Answer and Step-by-step explanation:
SOLUTION:
Given function:
h (x, y, z) = ln (x2 + y2 – 1) + y +6z, p0(1, 1, 0)
Derivatives of the function:
∂h / ∂x = (1 / x2 + y2 -1). (2x)
= 2x / x2 + y2 -1
∂h/∂y = (1 / x2 + y2 – 1) (2y + 1)
= (2y / x2 + y2 -1) + 1
∂h / ∂z = 6
Now compute the partial derivatives:
∂h (1, 1, 0) / ∂x = 2(1) / 1 +1 -1
= 2
∂h(1, 1, 0) / ∂y =( 2(1) / 1 +1 -1) + 1
= 3
∂h (1, 1, 0) / ∂z = 6
Δh (1,1,0) = ( 2, 3, 6)
The definition of gradient is:
Δf (x, y, z) = (∂f / ∂x , ∂f / ∂y)
Put the coordinate values to arrive at solution:
Umax = Δh (1,1,0) / | Δh (1,1,0) |
= (2, 3, 6) / |2, 3, 6|
= (2, 3, 6) / √(22+33+62)
= (2, 3, 6) / √49
= (2, 3, 6) / 7
= (2/7 , 3/7, 6/7)
Umin = - U max = ( -2/7, -3/7, -6/7)
Compute direction by finding unit vector:
Du h max = Δh (1,1,0) . u max
= (2, 3, 6) . (2/7, 3/7, 6/7)
= 2(2/7) + 3(3/7) + 6(6/7)
= 4/7 + 9/7 +36/ 7
= 49 / 7
= 7
Du h min = -Du h max
= -7
It took Jed 2/4 of an hour to complete his math homework on Friday, 2/3 of an hour on Saturday, and 3/6 of an hour on Sunday.How many hours did he take to complete his homework altogether?
It took Jed a total of 1 2/3 hours to complete his homework altogether
Can someone help me answer this
Monday 4hours and 30minutes were worked
do 12-8 then take the thirty minutes and add it on to the difference
because that is the time she is working
happy to help plz mark brainliest
You are filling piñatas for your sister's birthday party. The list shows the gifts you are putting into the piñatas. You want identical groups of gifts in each piñata with no gifts left over. What is the greatest number of piñatas you can make?
Answer:
The greatest number of piñatas you can make with the gifts is:
6 piñatas.Step-by-step explanation:
To identify the greatest number of piñatas, you must think in a number that can divide another and obtain a whole number with this:
182442Bigger the number, greater the number of piñatas, in this case, you can see the numbers given can be divided into four numbers obtaining a whole number: 1, 2, 3, and 6. Remember that the best number is the greatest, in this case, number six. Now you proceed to divide the numbers into 6:
[tex]\frac{18}{6}= 3[/tex][tex]\frac{24}{6}= 4[/tex] [tex]\frac{42}{6}=7[/tex]Taking into account the values obtained, you can see that each piñata would have: 3 bottles of nail polish, 4 pairs of earrings, and 7 lollipops.
A square red rug has a yellow square in the center. The side length of the yellow square is x inches. The width of the red band that surrounds the yellow square is 12 in. What is the area of the red band?
James paid $42 for 6 lb of chocolate how much does the chocolate cost per pound
Answer:
7$ gimme brainliest
Step-by-step explanation:
Answer: 7 pounds
Step-by-step explanation:
42/6=7
8 points if answered!!
You and your soccer team are interested in buying jerseys. The price of each jersey is $50. If you buy 4 jerseys, you will get 10% discount. How much do you have to pay if you buy 8 jerseys?
Answer: $4.84
Explanation:
County A: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!
$75 * 0.0725 = $5.4375
Add the original price and the sales tax.
$75 + $5.4375 = $80.4375
County B: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!
$70 * 0.08 = $5.6
Add the original price and the sales tax.
$70 + $5.6 = $75.6
Then take the difference.
80.4375 – 75.6 = 4.8375
Round to the nearest hundredth: $4.84
whats 8 and 2\5 as an improper fraction
it is very easy first multiply (8*2) then our ans 16
then add 16 + 5 = 21 21\5
answer 21\5
Tom had 48 coins and 8 friends. How many coins due each friend get?
Answer:
They will each get 6 a piece
Scott runs 3 km in 30 minutes and then rests for 15 minutes. He then runs 2 km in 15
minutes. What was Scott's average speed?
Answer:
5km/hr
Step-by-step explanation:
Given
Distance = 3km and 2km
Time = 30 mins, 15 mins, 15 mins
Required
Determine the average speed
To answer this, we need to determine the total distance.
