Answers
The partial differential expression is equal to the expression 30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²) and the total differential formula is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).
How to apply partial derivatives and total differentials
In the first part of this question we must apply the concept of partial derivatives to find the form of the entire expression, whose variables are two. Partial differentiation is a generalization of the ordinary differentiation:
[tex]\frac{\partial f}{\partial x} = 6\cdot x^{5}+12\cdot x^{3}\cdot y^{4}+y^{6}[/tex] (1)
[tex]\frac{\partial^{2} f}{\partial x^{2}} = 30\cdot x^{4}+36\cdot x^{2}\cdot y^{4}[/tex] (2)
[tex]\frac{\partial^{2} f}{\partial x \,\partial y} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex] (3)
[tex]\frac{\partial f}{\partial y} = 12\cdot x^{4}\cdot y^{3} +6\cdot x \cdot y^{5}[/tex] (4)
[tex]\frac{\partial^{2} f}{\partial y^{2}} = 36\cdot x^{4}\cdot y^{2} + 30\cdot x\cdot y^{4}[/tex] (5)
[tex]\frac{\partial f}{\partial y \,\partial x} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex] (6)
Then, the entire expression is:
30 · x⁴ + 36 · x² · y⁴ + 36 · x⁴ · y² + 30 · x · y⁴
30 · (x⁴ + x · y⁴) + 36 · (x² · y⁴ + x⁴ · y²)
30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²)
In the second part we must determine the total differential of z with respect to two variables:
[tex]\Delta z = \frac{\partial f}{\partial x}\cdot \Delta x + \frac{\partial f}{\partial y}\cdot \Delta y[/tex] (7)
If we know that z = sin (x³ + y³), Δx = 0.3 and Δy = 0.2, then the total differential of the function is:
Δz = 3 · cos (x³ + y³) · x² · (0.3) + 3 · cos (x³ + y³) · y² · (0.2)
Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³)
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Related Questions
A carpenter is building a rectangular table. He wants the perimeter of the tabletop to be no more than 28 feet. He also wants the length of the tabletop to be greater than or equal to the square of 2 feet less than its width.
Create a system of inequalities to model the situation, where x represents the width of the tabletop and y represents the length of the tabletop. Then, use this system of inequalities to determine the viable solutions.
A. Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
B. No part of the solution region is viable because the length and width cannot be negative.
C. The entire solution region is viable.
D. Part of the solution region includes a negative length; therefore, not all solutions are viable for the given situation.
Answers
The solution from the system of inequalities is (a). Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
The system of inequalityLet P represent the perimeter.
So, we have:
P ≤ 28 ---- i.e. perimeter not more than 28y ≥ (x - 2)²The perimeter is calculated using:
P = 2(x + y)
So, we have:
2(x + y) ≤ 28
y ≥ (x - 2)²
Next, we plot the system of inequalities (see attachment)
From the attached graph, we have some negative x values in the shaded region.
This means that not all solutions are viable
Hence, the true statement is (a)
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how can i solve this
Answers
Answer:
option c
Step-by-step explanation:
the first number of a exponential function is the y intercept when x = 0,
so we now the number will be 5 leaving only answers c or d
the easiest way see which one is correct is by inputting the numbers for x to find y so...
c) 5 x 2^1 = 5 x 2 = 10 so x = 1 than y = 10
d) 5 x 1/2^1 = 5 x 1/2 = 2.5 so x = 1 than y = 2.5
the table states that y = 10 when x = 1 making c correct
AND WELCOME TO BRAINLY!
