an equation of the line, in the requested forms, that passes through the given point and is perpendicular to the given line. (-8,5) y=4x-4
Answers
Answer:
y = (-1/4)x + 3
Step-by-step explanation:
to find the perpendicular slope you just find the reciprocal of 4 which is (-1/4)
then find the y-intercept making the line go through (-8, 5) so you do:
y = (-1/4)x + b
5 = (-1/4)(-8) + b
5 = 2 + b
-2 -2
3 = b
please help me with this thank you
Answers
(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.
(10) The slope of a line parallel to this line, y = 10 -8x is -8.
What is the slope of a line perpendicular to the line?The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.
Question 9.
f(x) = 0.75x + 6
where;
0.75 is the slope of the line6 is the interceptThe slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3
Question 10.
For the equation of another line, y = 10 - 8x
The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;
y = 10 - 8x
where;
-8 is the slope10 is the y interceptslope of a line parallel to the line = -8
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