Answers
====================================================
Work Shown:
Plug (x,y) = (3,2) into the F(x,y) function
[tex]F(x,y) = 2x^2 + 4y^2\\\\F(3,2) = 2(3)^2 + 4(2)^2\\\\F(3,2) = 34\\\\[/tex]
Next, find the gradient and plug in (x,y) = (3,2)
[tex]F(x,y) = 2x^2 + 4y^2\\\\\\\nabla F(x,y) = \Big< \frac{dF}{dx}, \frac{dF}{dy}\Big>\\\\\\\nabla F(x,y) = \Big< 4x, 8y \Big>\\\\\\\nabla F(3,2) = \Big< 4*3, 8*2 \Big>\\\\\\\nabla F(3,2) = \Big< 12, 16 \Big>\\\\\\[/tex]
This means,
[tex]z = \nabla F(3,2) \cdot \left(\vec{x} - \big< 3, 2 \big>\right) + F(3,2)\\\\\\z = \nabla F(3,2) \cdot \left(\big< x,y \big> - \big< 3, 2 \big>\right) + F(3,2)\\\\\\z = \nabla F(3,2) \cdot \big< x-3,y-2 \big> + F(3,2)\\\\\\z = \big< 12,16 \big> \cdot \big< x-3,y-2 \big> + 34\\\\\\z = 12(x-3)+16(y-2) + 34\\\\\\z = 12x-36+16y-32 + 34\\\\\\z = 12x+16y-34\\\\\\[/tex]
As a way to help check, note how plugging (x,y) = (3,2) into the last equation for z leads to z = 34. This helps confirm that we have the correct equation because the point (3,2,34) must be on F(x,y) and also on z since the plane is tangent to the F(x,y) curve at this point.
Related Questions
Select all expressions that equal -5-(-12)
a. -5+(-12)
b. -5+(-12)
c. -5+12
d. -5-12
Answers
Answer:
The answer is letter C.
Step-by-step explanation:
hope this helps
Given: -5-(-12)
=-5+12= 7
a. -5+(-12)= -17
b. -5+(-12)= -17
c. -5+12= 7
d.-5-12= -17
johns puppy friends want to reserve a karaoke studio this weekend. It cost $30 to reserve a room, plus $5 per person for pizza. How many people can be in the group if the total cost is $65?
Answers
Answer:
65-30=35/5=7
Step-by-step explanation:
Seven ppl
Help me with my review please
Answers
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What is 123.7666 rounded to the nearest tenth?
Answers
Answer:
123.8
Step-by-step explanation:
nearest tenth is 7 and the sixes aftr it are over half of a full decimal, so they round to 123.8
Solve: -9 + (-12) - -13 =
Answers
Answer:
-8
Step-by-step explanation:
-9 + (-12) - (-13) = -8
What is the value of the expression 3^2 +5^3-2^5?
A. 14
B. 34
C. 102
D. 166
Answers
Answer:
102
Step-by-step explanation:
3^2 +5^3-2^5
9+125-32
9+93
102
So 102 is the answer
is (11,9), (11,5), (9,3) a function
Answers
Answer:
[tex]\huge{ \boxed{ \sf{No}}}[/tex]
✑ Question :
Is ( 11 , 9 ) , ( 11 , 5 ) , ( 9 , 3 ) a function ?No , it's not a function.
✎ Reason :
This is not a function because one element 11 of set A is associated to elements 9 and 5 of set B.
♨ Explore about function :
↪ Function is a special type of relation. It is the refinement of relation. In a relation from A to B , every element of set A should have only one ( distinct ) image in B to be a function. In other words , if no two different ordered pairs have the same first component , then it is a function.
Hope I helped!
Have a wonderful day ! ツ
~[tex]\sf{TheAnimeGirl}[/tex] ♡
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What is the perimeter of JKLM
Answers
Answer:
15
Step-by-step explanation:
treswar3Qqar3qwEQDR
On December 13, 2007, one South African rand was worth 0.15 U.S. dollars.
(a) On that date, how many rand was 23.39 dollars worth? Round your answer to the nearest hundredth of a rand.
(b) On that date, how many dollars was 175.89 rand worth? Round your answer to the nearest hundredth of a dollar.
Answers
Answer:
153593.3333 rounded is 153593.3300
then part b
1172.60 - 1172.60
Step-by-step explanation:
NEED HELP LIKE NEOW!
Jason gained 30 yards on the first play. He lost 40 on the second play. He gained 10 yards on the third play.
Answers
First play = 30 yards gained
Second play = 40 yards lost
Third play = 10 yards gained
Total yards Jason has = +30 -40 +10
= +40 -40
= 0
Answer: 0
Step-by-step explanation:
30 - 40 + 10
30 - 40 = -10
-10 + 10 = 0
0 is your final answer
Use the equation below to find y, if m=8, x=4, and b=3.
y=mx+b
y =
Ú
Х
?
Answers
Answer:
y = 35
Step-by-step explanation:
Please, help. I can’t even do this, it’s not even funny. I Will give brainliest to correct answer. Tysm.
Answers
Answer:
Sales Tax Rate = $0.32
Markdown = 15
Percentage = about 14%
Step-by-step explanation:
Answer:
re
Step-by-step explanation:
Josh plans to go to the batting cages later today. The cost is $5 per a bucket of balls plus a one-time fee of $12 for a bat and helmet. If Josh has $37 to spend, how many buckets can he afford?
Answers
Answer:
He can afford 5 buckets
Step-by-step explanation:
y = 5x + 12
37 - 12 = 25/5 = 5
what is 4x + 9 = 68 in the clearest number possible
Answers
Answer:
x = 59/4
Step-by-step explanation:
4x + 9 = 68
Subtract 9 from both sides.
