Answers
The expression for the change of the variable z is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).
How to find the total differential of a multivariate function
In this question we must apply the concept of total differential to determine the change of the variable z in terms of the changes in variables x and y. That is:
[tex]\Delta z = \frac{\partial f}{\partial x}\cdot \Delta x + \frac{\partial f}{\partial y}\cdot \Delta y[/tex] (1)
If we know that z = sin (x³ + y³), Δx = 0.3 and Δy = 0.2, then the expression for the change of z is:
[tex]\Delta z = 3\cdot \cos (x^{3}+y^{3})\cdot x^{2}\cdot (0.3)+3\cdot \cos (x^{3}+y^{3})\cdot y^{2}\cdot (0.2)[/tex]
Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³)
The expression for the change of the variable z is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).
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Related Questions
6x - 3 - 2x = 5. What is the value of x?
Answers
6x-2x = 5+3
=> 4x=8
=> x = 8/4
=>[tex]\fbox{x=2}[/tex]
Hope this helps you :)
Answer:
x=2
Step-by-step explanation:
6x - 3 - 2x = 5
Combine like terms
4x -3 = 5
Add 3 to each side
4x-3+3 = 5+3
4x = 8
Divide each side by 4
4x/4 = 8/4
x = 2
3. Don’s Clothing advertised a clothing sale. On the first day, all clothing was marked 1/10 off. On the second day, unsold items were marked 2/5, the third day, 3/10 off, and so on. If the markdowns continued this way, on which day were prices marked 4/5, or 80% off?
Answers
Don’s Clothing advertised a clothing sale and Following the markdowns, prices will be marked 4/5, or 80% off on : The Fourth Day
Meaning of advert and sale
An advert is a form of publicity or awareness done to increase sale or increase the purchase of goods from a company or organization. it makes the public aware of an offer made by an organization or company.
Sale is the exchange of goods or services for money. it is between the company or organization and the consumer.
In Conclusion, Don’s Clothing advertised a clothing sale and Following the markdowns, prices will be marked 4/5, or 80% off on The Fourth Day
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16+ y =24
What is the value of y?
Answers
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
16+y=24, What is y?
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
When solving an equation, we need to make sure that all variables are on one side and all numbers are on the other side.
Since we have numbers on both sides, we need to move all of them to one side:-
[tex]\tt{16+y=24}[/tex]
[tex]\tt{y=24-16}[/tex]
[tex]\tt{y=8}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
In Chemistry class, Samantha finds that she can make a certain solution by mixing 0.04 liters of chemical A with 0.02 liters of water (this gives her 0.06 liters of the solution). She wants to make a total of 0.48 liters of this new solution. To do so, how many liters of water will she use?
Answers
Answer:
0.16 liters of water
Step-by-step explanation:
Samantha's recipe makes 0.06 liters of solution. She wants 0.48 liters of solution, an amount 0.48/0.06 = 8 times as great as made by one recipe.
The recipe calls for 0.02 liters of water. To make 8 times the amount of solution, Samantha will use 8 times as much water: 0.16 liters.
Samantha will use 0.16 liters of water to make 0.48 liters of solution.
__
Alternate solution
The fraction of solution that is water is (0.02 L)/(0.06 L) = 1/3. For 0.48 L of solution, the water needed is 1/3×0.48 L = 0.16 liters.