NO LINKS!! Please help me with this graph. Part 2
Answers
[tex]\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}[/tex]
Explanation:Absolute value of a graph formula:
y = a |x -h| + kIdentify the vertex : (h, k) = (6, -7)
Take two points: (6, -7), (9, -5)
[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}[/tex]
Join them to build the equation: [tex]\bf{y = \dfrac{2}{3} |x - 6| - 7}[/tex]
Answer:
[tex]g(x)=\dfrac{2}{3}|x-6|-7[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]
-----------------------------------------------------------------------------------------
Parent function: [tex]f(x)=|x|[/tex]
[tex]f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}[/tex]
From inspection of the graph, the vertex of the transformed function is at (6, -7). Therefore, there has been a translation of:
6 units right7 units down[tex]\textsf{6 units right}\implies f(x-6) =|x-6|[/tex]
[tex]\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7[/tex]
From inspection of the graph, we can see that it has been stretched parallel to the y-axis:
[tex]\implies a\:f(x-6)-7=a|x-6|-7[/tex]
The line goes through point (0, -3)
Substituting this point into the above equation to find [tex]a[/tex]:
[tex]\implies a|0-6|-7=-3[/tex]
[tex]\implies 6a=4[/tex]
[tex]\implies a=\dfrac{2}{3}[/tex]
Therefore,
[tex]\implies g(x)=\dfrac{2}{3}|x-6|-7[/tex]
Ivan bought a suit on sale for $152. This price was 60% less than the original price.
What was the original price?
Answers
Work Shown:
x = original price in dollars
x - 60% of x = x - 0.60x = 0.40x = sale price in dollars
0.40x = 152
x = 152/0.40
x = 380
In October 2017 a pound of apples cost $1.55, while oranges cost $1.19. Two years earlier the price of apples was only $1.34 a pound and that of oranges was $1.05 a pound. What was the annual compound rate of growth in the price of apples
Answers
The annual growth rate in the price of the apple will be 7.83%.
What is the growth rate?
The growth rate is defined as the increment of any quantity over a period of time.
Given that:-
In October 2017 a pound of apples cost $1.55, while oranges cost $1.19.Two years earlier the price of apples was only $1.34 a pound and that of oranges was $1.05 a pound.The growth rate will be calculated as::-
Growth rate = Cost in 2017 / Cost in 2015
Growth rate = 1.55 / 1.34 = 1.15
The growth rate will be 15.67% for the apple in 2 years so for 1 year it will be
15.67 / 2 = 7.8%
Therefore the annual growth rate in the price of the apple will be 7.83%.
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If there are 12 people, and each person has 3 coins, there are ____ times as many coins as people
Answers
12 * 3 = 36
There are 36 coins in total.
To get the answer of “there are ___ times as many coins, we simply take the amount of coins and divide it by the amount of people.
36 / 12
This gets you three.
Meaning there are 3 times as many coins as people.
Answer:
Step-by-step explanation:
A cylinder has a base diameter of 6 cm and a height of 18 cm. What is its volume in cubic centimeters to the nearest tenths place?
Answers
Answer:
108 cm that my answer
sana makatulong
The answer is 508.9 cubed
108cm cubed is wrong
If the diameter of a circle is 14 inches, which of the following is the best approximation of the area of the circle?
Answers
Answer: 153.93791 inches³
Step-by-step explanation:
Area of a circle = pi * r²
Area of a circle = pi * 7²
Area of a circle = 3.14159 * 49
Area of a circle = 153.93791 inches³
We can't see you answer choices, so select the best answer choice that is closest to 153.93791 in³
PLEASE HELP!!! IMA DESPRATE!!!!!Use first and second differences to find the next three terms in the following sequence.
8, 11, 19, 35, 62,...
Answers
The next term of the given sequence using first and second differences is; 104
How to find the terms of a Sequence?We are given the sequence as;
8, 11, 19, 35, 62,.....
Thus, using the first and second differences, we have the sequence pattern as;
8 11 19 35 62 104
3 8 16 27 42
5 8 11 15
3 3 4
From the above pattern, we can see that the next term of the sequence is 104
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Consider the line 9x+8y=-2.
Find the equation of the line that is parallel to this line and passes through the point (-3, 2).
Find the equation of the line that is perpendicular to this line and passes through the point (-3, 2).
