Use the chain rule to find ∂z∂s and ∂z∂t, where z=x2+xy+y2,x=10s+7t,y=10s+3t

Answers

Answer 1
[tex]\dfrac{\partial z}{\partial s}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial s}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial s}[/tex]
[tex]\dfrac{\partial z}{\partial s}=(2x+y)(10)+(x+2y)(10)=30x+30y[/tex]
[tex]\dfrac{\partial z}{\partial s}=30(10s+7t)+30(10s+3t)=600s+300t[/tex]

[tex]\dfrac{\partial z}{\partial t}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial t}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial t}[/tex]
[tex]\dfrac{\partial z}{\partial t}=(2x+y)(7)+(x+2y)(3)=17x+13y[/tex]
[tex]\dfrac{\partial z}{\partial t}=17(10s+7t)+13(10s+3t)=300s+158t[/tex]

Related Questions

1/10 of 400,000 is 10 times as much as?

Answers

40,000 is the answer

One and two thirds times a right angle

Answers

a right angle = 90 degrees

1 2/3 * 90 = 
5/3 * 90 =
450/3 =
150 <===

Answer:

150 Degrees

Step-by-step explanation:

We have to find one and two third of a right angle.

That is we have to basically find [tex]1\displaystyle\frac{2}{3}\text{ of a right angle.}[/tex]

The measure of a right angle in degrees is 90 degrees.

[tex]1\displaystyle\frac{2}{3}\times 90[/tex]

We convert the mixed fraction into unlike fraction

[tex]\displaystyle\frac{5}{3}\times 90 = 150[/tex]

Thus, one and two third of a right angle is 150 degrees or [tex]150^\circ[/tex]

Jared is 10 years old and peter is 15 years old they are brothers . Together they run 150 yards . How far does each brother run

Answers

So, pretty much age would be a distractor, so if they both run 150 yards, they could possibly run 75 yards

Answer: About 70 yards :D.

Hope this helped

Complete the following proof. Given: 2x 11 = 15 Prove: x = 2

Answers

Answer:

Hence, x = 2.

Step-by-step explanation:

Given  : Given: 2x + 11 = 15 .

To find : Prove: x = 2.

Solution : We have given   2x + 11 = 15 .

On subtracting both sides by 11

2x = 15 - 11

2x = 4

On dividing both sides by 2

x = 2

Hence, x = 2.

Therefore,  Hence, x = 2.

What are the solutions of 3x+5=2x-7

Answers

So you need to isolate the variable in order to get your answer. This is how you do it.

3x + 5 = 2x - 7
Subtract 2x from both sides.
1x + 5 = -7
Subtract 5 from both sides to have the variable by itself.
1x = -12
Divide 1 to both sides to find the value of x.
x = -12

Now we need to check.
3(-12) + 5 = 2(-12) - 7
-36 + 5 = -24 - 7
-31 = -31
Since both sides or the same you now know that -12 is the solution.
I hope this helps love! :)

[tex]3x+5=2x-7[/tex]                                          equation

[tex]x+5=-7[/tex]                                                 Subtract 2x from both sides

[tex]x=-12[/tex]                                                   Subtract 5 from both sides



[tex]3(-12)+5=2(-12)-7[/tex]                              Plug in for X

[tex]-36+5=-24-7[/tex]                                       Distribute 3 and 2 into -12

[tex]-31=-31[/tex]                                               simplified by + and -


Determine whether the statement is always, sometimes, or never true. If △ABC has angles that measure 10° and 40°, and △DEF has angles that measure 40° and 120°, then △ABC ≅ △DEF.

Answers

Never true 50 does not equal 160
Final answer:

The statement is sometimes true. If two triangles have congruent angles, they are similar but not necessarily congruent.

Explanation:

The statement is sometimes true. If △ABC has angles that measure 10° and 40°, and △DEF has angles that measure 40° and 120°, we can determine their congruence by comparing their angles. If two triangles have congruent angles, they are similar but not necessarily congruent. Therefore, △ABC and △DEF are similar triangles but not necessarily congruent.

Learn more about Triangles here:

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You are given two sides of a triangle, a = 4.5 and b = 6. the angle between them is 35 degrees. write a script to find the length of the third side and the area of the triangle. hint: use trigonometric formula.

Answers

Attached a solution and showed work.

if two positive fractions are less than 1, why is their product also less than 1?

Answers

The product of two positive fractions are also less than one because you are multiplying a number which is already less than 1.

For example.

1/ 2 = is 50% of a whole.

When you multiply 1/2 by 1/2 you do not get the 100% of the whole because you are only getting 50% of the 50% of the whole, which in turn is equivalent to 25% of the whole.

1/2 * 1/2 = 1/4 of the whole.

The only time you can get a result of 1 and above where two fractions are less than 1 is when you perform addition of these fractions.