Answer:
0.16L
Step-by-step explanation:
Let f(x)=x-3 and g(x)= x^2-x. Find and simplify the expression. (f+g)(2)
Answers
Answer:
(f+g)(2) = 1Step-by-step explanation:
Given :
f(x) = x − 3
g(x) = x² − x
Note : (f+g)(x) = f(x) + g(x)
then
(f+g)(2) = f(2) + g(2)
= (2 - 3) + (2² - 2)
= -1 + 2
= 1
another method:
(f+g)(x) = f(x) + g(x) = x − 3 + x² − x = x² - 3
then
(f+g)(2) = 2² - 3 = 4 - 3 = 1
Evaluate 3 x 2/7 give your answer as a fraction
Answers
[tex]\huge{\underline{\mathtt{\red {A}\pink{N}\green{S}\blue{W}\purple {E}\orange{R}}}}[/tex]
[tex] \huge\frac{6}{7} [/tex]
step by step Explanation :
= 3 × [tex] \huge\frac{2}{7} [/tex]
We have to just multiply 3 with numerator which is 2 and product will be 6 .= [tex] \huge\frac{6}{7} [/tex]
hope it helps you
Answer:
6/7
Step-by-step explanation:
You multiply 3 by the numerator of the fraction
3 multiplied by 2 is 6
Your answer is 6/7
Find the domain and range of the given relation (6,3), (-7,-3), (-4,1), (1,-4)
Answers
Answer:
Step-by-step explanation:
The domain are all the x values
(-7,-3), (-4,1), (1,-4), (6,3)
x here is from -7 to 6
domain ∈ [-7, 6]
The range are all the y values
(1,-4), (-7,-3), (-4,1), (6,3)
y here is from -4 to 3
range ∈ [-4, 3]
5y3 – 4y – 1
Leading term:
Leading coefficient:
Constant term:
Answers
Answer:
Leading term:
5y^3
Leading coefficient:
5
Constant term:
-1
Step-by-step explanation:
5y^3 -4y -1
The leading term is the term with the highest power of the variable
5y^3 is the leading term
the leading coefficient is the number in front of the highest power of the variable
5 is the leading coefficient
The constant term is the number alone
-1 is the constant term
Which of the following are solutions to the inequality below? Select all that apply.
11 ≥ a a = 10 a = 2 a = 8 2 = 3
Answers
Answer:
a = 10
a = 2
a = 8
Step-by-step explanation:
The inequality:
11 ≥ a
We will go through all the options:
-> In short, all values less than or equal to 11 will be solutions.
a = 10
11 ≥ a
11 ≥ 10 ✓
-
a = 2
11 ≥ a
11 ≥ 2 ✓
-
a = 8
11 ≥ a
11 ≥ 8 ✓
-
2 = 3
N/A, no 'a' variable given.
Question
Type of cookie
Cost per cookie,
in dollars
Chocolate chip
$0.73
Double chocolate
$0.82
Oatmeal raisin
$0.70
Sugar
X
Butter pecan
$0.86
The table above shows a bakery's cost per cookie for each of the five types of cookies the bakery sells. If
the mean cost per cookie is $0.73, what is the cost per cookie, in dollars, for a sugar cookie?
O $0.54
O $0.67
O $0.79
O $0.84
Answers
The cost per cookie, in dollars, for a sugar cookie is A; $0.54.
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
WE know that Chocolate chip = $0.73
Double chocolate = $0.82
Oatmeal raisin = $0.70
Sugar = X
Butter pecan = $0.86
We need to find the cost per cookie, in dollars, for a sugar cookie.
So, Mean = $0.73
Mean = 0.73 + 0.82 + 0.70+ X + 0.86 / 5
0.73 (5) =0.73 + 0.82 + 0.70+ X + 0.86
x = 0.54
Therefore, The cost per cookie, in dollars, for a sugar cookie is A; $0.54.
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What is the measure of angle x?
Answers
Answer:
90 degrees cuz the lil square thang
Answer:
x = 48°
Step-by-step explanation:
The sum of angles on a line is 180°.
The angles 42°, 90°, and x° lie on the same line.
42 + 90 + x = 180x + 132 = 180x = 48°1. The mass of lab sample A is 2.4 x 10^-2 kg. The mass of lab sample B is 3.6 x 10^2kg. Given that
information, Jason says that sample B is 15 times the mass of sample A. Narissa asserts that sample B is 15,000 times that of sample A. Julius states that sample B is 1.5 times greater than sample A. Compare the masses of the two samples to decide who is correct. State which person is correct and
explain your answer using mathematics.