Distance =3km + 2km = 5km
Then, we calculate the total time
Time = 30 mins + 15 mins + 15 mins = 1 hr
Next, we can now determine the average speed using:
Average Speed = Total Distance/Total Time
Average Speed = 5km/1 hr
Average Speed = 5km/hr
You buy milk that contains 180 calories per 2 cups. Use a ratio table to find the number of calories in 18 cups.
Answer:
1620
Step-by-step explanation:
180/2=90
90*18=1620
You buy milk with 180 calories in two glasses. Now compute the caloric value of 18 cups. 18 cups contain 1620 calories.
What is meant by caloric value?Calorific value, also known as heating value or heat of combustion, is a unit of measurement for the total energy content produced in the form of heat when a substance is completely combusted with air or oxygen. The amount of heat energy released during complete combustion of a unit mass of a fuel is defined as its calorific value. It is measured in kJ/kg.It is the measurement of the heat value or amount of energy released, and it is expressed in either gcv or ncv. Gross calorific value (GCV), also known as Higher Heating Value (HCV), is the amount of heat released by complete combustion when a unit of fuel is burned.Therefore,
You buy milk with 180 calories in two glasses.
Now compute the caloric value of 18 cups.
Let 18 cups have a calorie count of As, and 2 cups have 180 calories.
A serving of two cups contains 180 calories.
As a result, the ratio would be 2: 180.
As a result, 18 cups contain X calories.
18 cups are equal to X calories.
Consequently, the ratio would be X : 18
We now set a ratio to determine how many calories are in 18 cups:
2 : 180 :: 18 : X
Simplifying,
2/ 180 = 18/X
Cross multiplying results in:
2X = 18 × 1 80
= 3240
By multiplying both sides by 2, we obtain:
X = 3240/2
= 1620
Hence, 18 cups have 1620 calories in them.
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Which of the following expressions are equivalent to 12x+20? Select all that apply.
A.-2(6x - 10)
B.4(3x+ 20)
C.4(3x + 5)
D.12(x+1 2/3)
E.-2(10 – 6x)
Answer:
C
Step-by-step explanation:
4(3x+5) = 12x+20
Answer:
c
Step-by-step explanation:
The square root of 10 lies between what 2 numbers?
A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The square root of 10 lies between 3 and 4.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
In order to find the square root of 10 lies between which two numbers the approximate value of the root is needed to be calculated.
√10 = 3.162.......
Now, if we plot √10 on the number line its value will lie between 3 and 4.
Hence, The square root of 10 lies between 3 and 4.
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Given g(x) = -X – 1, solve for x when g(x) = 3.
Answer:
-4 = x
Step-by-step explanation:
g(x) = -X – 1
g(x) = 3
3 = -x-1
Add 1 to each side
3+1 = -x-1+1
4 = -x
Multiply by -1
-4 = x
I need help, please
Answer:
2
Step-by-step explanation:
1+1=2
i have to solve this −2×8/3=
Answer:
-2 times 8\3
Step-by-step explanation:
the answer is -48
Answer: -5 1/3
Step-by-step explanation: First, convert -2 into a fraction by putting a 1 under the -2. So, you should have -2/1. Since, you‘re multiplying a negative times a positive, you’re answer should be negative. Next, multiply -2/1 x 8/3 by cross multiplying. You should end up with an answer of -5 1/3.
if the standard deviation of the values in a sample is 14 what is the variance of the data values
Answer:
196
Step-by-step explanation:
THATSSS THE ANSWERRRRR!!
What value of x makes this equation true?
0.6x - 5 = 0.1x + 7
Answer:
x=24
Step-by-step explanation:
0.6x - 5 = 0.1x + 7
add 5 to both sides:
0.6x = 0.1x + 12
take away 0.1x from both sides:
0.5x = 12
divide both sides by 0.5
x = 12÷0.5
x=24
hope this helps
brainliest plz?
x
Which number is the greatest?
O 1.2
O 1.3
O 1.235
O 1.003
Answer:
bStep-by-step explanation:
Answer:
b
Step-by-step explanation:
go it right on edge
Hey
What’s 8=D mean? I see it all the time but can’t figure it out! Help! My peers laugh at me. Is it simple math?
Answer:
it's a dirty joke, like when you type things into a calculator and turn it upside down to make it look like a word. It's not an equation
Step-by-step explanation:
Answer:
its a depiction using symbols from a calculator about mens sexual organs its really dirty and you shouldn't use it especially if you are too inoccent to know what it is
help a girl out plz
Answer:
-1 0 1 2 2 1/4 2.33 2.5 √8 3 | | . | | ^ ^ . ^ ^ . |
Step-by-step explanation: All the values are between 2 and 3
I hope this shows up correctly and helps.
ent
Use the interactive to find an expression equivalent to
4x - 4 - 2x + 3.
