Answer:
Step-by-step explanation:
[tex]Given \ f (p,q) = 8qe^{-p} + 4pe^{-q} \ where \ P_o(0,0) \\ \text{thus the gradient of f is: } \\ \\ \bigtriangledown f(p,q) = \Big(\dfrac{\partial f}{\partial p}, \dfrac{\partial f}{\partial q} \Big) \\ \\ \dfrac{\partial f}{\partial p} = -8qe^{-p} + 4pe^{-q} \\ \\ \dfrac{\partial f}{\partial p} = 8qe^{-p} - 4pe^{-q} \\ \\ Then: \bigtriangledown f(p.q) = (-4qe^{-p}+ 8qe^{-q}, 4qe^{-p}- 8qe^{-q}) \\ \\ f(0,0) = (-4*(0)e^{-0}+ 8*(0)e^{-(0)}, 4*(0)e^{-(0)}- 8*(0)e^{-(0)}) \\ \\ = (0+8,4-0) = (8.4)[/tex]
[tex]\Big| \Big | \bigtriangledown f(0,0) = \sqrt{(8)^2+4^2} \\ \\ = \sqrt{64+16} \\ \\ = \sqrt{80}[/tex]
[tex]\mathbf{the \ direction \ of \ maximum \ change \ is }= \mathbf{\sqrt{80}} \\ \\ \mathbf{direction }(8,4)[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. 25a 2 - 30a + 9
Answer:
(5a−3)^2
Step-by-step explanation:
25a^2 - 30a + 9
Factor the expression by grouping. First, the expression needs to be rewritten as 25a^2+pa+qa+9. To find p and q, set up a system to be solved.
p+q=−30
pq=25×9=225
Since pq is positive, p and q have the same sign. Since p+q is negative, p and q are both negative. List all such integer pairs that give product 225.
−1,−225
−3,−75
−5,−45
−9,−25
−15,−15
Calculate the sum for each pair.
−1−225=−226
−3−75=−78
−5−45=−50
−9−25=−34
−15−15=−30
The solution is the pair that gives sum −30.
p=−15
q=−15
Rewrite 25a^2 - 30a + 9 as (25a^2−15a)+(−15a+9).
(25a^2−15a)+(−15a+9)
Factor out 5a in the first and −3 in the second group.
5a(5a−3)−3(5a−3)
Factor out common term 5a−3 by using distributive property.
(5a−3)(5a−3)
Rewrite as a binomial square.
(5a−3)^2
(40 POINTS!!) solve for x
Answer:
do 13+7 you will have your answer. (go down for answer)
Step-by-step explanation:
its 20
Please help is for noww
Answer:
25¢
Step-by-step explanation:
Answer: Answer: $0.25
Step-by-step explanation:
Let x be the total money was in her wallet and m be the cost of each petunia,
From the given table , the money left in wallet after purchasing 2 petunia =$6.50
Then we have the following equation: 6.50 = x - 2m - - - - - ( 1 ) Also, the money left in wallet after purchasing 8 petunia =$5 Then, we have 5 = x - 8m - - - - - - - - - ( 2 ) Subtracting (2) from (1) , we get 6.50 - 5 = -2m - (8m) then -2m + 8m = 1.50 then we 6m = 1.50. m = 1.50/6 = 0.25 hope this helped.
which value from the set makes 12n-15=42 true?
A.2.25
B.2.8
C.3.5
D.4.75
50 POINTS QUICK Mary is three times as old as her son . In 12 years Mary will be twice as old as her son. How old is each of them now?
Answer: Mary is 36 and her son is 12; in 12 years her son will be 24 and she will be 48
Step-by-step explanation:
Answer:
Mary's age = 36
Son's age = 12
Step-by-step explanation:
Let x be age of Mary and y be age of her son.
According to question,
x = 3y...........(1)
And,
x + 12 = 2(y + 12)
x + 12 = 2y + 24
Replacing value of x from (1),
3y + 12 = 2y + 24
3y - 2y = 24 - 12
y = 12
And x = 3 x 12 = 36
what is the least common denomimator for 1/3 and 1/2
Answer:
its equals 6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
PLEASE HELP, WILL GIVE BRAINLIEST!!!!!!!!
Using rules, we can simplify expressions with exponents, factorize, or expand them. [tex]2 x \sqrt{10 x}-2 x \sqrt{5}.$[/tex] Thus option D is correct,
What is the exponents and algebraic manipulation?We can simplify the expression using the rules of exponents and algebraic manipulation.
[tex]$\sqrt{5 x}\left(\sqrt{8 x^2}-2 \sqrt{x}\right) = \sqrt{5 x} \cdot \sqrt{8 x^2} - 2\sqrt{5 x} \cdot \sqrt{x}$[/tex]
[tex]$= \sqrt{(5x)(8x^2)} - 2\sqrt{(5x)(x)}$[/tex]
[tex]$= \sqrt{40x^3} - 2\sqrt{5x^2}$[/tex]
[tex]$= \sqrt{4x^2 \cdot 10x} - 2x\sqrt{5}$[/tex]
[tex]$= 2x\sqrt{10x} - 2x\sqrt{5}$[/tex]
Hence, the simplified product where [tex]$x \geq 0: \sqrt{5 x}\left(\sqrt{8 x^2}-2 \sqrt{x}\right)$ is $2 x \sqrt{10 x}-2 x \sqrt{5}.$[/tex]
Therefore, Using rules, we can simplify expressions with exponents, factorize, or expand them. the correct option is $(D) [tex]2 x \sqrt{10 x}-2 x \sqrt{5}.$[/tex]
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!!!!please helppppppp
9514 1404 393
Answer:
13/18
Step-by-step explanation:
5 of the 18 students have a cat, so 13 of them do not.