Answers
Answer:
Given:
[tex]\textsf{Mass of Sample A}=2.4 \times 10^{-2}[/tex][tex]\textsf{Mass of Sample B}=3.6 \times 10^{2}[/tex]As the exponent of Sample A is negative, this means that the mass of Sample A is smaller than that of Sample B.
Therefore, to find the proportional relationship between the samples, divide the mass of the larger sample (B) by the mass of the smaller sample (A):
[tex]\begin{aligned}\implies \dfrac{\textsf{Sample B}}{\textsf{Sample A}}=\dfrac{3.6 \times 10^2}{2.4 \times 10^{-2}} & =\dfrac{3.6}{2.4} \times \dfrac{10^2}{10^{-2}}\\\\ & =1.5 \times 10^{(2-(-2))}\\\\& = 1.5 \times 10^4 \end{aligned}[/tex]
To convert the scientific notation [tex]1.5 \times 10^4[/tex] to a decimal, move the decimal point to the right 4 places:
[tex]\implies 1.5000 \times 10^4=15000[/tex]
(If the exponent is positive, move the decimal point to the right. If the exponent is negative, move the decimal point to the left. The number of places to move the decimal point is the numerical value of the exponent).
Therefore, the mass of sample B is 15,000 times the mass of sample A, so Narissa is correct.
Sum of integers from -10 to 50
Answers
Answer:
1220
Step-by-step explanation:
This can easily be done as follows,
Take the first term of the series, (a = -10)
Take the last term of the series, (l = 50)
The numbers of terms is n = 50+10+1 = 61
Now,
For sum,
S= n/2 (a+l) =60/2 (50+-10) = 61/2 (50-10) = 61/2*40 = 1220
PLSS HELP ME WITH THIS 15 POINTSS!
Answers
Answer:
D. y= 1/9x
Step-by-step explanation:
y= 1/9x
(x)=9y
so I think d is your answer sorry if its wrong but i hope i helped.
Answer: D. y= 1/9x
Step-by-step explanation: i think you answer is correct if not it's ok
Each has a radius of 5 in and a height of 12 in. How much more water can the cylinder hold than the cone? (Use л=3.14)
Answers
The cylinder holds 3 times more water than the cone
volume of the cylinder is (pi) (r^2) (height), volume of the cone is (1/3)(pi)(r^2)(height)
Cone is 1/3 of cylinder volume so cylinder holds 3 times the amount
Cylinder holds 942 cu units, cone holds 314,
Answer cylinder holds 628 cu units more than cone
cyl= 3.14 x 5^2 x 12=942
Cone= 1/3 x 3.14 x 5^2 x 12 = 314
What is 1 + 1 and explain why using irrational numbers
Answers
Answer: 1+1 = Dr. Phill
Step-by-step explanation:
Dr. Phill is the answer for everything, you see, his phillyness is underrated. he has magical wiggly fingers that shine in the sun. he can summon the enderdragon but as a gay drag queen.
therefore, magical wizard, dr. philly pill.
1
James purchases a rare coin for $450. The coin appreciates at a rate of 1.2% each year. How much will the coin be worth after 25 years?
Answers
Step-by-Step Explanation:
Price of Rare Coin = $450
Rate at which it appreciates = 1.2%
Price of Rare Coin after 25 years = ?
Therefore,
= 1.2 * 25 = 30%
Hence, price of coin after 25 years:
= (30/100 * 450) + 450
= 135 + 450
= 585
Therefore,
The coin would cost $585 after 25 yrs.
Jackie is a student of UEW. This year, her age is a multiple of 6. Next year, her age will be a multiple of 5. If Jackie is younger than 40, how old will she be next year?
Answers
Using the multiples of 5 and 6, it is found that she will be 25 years old next year.
What are the multiples of 5 and 6?They are given as follows, considering numbers less than 40:
M(5) = {0, 5, 10, 15, 02, 25, 30, 35}.M(6) = {0, 6, 12, 18, 24, 30, 36}.This year, her age is a multiple of 6. Next year, her age will be a multiple of 5, hence, her age next year is a multiple of 5, whose predecessor is a multiple of 6, hence the only option is that she will be 25 years old next year.