1/2 + 1/2 = 1 - ALL CREDITS GO TO @TASKMASTERS!
When you multiply something (x) by a proper fraction ( less than 1 ), you always get something less than x, or the original number, because you're taking part of x and a part can't be larger than the whole.

Here's an example :
5 * 1/5 = 1
1<5

When you start with something that's less than 1 ( and positive), and you multiply it by a fraction, you get part of that positive fraction, so it will never be greater than 1.

Hope this helps!
I'm sorry if this is confusing ... it's too late for my brain to work at max level.

what is 3a^2 +a^2 added to a+6?

Answers

4a^2+a+6 Unless you have a Value for a this is what the answer should look like
Hope this Helps :D  

Answer:

Step-by-step explanation:

not sure if i am doing it right help please?

3a^2+a^2+a+6

3a^4+a+6

NEED HELP 25 POINTS PLEASE HELP.The students at Harrison Middle School are being split into groups for a community service project. The school faculty has decided that each grade (6th, 7th, and 8th) will be split up into their own set of groups. The faculty has also decided that it is important for each grade to be split evenly into groups, with no leftover students, so that each group in a grade has exactly the same number of boys and girls. For each of the following grades, determine the largest number of groups that can be made and the number of boys and girls that will be in each group. The 6th grade has 64 girls and 72 boys. The 7th grade has 81 girls and 63 boys. The 8th grade has 68 girls and 60 boys. Please list down how many groups each grade has for both boys and girls.

Answers

Each group will have the same number of boys and girls in a group. Find common factors for the number of boys and girls.

6th grade :
64 girls = 8 * 8
72 boys = 8 * 9
There will be 8 groups consisting of 8 girls and 9 boys

7th grade :
81 girls = 9 * 9
63 boys = 9 * 7
There will be 9 groups consisting of 9 girls and 7 boys

8th grade :
68 girls = 4 * 17
60 boys = 4 * 12
There will be 4 groups consisting of 17 girls and 12 boys

if y is directly proportional to x^2 and y=216 when x=9 find y if x=19

Answers

Sure. Let'd go eith tht

Ted can wax a car in 20 minutes or wash a car in 60 minutes. tom can wax a car in 15 minutes or wash a car in 30 minutes. what is each man’s opportunity cost of washing a car?

Answers

well tom has a better chance of getting paid more than ted

How to find the slope of (20/8) and (9,16)?

Answers

is that supposed to be (20,8)?

When the r2 of a regression equation is very high, it indicates tha?

Answers

... that the regression line is a strong indicator of the actual relationship between x and y.

Kate is 17 years old, and Victor is 12 years younger. In how many years will Kate be twice as old as Victor?

Answers

10 to 12 years I'm sure

Answer:

In 7 years

Step-by-step explanation:

Victors age: 17-12=5

Kate's age:17+7=24

Victors age:5+7=12

24 divided by 2 equals to 12.

~~~~~~~

Check your answer

5+12=17

24-7=17

12-7=5

12*2=24

A Color printer will print 8 pages per min. How many mins. will it take to report that has 136 pages?

Answers

it will take 17 minutes to print 136 pages.
It will take 17 minutes hope this helps:)

5/8(x-1/3)=5/12 can someone help me figure out what x is?

Answers

Solve for x:(5 (x - 1/3))/(8) = 5/12
Put each term in x - 1/3 over the common denominator 3: x - 1/3 = (3 x)/3 - 1/3:(5 (3 x)/3 - 1/3)/(8) = 5/12
(3 x)/3 - 1/3 = (3 x - 1)/3:(5 (3 x - 1)/3)/(8) = 5/12
3×8 = 24:(5 (3 x - 1))/24 = 5/12
Multiply both sides of (5 (3 x - 1))/24 = 5/12 by 24/5:(24×5 (3 x - 1))/(5×24) = (24×5)/(5×12)
(24×5)/(5×12) = (24×5)/(5×12):(24×5 (3 x - 1))/(5×24) = (24×5)/(5×12)
(24×5 (3 x - 1))/(5×24) = (5×24)/(5×24)×(3 x - 1) = 3 x - 1:3 x - 1 = (24×5)/(5×12)
(24×5)/(5×12) = 5/5×24/12 = 24/12:3 x - 1 = 24/12
The gcd of 24 and 12 is 12, so 24/12 = (12×2)/(12×1) = 12/12×2 = 2:3 x - 1 = 2
Add 1 to both sides:3 x + (1 - 1) = 1 + 2
1 - 1 = 0:3 x = 2 + 1
2 + 1 = 3:3 x = 3
Divide both sides of 3 x = 3 by 3:(3 x)/3 = 3/3
3/3 = 1:x = 3/3
3/3 = 1:Answer:  x = 1

The above answer is correct, this answer I am sure is correct, I hope you can adopt.

What is another way to write 9×200?

Answers

If we break down 9 and 200 into their most essential components, their prime factors, every possible combination of those factors will give us the ways we could write 9 x 200.

9's prime factorization is 3², and 200 breaks into 2³x5², so the full prime factorization of 9x200 is 2³ x 3² x 5². Any multiplicative combination of those prime factors will give us another way of expressing 9x200. For example, we could take two of the 2's and one of the 5's to get 2 x 2 x 5 = 20 for our first term, and use the rest (2, 3², and 5), to make 2 x 3² x 5 = 90; Checking our work, 20 x 90 = 9 x 200 = 1800, so that would be another valid way of expressing the product.

A rectangular prism is completely packed with 90 cubes of edge length fraction 1 over 2 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism? 11 unit cubes and 1 smaller cube of volume fraction 1 over 8 cubic inch 22 unit cubes and 4 smaller cubes of volume fraction 1 over 8 cubic inch each 11 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each 22 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each Could someone teach me the steps please? I reviewed the lesson, I still don't understand

Answers

check the picture below.

ok, notice the volume of the smaller cube forming the larger cube.  Keeping in mind that the larger cube has 90 of those small ones.

[tex]\bf \stackrel{\textit{larger cube}}{V}=90\stackrel{\textit{small cube}}{V}\implies \stackrel{\textit{larger cube}}{V}=90\cdot \cfrac{1}{8}[/tex]

Answer:

A

Step-by-step explanation:

ur welcomes

Cheryl is moving to a new house. Her old house is 3 kilometers and 457meters from her new house. How many meters is her old house from her new house.

Answers

Answer:

Her old house is 3000m+457m = 3457m from her new house.

Step-by-step explanation:

Conversion of units problems can always be modeled as a rule of three problem.

Rule of three problem:

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In the case of a conversion of units problem, the measures are:

- the value in one unit

- the value in another unit

As the value of the first unit increases, so will the value of the second unit. It means that in a conversion of units problem, we will always have a direct rule of three.

The problem states that Cheryl's new house  is 3 kilometers and 457meters from her old house. The problem wants to know this distance purely in meters, so we have to convert 3km to meters. 1km = 1000m, so:

1km - 1000m

3km - xm

x = 1000*3

x = 3000m

Her old house is 3000m+457m = 3457m from her new house.

How much greater is the weight of the large box at 3/4lb than the small box at
1 1/8lbs

Answers

well, is just their difference, let's first convert the mixed fraction to "improper" and then subtract.

[tex]\bf \stackrel{mixed}{1\frac{1}{8}}\implies \cfrac{1\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{9}{8}}\\\\ -------------------------------\\\\ \cfrac{9}{8}-\cfrac{3}{4}\impliedby \textit{our LCD is then 8}\implies \cfrac{(1\cdot 9)~~-~~(2\cdot 3)}{8} \\\\\\ \cfrac{9-6}{8}\implies \cfrac{3}{8}[/tex]

The temperature of dry ice is -109.3°F, which is 183.6°F less than the outside temperature. What is the outside temperature?

Answers

Final answer:

To find the outside temperature, add the difference of 183.6°F to the dry ice temperature of -109.3°F, yielding an outside temperature of 74.3°F.

Explanation:

The student is asking to find the outside temperature given that dry ice temperature is -109.3°F and that the outside temperature is 183.6°F higher than the dry ice. We can solve this by adding the temperature difference to the dry ice temperature.

Let's denote the outside temperature as T.

T = (-109.3°F) + 183.6°F

Now, let's perform the addition:

T = 74.3°F

Therefore, the outside temperature is 74.3°F.

Final answer:

The outside temperature can be calculated by subtracting 183.6°F from the temperature of dry ice (-109.3°F).

Explanation:

The outside temperature can be calculated by adding the temperature difference to the temperature of dry ice. The temperature difference is given as 183.6°F less than the outside temperature, which means we need to subtract 183.6°F from the temperature of dry ice (-109.3°F). So, the outside temperature would be -109.3°F + (-183.6°F) = -293.9°F.

Trish has 9 boxes of pencils. Raj has 2 boxes of pencils. There are 10 pencils in each box. How many they have

Answers

Trish has 90 pencils 
Raj has 20 pencils
9x10=90 2x10=20 so 20+90 =110

round 101 to the nearest ten

Answers

To round 101 to the nearest 10, we first need to locate the tens place, which holds the value 0. Now, we basically need to round to 10 or to 0. To do this, we look at the one's place, which holds the value 1. One is closer to 0 than 10, so we round down, which gives us a final answer of 100. Hope this helps and have a fabulous day!

101 rounded to the nearest ten is 100.

What is Rounding Off?

Rounding off of a number is defined as the simplification of the number by keeping the value of the number same but is made closer to the next number.

Rounding can be done for whole numbers as well as decimals.

Here the given number is 101.

101 is between 100 and 110. We can round it to either of these two.

We have to round it to the nearest ten.

The number in the tens place is 0.

Look at the number next to tens place, which is at ones place.

The digit at ones place is 1, which is less than 5.

So keep the number in tens place as such and add 0 to ones place.

So the number is 100.

Hence 101 when rounded to nearest ten is 100.

Learn more about Rounding Off Numbers here :

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Each time Gertrude gets​ paid, 10​% of her pay check goes to taxes. Last​ week, ​$ 40 was taken out of her check for taxes. What was the amount of​ Gertrude's pay check last​ week?

Answers

The answer is 400. every 10% equal 100
Final answer:

Gertrude's paycheck last week was $400.

Explanation:

To find the amount of Gertrude's paycheck last week, we can set up an equation using the information given. Let's assume her paycheck amount is represented by 'x'. According to the problem, 10% of her paycheck, or 0.10x, is taken out for taxes. This amount is given as $40. So we can write the equation as 0.10x = 40. To solve for x, we divide both sides of the equation by 0.10: x = 40 / 0.10 = $400.

a candle maker has 4 1/2 pounds of wax. He wants to cut the wax into pieces that are 2/3 pound each. How many 2/3 pound pieces can he divide the wax into?

Answers

10 1/8 is your answer

Answer:

[tex]6\frac{3}{4}[/tex] pieces.

Step-by-step explanation:

Let x represent number of pieces.

The amount of wax used in making x pieces would be [tex]\frac{2}{3}x[/tex].

We have been given that a candle maker has 4 1/2 pounds of wax. We can represent this information in an equation as:

[tex]\frac{2}{3}x=4\frac{1}{2}[/tex]

[tex]\frac{2}{3}x=\frac{9}{2}[/tex]

[tex]\frac{3}{2}*\frac{2}{3}x=\frac{3}{2}*\frac{9}{2}[/tex]

[tex]x=\frac{27}{4}[/tex]

[tex]x=6\frac{3}{4}[/tex]

Therefore, the candle maker can make [tex]6\frac{3}{4}[/tex] pieces.

How much pizza will each person get if 4 people share 3/4 of a pizza equally?

Answers

2 half turn half because when you have 4 and it clearly you have right now and then then you have to he wanted to happiness
Okay. So in order to solve this problem, we have to do division, because 4 people share 3/4 of a pizza equally. To divide fractions, keep 3/4 the same, turn the division symbol into multiplication symbol, and flip 4/1 over into 1/4. 3/4 * 1/4 = 3/16. Each person will get 3/16 of a pizza.

5x - x + 12 +2x - 7 = 10

Answers

Combine like terms. Like terms are completely the same excluding coefficients.
6x+5=10

Subtract 5 from both sides
6x=5

Divide bith sides by 6
x=5/6

Final answer: B
5x - x + 12 + 2x - 7 = 10

We're simply just trying to isolate x :)

However, we must first simplify the equation by adding like terms.

(5x - x + 2x) + (12 - 7) = 10

Simplify.

6x + 5 = 10

Then, we must subtract 5 from both sides.

6x = 10 - 5

Simplify.

6x = 5

Divide both sides by 6.

6x ÷ 6 = 5 ÷ 6

Simplify.

x = 5/6

B. x = 5/6

~Hope I helped!~

find the inverse of f(x) = 2x + 3

Answers

Answer:

f−1(x)=x−32

Explanation:

Follow the steps:

f(x)=2x+3

1- replace f(x) with y →y=2x+3

2- simply switch x and so the equation looks like x=2y+3

3- use algebra to solve for y. (isolate y)
x=2y+3

x−3=2y

x−32=y

This is the inverse function and is written as

f−1(x)=x−32

PLEASE HELP ASAP!!(3 QUESTIONS) I WILL GIVE BRAINLIEST AND 5 STARS!!

Identify the corresponding word problem given the equation: 5.59x = 27.95
A) How many boxes of nectarines can you buy with $27.95.
B) How much does a box of nectarines cost if five boxes costs $27.95?
C) How much does five boxes of nectarines cost if one box costs $5.59?
D) How many boxes of nectarines can you buy with $27.95 if one box costs $5.59?

Tom has saved $128, and his goal is to save $500. How much more must he save?


Which equation BEST represents this situation?
A) x + 128 = 500
B) x - 128 = 500
C) x + 500 = 128
D) x - 500 = 128

8, minus some number divided by 3, equals 6. Find the number.
A) -14/3
B) 4
C) 6
D) 2/3

Answers

A B and  Its soooooo easy

Answer:

The first one is

1.) D)How many boxes of nectarines can you buy with $27.95 if one box costs $5.59?

2.) is B

3.) D

Step-by-step explanation:

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