Equation of parallel line:
Equation of perpendicular line:
Answers
Considering the definition of parallel and perpendicular line:
the equation of parallel line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{11}{8}[/tex].the equation of of perpendicular line is y= [tex]\frac{8}{9}[/tex]x + [tex]\frac{14}{3}[/tex].Linear equationA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of parallel line in this caseIn this case, the line is 9x+8y=-2. Expressed in the form y = mx + b, you get:
8y= -2 - 9x
y= (-9x -2)÷ 8
y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex]
Two lines are parallel if they have the same slope. So, in this case, the parallel line has a slope of -[tex]\frac{9}{8}[/tex] and has a form of: y= -[tex]\frac{9}{8}[/tex]x + b
The line passes through the point (-3, 2). Replacing in the expression for parallel line:
2= -[tex]\frac{9}{8}[/tex]× (-3) + b
2= [tex]\frac{27}{8}[/tex] + b
2- [tex]\frac{27}{8}[/tex]= b
- [tex]\frac{11}{8}[/tex]= b
Finally, the equation of parallel line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{11}{8}[/tex].
Equation of perpendicular line in this caseThe line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex].
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -[tex]\frac{9}{8}[/tex]. So:
-[tex]\frac{9}{8}[/tex]× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-[tex]\frac{9}{8}[/tex])
slope perpendicular line= [tex]\frac{8}{9}[/tex]
So, the perpendicular line has a form of: y= [tex]\frac{8}{9}[/tex]x + b
The line passes through the point (-3, 2). Replacing in the expression for parallel line:
2= [tex]\frac{8}{9}[/tex]× (-3) + b
2= -[tex]\frac{8}{3}[/tex] + b
2+ [tex]\frac{8}{3}[/tex]= b
[tex]\frac{14}{3}[/tex]= b
Finally, the equation of of perpendicular line is y= [tex]\frac{8}{9}[/tex]x + [tex]\frac{14}{3}[/tex].
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Use the net to find the surface area of the regular pyramid.
A net includes four equilateral triangles. One triangle is shaded and it is a base. Each unshaded triangle shares a side with the shaded triangle. The shaded triangle has a side edge of 10 millimeters and area of base is 43.3 squared millimeters. The height of each unshaded triangle is 9 millimeters.
mm2
Answers
Answer: The surface area is 173.2 mm²
Step-by-step explanation: If the four triangles are equilateral and one of the sides is 10 then all the other sides must be 10 as well, meaning that the surface area of each triangle is 43.3 mm². That means that to find the surface area of the whole pyramid you must multiply 43.3 by 4 because there are 4 separate triangles.
43.3 × 4 = 173.2
Natalie invested $40,000 in an account paying an interest rate of 8 % compounded
continuously. Mackenzie invested $40,000 in an account paying an interest rate of
9 % compounded daily. After 20 years, how much more money would Mackenzie
have in her account than Natalie, to the nearest dollar?
%
Answers
Answer:
8000
Step-by-step explanation:
Natalie
Divide 40k by 2 to get 20k and divide 20k by 5 to get 4k we are at 10%
4k / 5 = 800 that means that every 2% is 800 now we multiply by 4x
To get 8% and we get 3200 and multiply by 20 representing the yrs
3200 x 20 = 64k + 40+ = 104k
Mackenzie
40k divide by 2 to get 50% 40k / 2 = 20k and now we divide by 5 to get 10% 20k / 5 = 4k now we divide by 10 to get the amount of each percents worth 4k / 10 = 400 we multiply by 9 to get the compounded interest
400 x 9 = 3600 multiply by 20 to get the compounded daily investment after 20yrs 3600 x 20 = 72k + 40k = 112k
112k - 104k = 8k
what is 747-329 equal
Answers
Answer:
418
Step-by-step explanation:
you take out a cash advance of
Answers
Answer:
$0
Step-by-step explanation:
Since there is no useful data in this question, we will fill in the blanks with what we know:
Amount of cash taken: $0
Therefore, you have taken a cash advance of $0
LOL
Select the correct vocabulary word from each drop-down menu to correctly complete the sentences.
A(n)
Choose...
is a chore, but it is not a game.
A(n)
Choose...
is a bond, but it is not a separation.
Answers
An ERRAND is a chore, but it is not a game and A CONNECTION is a bond, but it is not a separation.
What is Errand?An ERRAND is a chore, but it is not a game.
The correct vocabulary word from each drop-down menu that correctly complete the first sentences is errand.
What is Connection?A CONNECTION is a bond, but it is not a separation
The correct vocabulary word from each drop-down menu that correctly complete the second sentences is connection.
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Select the reason that best supports Statement 8 in the given proof.