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What multiplication problem is represented by this grid?
Answers
The multiplication problem represented by this grid is 0.7 x 0.4 = 0.28
Sure hope this helps you
pretend this is a 20 letter question please help me
Answers
Answer:
1.64+0.94v
Step-by-step explanation:
0.2(8.2+4.7v)
0.2(8.2)+0.2(4.7v)
1.64+0.94v
I'm not very confident with this answer but I hope this helps
May 31.2022
15. Suppose a kite is being flown with 135 meters of string. If the kite forms
a 47° angle with the level ground as shown in the diagram below, how
high is the kite to the nearest meter?
Answers
Answer:
99 m to nearest metre.
Step-by-step explanation:
Hypotenuse = 135, opposite side = ?
- so we need the sine function
sin 47 = x / 135 were x is the height of the kite.
x = 135 * sin 47
= 98.73 m
Which equation can we use to find the length of the side labeled x?
Answers
Answer:
(D) sIn(30°) = 5/x
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between sides and trig functions for a right triangle. Here, the hypotenuse and the side opposite the angle are marked. The relevant relationship is ...
Sin = Opposite/Hypotenuse
Filling in figure values, we have ...
sIn(30°) = 5/x
How can you estimate and compare square roots?
Answers
Answer:
To estimate the square root of a number, you're going to use:
Multiplication knowledge to find the whole numbers you are working betweenRulerNumberlineSentence formGet as close as possible to the number you're trying to square root by finding two perfect square roots that give a close number.
Someone help ASAP please !! I’ll vote Brainliest !
Answers
Answer:
2nd row
Step-by-step explanation:
The y-intercept corresponds to the ordered pair having an x-value of 0. The second row of the table has an x-value of 0, and y-value of 2. Therefore, the y-intercept is (0, 2).
Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.
Long beakNot a long beakTotalFlies11719Does not fly31315Total142034
Answers
The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.
What is an odds ratio?An odds ratio is a measure of the strength of an association with the exposure and outcome.
The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).
Data and Calculations:Contingency Table
Flies Does not fly Total
Long beak 11 7 19
Not a long beak 3 13 15
Total 14 20 34
Probability of long beaks flying = 0.79 (1/14)
Probability of not having long beaks flying = 0.21 (3/14)
Odds ratio = 3.76 (0.79/0.21)
Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.
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Answer:
Step-by-step explanation:
6.81
Question: How many miles can we paddle in 1 hour at the Los Angeles river?
The river is going at 25 mph
and you are paddling at a consistent rate
Answers
Answer:
125 mph
Step-by-step explanation:
The river is going 25 mph every 20 minutes
[tex]20[/tex] [tex]minutes=25[/tex][tex]40[/tex] [tex]minutes=50[/tex][tex]60[/tex] [tex]minutes=75[/tex] [tex]80[/tex] [tex]minutes =100[/tex][tex]1[/tex] [tex]hour = 125[/tex]Therefore we can paddle 125 miles at consistent rate.
A castle built for the man who founded the town of Redstone, CO, can now be yours, for $19.75 million. (Sherman, T.)
A coal magnate, John Cleveland Osgood, built the castle for his wife near the town of Redstone, which was founded as a company town for people working in the coal mining industry. Construction began in 1897 and was completed in 1902. (Sherman, T.)
In the early 1900s, John Cleveland Osgood was known as the King of Coal in the West. He was sixth richest of the Robber Barons, a group of elite industrialists. As a social and industrial experiment, Osgood decided he wanted to build a town in the Colorado mountains that would provide better living conditions for the miners working nearby. Instead of the tents and tiny cabins common in mining towns, Osgood built Swiss-style cottages – with electricity and running water - along the river. He also built a clubhouse with a theater, school, library, lodge, community garden and stables. (Kesting, A.).