4x + 9 - 9 = 68 - 9
4x = 59
Divide both sides by 4.
4x/4 = 59/4
x = 59/4
Answer:
X=0.75
Step-by-step explanation:
Step 1:
68-9=59
Step 2:
59 divided by 4= 14.75
Step 3:
0.75=3/4
14 3/4=14.75
Solution:
X=0.75
Another way is 59/4=14.75
please help soon ghhh
Answers
Answer:
the lines are NOT perpendicular because their slopes aren't negative reciprocals
if f(x)=2x^4-x^3-3x^2+14 then f'(3)=
Answers
Answer:
f(3)=122
Step-by-step explanation:
Enter the decimal represented by the shaded square.
The shaded square represents
Answers
Answer:
0.8
Step-by-step explanation:
80 out of a 100 squares are shaded in.
1.5x + 12 = 3x + 17
x=
Answers
Answer:
x = -3.3
Step-by-step explanation:
Answer:
x=−3.333333
Step-by-step explanation:
(5 x 4) - (3 x 4)= equals????
Answers
Answer:
it equals 8 cause it does
Step-by-step explanation:
:)
Each side of a 7-sided shape is 3 feet long. What is the perimeter of this shape?
Answers
Answer:
21 feet
Step-by-step explanation:
You could either do
3 + 3 + 3 + 3 + 3 + 3 + 3 = 21
or
3 x 7 = 21
Answer:
21ft
Step-by-step explanation:
3ft times 7 is 21
Frank's been traveling a lot lately as part of his job. During the past 30 days, he's been out of town 18 days. What fraction represents the number of the past 30 days that Frank has been out of town? Explain how you got your answer.
Answers
I have a picture with the explanation and work!!
I hope this helps, good luck!! :)
Answer:
3/5 represents the number of days he has been out of town in the past 30 days.
Step-by-step explanation:
I hope this helps I took the quiz and got it right.
Which expression means 5 less than the product of 9 and a number w
Answers
Answer:
9 x w = x
x - 5= y
Step-by-step explanation:
9 x w = x w = a variable that equals the second multiplier.
x = a variable that equals the product of 9 and x.
x - 5 = y y = a variable that equals the end value.
I WILL GIVE BRAINLIEST
Answers
Answer:
1
Step-by-step explanation:
The y-intercept is when the line goes through the y-axis (vertical axis)
In this case it goes through at y=1
Answer:
The y-intercept of the line in the given graph is 1
1 is the right answer.The sum of 2 numbers is 50. The sum of 1/4 of the first number and 2/3 of the second number is 25.What are the numbers?
HELLLLLPPPPPP
Answers
Answer:
First number: 20
Second number: 30
Step-by-step explanation:
First#: x
Second#: y
Constraints:
x + y = 50
1/4x + 2/3y = 25
Isolate variable y:
x + y = 50
-1/4 (x + y = 50 )
-1/4x - 1/4y = -12.5
Add equations the two equations to eliminate x:
-1/4x - 1/4y = -12.5
1/4x + 2/3y = 25
_________________
5/12y = 12.5
5y = 150
y = 30
Substitution to find x:
x + y = 50
x + 30 = 50
x = 20
A recipe for 1 batch of tropical fruit punch says combine 4 cups of pineapple juice with 5 cups of orange juice how many cups of pineapple juice and orange juice will be in 3 batches ?
Answers
Answer:
12 cups of pineapple and 15 cups of orange juice
Step-by-step explanation:
1 batch=4 pineapple with 5 cups orange
3 batches=12 pineapple with 15 cups of orange juice
The formula for the volume
of a cone is V= 1/3 pi r^2h. Write the formula expressed as the radius, r.
Answers
Answer:
[tex]\sqrt{ \frac{{3V\pi } }{h}[/tex] = r
Step-by-step explanation:
V = 1/3 pi r^(2) *h
Rewrite:
V = pi * r^(2) * h/3
Inverse operations:
V / h / 3 = pi * r^2
Simplify:
3V/h = pi * r^2
Inverse operations:
3V/h / pi = r^2
Simplify:
3Vpi/ h = r^2
Inverse operations:
sqrt( 3Vpi/h) = r
[tex]\sqrt{ \frac{{3V\pi } }{h}[/tex] = r
Please help me thank you
Answers
Answer:
I don't see the photo
Step-by-step explanation:
y = 5/2x -11 that is the correct answer mark me as brainliest
I NEED HELP ASAP PLEASE!!!
Answers
Answer:
-3x+1y=-1
or
3x-1y=1
or
by multiplying with 1/3 the first equation we get
-1x+1/3y=-1/3
or from second equation
1x-1/3y=1/3
Step-by-step explanation:
y-y1=m(x-x1)
y1=-7
x1=-2
m=3
so
y-(-7)=3(x-(-2))
y+7=3(x+2)
y+7=3x+6
-3x+y=6-7
-3x+ 1y= -1
2. Twenty-four fourth graders are going on a field trip to the Academy of Science. They need to form 3 groups of students for the tour guides. How many students will be in each group? Show how you found your answer.
Answers
Answer:
8persons/group
Step-by-step explanation:
Give parameters:
Number fourth graders = 24
Number of groups = 3 groups
Unknown:
Number of students in each group = ?
Solution:
Solving this problem involves finding the number of persons per group.
Number of persons per group = [tex]\frac{number of fourth graders}{number of groups}[/tex]
Insert the parameters and solve;
Number of persons per group = [tex]\frac{24}{3}[/tex] = 8persons/group
336 × 0.4 help me pl
Answers
Answer:
336 × 0.4 = 134.4
Step-by-step explanation:
used a calculator