O 2x - 1
O 6x - 1
O 2x - 7
O-2x + 3
Please hurry help
Answer:
it's A
Step-by-step explanation:
2x - 1
I put b and got it wrong
Nico wanted to determine the number of students in his school who buy school lunch.he walked around the cafeteria one lunch period looking to see whether every fifth person in the cafeteria purchased lunch or brought their own.which method did he use to collect his data
Answer:
Observational study
Step-by-step explanation:
Answer:
D: Observational Study
Step-by-step explanation:
edg2020
He did not go around asking people how many of them buy lunch, so it is not a survey. He did not create the settings and conditions or simulate possible examples, so its not B. He did not control or change any variables, so it is not an experiment. He simply walked around and Observed people to get information for his study. Thus it is D.
Given: -7(x+2)+4x=6(2x-4) prove: x=2/3
Answer:
2/3
Step-by-step explanation:
multipy (X+2) by 7 the you multiply (2x-4) by 6 I.e
-7×X- (-7×2)+4x=6×2x-6×4
-7x-14+4x=12x-24
collect like terms
-7x+4x-12x=-24+14
-15x=10
divide both side by -15, so that X can stand alone
-15x/-15=-10/-15
-15 cancels -15, minus cancels minus
X=10/15
X=2/3
Holiday Inn charges its cost one dollar plus $.80 per minute for long distance calls. Across the street, La Quinta charges its guests $2 plus $0.75 per minute for long distance calls. Which equation correctly models the length of a call for which the two hotels charge the same amount
Solve: -4 (x + 6) + 2 ( x -2) Show your work
Answer:
-2x - 28
Step-by-step explanation:
-4(x+6) +2 (x-2) Distribute the -4 to (x+6) and the 2 to (x-2):
-4x - 24 + 2x - 4 Combine like terms -4 + 2x and -24-4:
-2x - 28
Hope this helped :)
Answer:
Please see explanation.
Step-by-step explanation:
-4(x+6) + 2(x-2) First, distribute the -4 to x+6
-4x - 24 + 2(x-2) Now distribute the 2 into x-2
-4x - 24 + 2x - 4 Combine like terms
-4x + 2x - 24 - 4
-2x - 28 This might be your answer but if you are looking for what x is equal to then keep following along.
If you are solving for x then most likely the equation says that it is equal to zero
-2x - 28 = 0 Add 28 to both sides
-2x = 28 divide both sides by -2
x = -14
Can someone help me
Answer:
with what?
Step-by-step explanation:
Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. A manufacturer of spark plugs claims that its plugs have an average life in excess of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles, the sample standard deviation was 1,500 miles and the computed test statistic was 3.677. Based on these findings, there is enough evidence to accept the manufacturer's claim at the 0.05 level.
Answer:
There no sufficient evidence to support the manufactures claim at the 0.05 level
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 22100 \ miles[/tex]
The sample mean is [tex]\= x = 23400 \ miles[/tex]
The sample size is [tex]n = 18[/tex]
The standard deviation is [tex]\sigma = 1 500 miles[/tex]
The test statistics is [tex]t = 3.677[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 22100[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 22100[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(t >3.677 )[/tex]
From the z-table [tex]P(t >3.677 ) = 0.000118[/tex]
So
[tex]p-value = 2 * 0.000118[/tex]
=> [tex]p-value = 0.000236 [/tex]
From he value given and obtained we see that [tex]p-value < \alpha[/tex]
Hence we reject the null hypothesis
Hence there no sufficient evidence to support the manufactures claim
How do you write 1.8 × 10^1 in standard form?
Answer:
probable as
1.8 × 10 = 18
brainliest ig?
A box of Shredded Wheat weighs 0.35 kg and a box of Weetabix weighs 9/25 kg?
Which box is heavier?
Show your work
PLEASE HELP DUE TONIGHT THANK YOU SO MUCH
Answer: The box of Weetabix is heavier by 0.01 kg
Step-by-step explanation:
Divide 9/25 to get the decimal equivalent
9÷25 =0.36
Compare Shredded Wheat at 0.35 kg to Weetabix at 0.36 kg
Weight of the box of Shredded Wheat is [tex]0.35[/tex] kg and weight of the box of Weetabix is [tex]0.45[/tex] kg.
So, the box of Weetabix is heavier.
Weight of the box of Shredded Wheat [tex]= 0.35[/tex] kg.
Weight of the box of Weetabix [tex]= \frac{9}{25}[/tex] kg.
Here to compare the two weights, first make both of them similar.
Either make both of them decimals or both of them fraction.
Here, we will make both the weights decimals.
[tex]\frac{9}{20} = 0.45[/tex]
Now, [tex]0.45>0.35[/tex]
So, the box of Weetabix is heavier.
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