A. Addition Property of Equality
B. Division Property of Equality
C. Substitution
D. Subtraction Property of Equality
Given: Ray BV bisects
Answers
Statement 8 (x = 10/5 or x = 2) is given by the division property of equality. Then the correct option is B.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Suppose that we're taking about
It means, we divide p into q equal parts.
And each part is of value p/q
Statement 7 is given below.
5x - 10 = 0
Then statement 8 is given by the division property of equality.
5x = 10
x = 10/5
x = 2
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Help !!!
Geometry and the circle
Answers
Answer:
Look at the explanation.
Step-by-step explanation:
To begin with, the center of a circle is obviously the point in the middle of the circle and it has the same distance where ever you distance the center point from a point on the edges. Hope this makes sense so far. The diameter is from one point of the circle to another point of the circle and the diameter is in the middle meaning if you folded the circle upon the diameter it should be half and half. Radii are half of the diameter. Chords of a circle are "the line segment joining any two points on the circumference of the circle".
So now:
Center is Point F, Radii could be segments FU or Segment KF, Diameter is KU, Chords of the circle could be Segment, VL, GL, or DX. I hope this is correct and hope it helps....
Answer:
Step-by-step explanation:
Center
Which point is the center is just a guess. You are intended to say F.
Radii
KF FUA radius is a line that goes from the center of a circle to the circumference.
Chord
A chord is a line segment that joins two points on the circumference. Believe it or not, the diameter of a circle is a chord.
KUDKVLGLDiameter
KU
Suppose that y varies inversely with x where x=4 and y=5. Solve for the constant
k and find the value of y when x=11
Answers
Round 2.486.3 to The hundred this place.
Answers
2.500
Step-by-step explanation:
If you look over to your hundredth place, which would be the 8, you would round up the 4 to a 5 and put two zeros after the five.
In the whole number 70,819 the place value of the digit 1 is
Answers
Step-by-step explanation:
a number is a sequence of digits with every position being multiplied by increasing powers of 10.
and the whole number is then the sum of of these little multiplications.
the first position left of the decimal point is for 10⁰ (1). the second position is 10¹ (10). the third position for 10² (100). and so on.
the given number is therefore just the short version of
7×10⁴ + 0×10³ + 8×10² + 1×10¹ + 9×10⁰
and therefore, the digit 1 in this number has the value 1×10¹ = 10, which is also the place value, 10¹ = 10.
A cylinder has a diameter of 5 centimeters and a height of 50 millimeters. Which of the following steps should be done
first in order to find the surface area of the cylinder?
O multiply the circumference of the circle by the height of the cylinder
o calculate the circumference of the circle
convert the diameter and the height to the same unit
o determine the radius and multiply by 2
NEXT QUESTION
ASK FOR HELP
TURN ITIN
Answers
Answer:
convert the diameter and the height to the same unit
Step-by-step explanation:
Answer: convert the diameter and the height to the same unit
Step-by-step explanation:
The surface area of a cylinder can be found with A = 2πrh + 2πr². To use this formula, all units of measurement must be the same.
This can be converting 5 centimeters to millimeters or converting 50 millimeters to 5 centimeters.
In a popular online role playing game, players can create detailed designs for their
character's "costumes," or appearance. Gabriella sets up a website where players can
buy and sell these costumes online. Information about the number of people who
visited the website and the number of costumes purchased in a single day is listed
below.
27 visitors purchased no costume.
75 visitors purchased exactly one costume.
11 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
more than one costume as a fraction in simplest form.
Answers
Probability that the next person will purchase more than one costume as a fraction in simplest form is; 11/113
How to find probability?
We are given the data for number of people who visited the website and the number of costumes purchased in a single day as;
Number of visitors that purchased no costume = 27 visitors
Number of visitors that purchased exactly one costume = 75
Number of visitors that purchased more than one costume = 11
Total number of visitors = 27 + 75 + 11 = 113
Thus;
Probability that the next person will purchase more than one costume as a fraction in simplest form is;
P(purchase more than one costume) = 11/113
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three times the sum of x and y is increased by 5
Answers
Answer:
Here is the answer .Please mark as brainliest plshope its help you
Step-by-step explanation:
3(x+y)+5=0
3x+3y+5=0
or,3x+3y= -5
Answer:
3*(x+y) + 5
Step-by-step explanation:
This is an mathematical expression....it isi NOT an equation...the question does NOT say this is equal to zero (or anything else)
it is this 3 (x+y) + 5 or 3x + 3y + 5
What is 75% of 99. Round your answer to the nearest hundredths.