Known as Redstone Castle and as the "Ruby of the Rockies," the 42-room castle has almost 30,000 square feet of interior space. It also has over 150 acres of land, surrounded by beautiful scenery along the Crystal River. (Sherman, T.)
It's not the first time the castle has been up for sale in recent years. Steve and April Carver purchased it at an auction for $2.2 million in 2016. (Oravetz, J.)
The Carvers worked to renovate and restore the castle and have operated it as a hotel since 2018. (Oravetz, J.)
1. Calculate the annual compound growth rate of the Redstone Castle price since the house was purchased by Steve and April Carver (in 2016) until it was listed for sale in 2020. (The growth rate should be calculated to two decimals in percentage form. Round the number of years to the whole number). Please show your work.
2. Assume that the average compound growth rate prevailed since John Cleveland Osgood built the Castle in 1902 until 2016 was 5.52% per year compounded annually. Calculate the price of the house in 1902. (Round the number of years to the whole number). (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work.
3. You were using the time value of money concept to answer question #2. Think about the timeline for that problem. What year is considered as the time point 0 in that problem? Please explain your answer
4. Assume that the average compound growth rate you were using in the question #2 now is compounded daily. Calculate the price of the house in 1902. Compare with your answer to the question #2. (Round the number of years to the whole number). (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work.
5. Assume that the house was purchased for the price listed in 2020. A commercial bank loaned the buyer the whole price (zero down payment) for 30 years. The loan must be repaid in equal monthly payments at the end of the month. The annual interest rate on the loan is 3.45% of the unpaid balance. What is the amount of the monthly payments? Please show your work.
Answers
The annual compound growth rate of the Redstone Castle price is 73.10%.
How to calculate the compound growth rate?From the information given, the formula to calculate the annual compound growth rate will be:
g = (F/P)^(1/n) - 1
where g = growth rate
f = final value = 19750000
p = initial value = 2200000
n = period = 2020 - 2016 = 4
g = (F/P)^(1/n) - 1
g = (19750000/2200000)^(1/4) - 1
g = 73.10%
Therefore, the growth rate is 73.10%
The price of the house in 1902 will be calculated thus:
PV = F/(1 + g)^n
= 19750000/(1 + 73.10%)^4
= $4811
The year that is considered as the time point 0 in that problem is 1902.
When the average compound growth rate in the question #2 now is compounded daily, the price of the house in 1902 will be $4071. The difference in values will be:
= $4811 - $4071
= $740
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On June 1, Bonnie's car had 23,825 miles. On
September 1, her car had 24,385 miles. What is
the average rate of change?
Answers
Step-by-step explanation:
well, it changed by 560 miles overall. in a matter of 3 months.
but for the rate of change I have to ask what is the unit of time for that consideration ?
the rate of change is the change of the functional value over an interval divided by the length of the interval.
if 3 months is the unit of time, then the change rate is 560/1 = 560 miles per quarter.
if the unit of time is 1 month, then the change rate is 560/3 miles per month.
if the unit of time is days, then we have 30+31+31 = 92 days in that interval, and the change rate is 560/92 = 140/23 miles per day.
and so on.
don't have to answer all just at least 1 pls and write yes if the statement is a proportion or no if it is not a proportion.
2:3 = 9:4
3/8 = 12/32
10/12 = 20/25
4/9 = 17/38
Answers
Answer:
3/8 = 12/32 is a proportion
Step-by-step explanation:
2:3 and 9:4 is not a proportion, 10/12 and 20/25 is not a proportion, 4/9 and 17/38 is not a proportion
From this data, how many male, female, adult, and baby mountain goats do you predict are in the park
Answers
Answer:
See below ~
Step-by-step explanation:
Part A
Male elk = 105/450 = 7/30Female elk = 120/450 = 4/15Adult elk = 173/450Baby elk = 52/450 = 26/225Part B
Male elk = 7/30 = 0.233 = 23.3%Female elk = 4/15 = 0.267 = 26.7%Adult elk = 173/450 = 0.384 = 38.4%Baby elk = 26/225 = 0.116 = 11.6%