Answers
Answer: 74.25
Step-by-step explanation:
75% ÷ 100 = 0.75
0.75 * 99
= 74.25
Robert delivers papers every morning. On Sundays he has to deliver 61 papers and on each of the other days he only has to
deliver 44 papers. How many papers does Robert deliver each week?
A. 369
B. 325
C. 413
D. 427
Answers
Answer:
B. 325
Step-by-step explanation:
y = the total value of the amount of papers he has to deliver each week
44x + 61 = y
(7 days in a week - sunday = 6 days)
44(6) + 61 = y
264 + 61 = y
325 = y
Step-by-step explanation:
sundays + 6 other days * papers delivered = total papers delivered
65 + 6 * 40 = total papers
65 + 240 = total papers
305 = total papers
b) In one year, Clara and Dave borrowed books from a library in the ratio 3:7. Dave borrowed 35 books. Work out the number of books borrowed by Clara.
Answers
3:7 =
3/7
3/7 = x/35
7x = 105
x = 15
answer : clara borrowed 15 books
I think it would be 15, because 3 doesn't go in evenly into 35. You might have the order of the ratio messed up.
Need Help please 3rd time posting this.
Answers
Side-edge is 20 cm : 4 ft(60.96cm)
Poster Area needed = (30.48*60.96)=1858cm2
Paper size = 10*20=200cm2
Need papers= 1858/200=9.3 ~10
.: 10 papers is needed for actual poster.
Please help surface area of a triangle
Answers
Answer:
A≈391.18
Step-by-step explanation:
The formula to find the surface area of a triangular prism is as follows:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
Plug in . .
A=ah+bh+ch+[tex]\frac{1}{2}[/tex][tex]\sqrt{ a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4}[/tex]
A = 6 * 20 + 6 * 20 + 6 * 20 + [tex]\frac{1}{2}[/tex] * [tex]\sqrt{64 + 2 * (6 * 6)2 + 2 * (6 * 6)2 - 64 + 2 *(6 * 6)2 * 64}[/tex]
A≈391.18
Answer:
391.2 square cm
Step-by-step explanation:
Surface area of triangular prisml = 20 cm
Base area = 15.6 square cm
[tex]\sf \boxed{\text{Surface area of triangular prism = Perimeter of base * l + 2*base area}}[/tex]
= (6+6+6)*20 + 2*15.6
= 18*20 + 31.2
= 360 +31.2
= 391.2 square cm
Solve by factoring y=4x^2-24x+36
Answers
Answer:
(x-3) (x-3)
Step-by-step explanation:
[tex]4x {}^{2} - 24x + 36 \\ dividing \: through \: by \: 4 \\ x {}^{2} - 6x { }^{} + 9 \\ two \: numbers \: such \: that \: when \: you \: add \: them \: they \: give \: you \: - 6 \: and \: when \: you \: multiply \: them \: they \: give \: 9 \\ the \: numbers \: are \: \: - 3 \: and \: - 3 \\ x {}^{2} - 3x - 3x + 9 \\ x( x - 3) - 3(x - 3) \\ (x - 3)(x - 3)[/tex]
Given that circumference of a circle is 44m. Calculate it's area
Answers
Answer:
Area=154.062 [tex]m^{2}[/tex]
Step-by-step explanation:
As Circumference of a circle is given by;
[tex]C=2\times \pi\times r[/tex]
As the circumference is 44m so we can calculate the value of r by using the above formula.
[tex]44=2\times \pi \times r\\\\\frac{44}{2\pi} =r\\\\\implies r=\frac{22}{\pi} =7.003 m[/tex]
Now to Calculate the Area of a Circle.
As the area of a circle is,
[tex]Area =\pi \times r^{2}\\ Area=\pi \times (7.003)^{2} \\Area=\pi \times 49.039\\Area=154.062m^{2}[/tex]