The probability that a student in the group does not have a cat is 13/18.
which polynomial function has a real root of multiplicity 2?
A.y=7-6x+3x^2
B. y=4-12x+9x^2
C. y= 4x^2-5x+5
D. y=4-9x^2
(^2 means the power to)
Tess works at a sandwich shop. When assembling their turkey sandwich, they are instructed to use 5 pieces of sliced turkey and 2 pieces of cheese. If Tess is assembling a party platter of these turkey sandwiches and uses 12 pieces of cheese, how many slices of turkey will she use?
What is 70000% + 8100000
Answer:
8100700
Step-by-step explanation:
I used a calculator
Could you pls mark me brainliest I only need one more
Answer:
8100700
hop i helped look at my drawing
Step-by-step explanation:
The area of a triangle varies jointly with the height of the triangle and the length of its base. The area of one triangle is 200 square centimeters when its height
is 25 centimeters and its base length is 16 centimeters. What is the area of a triangle having a height of 20 centimeters and a base length of 15 centimeters?
0600 square centimeters
O 300 square centimeters
O 150 square centimeters
160 square centimeters
Answer:
150 square centimeters
Step-by-step explanation:
Area of a triangle:
The area of a triangle is the multiplication of 0.5, the base length and the height length.
What is the area of a triangle having a height of 20 centimeters and a base length of 15 centimeters?
[tex]A = 0.5*20*15 = 10*15 = 150[/tex]
The area of the triangle is 150 square centimeters.
Solve for y
(4y+7)
(3y+5)
Answer:
24
Step-by-step explanation:
(4y + 7) + (3y + 5) = 180. (angle on a straight line =180)
4y + 7 + 3y + 5 =180
4y + 3y + 7 + 5 = 180
7y + 12 = 180
7y = 180 - 12
7y = 168
y = 168/7
y = 24
Answer:
24 if im correct
Step-by-step explanation:
ASAP I WILL GIVE BRAINIEST IF ANSWERED ASAP!! PLEASE PLEASE HELP
Answer:
2x + 3 =84
Step-by-step explanation:
Answer:
2x + 3 = 84
Step-by-step explanation:
What is the total number of digits required in numbering the pages of a book which has 1210 pages?
Answer:
3693 digits
Step-by-step explanation:
Answer:
3733
Step-by-step explanation:
9x1=9
90x2=180
900x3=2700
211x4=844
9+180+2700+844=3733
Plz help me well mark brainliest if correct
Find the missing data
A) 41
B) 42
OC) 44
OD 53
Answer:
44? Im not to sure
Step-by-step explanation:
Answer:
44
Step-by-step explanation:
sequence starts at five and adds up by 6
Jorgensen Company has sales of $380,000,000, and the break-even point in sales dollars is $323,000,000. Determine Jorgensen Company’s margin of safety as a percent of current sales
Answer:
1) a. break even point in units = fixed cost / contribution margin = 1,750,000 / 5 = 350,000 units
Step-by-step explanation:
What does "Uninsured Motorist Bodily Injury" typically cover
Answer:
Uninsured motorist bodily injury, or UMBI, pays for medical bills, pain and suffering, lost wages if you can't work after an accident and funeral expenses after a crash with an at-fault driver who doesn't have car insurance. It may also cover you if you're hit as a pedestrian or while riding your bike.
Step-by-step explanation:
PLEASE HELP ME!
20 points and brainlist.
Answer:
greatest common factor
Answer:
Greatest common factor
Step-by-step explanation:
You need the upside down birthday cake method to find prime numbers and gcf
Which statement describes the graph of f(x)=Lx]-2 on [0, 3)?
The steps are at y = -2 for 0 5x < 1, at y=-1 for 1 Sx < 2, and at y = 0 for 2
O The steps are at y = 0 for I Sx <1, at y = 1 for 1
O The steps are at y = 1 for 0
O The steps are at y = -3 for i Sx <1, at y=-2 for 1 Sx <2, and at y = -1 for 2
f(x) = -Lxl is the function and -3 ≤x≤3 is the domain that could represent the given graph .
What is a function ?Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
here, we have,
We know, domain is:
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Thus , from the graph it can be clearly depicted that it is representing f(x)=-Lxl for an entire range of -3 ≤x≤3 .
Hence , f(x) = -Lxl is the function and -3 ≤x≤3 is the domain that could represent the given graph .
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Complete question:
Which function and domain could represent the given
graph?
O f(x)=1-Lx]; -3 O f(x) = 1 + Lx]; -3 ≤x≤ 3
O f(x)=-Lxl; -3 ≤x≤3
O f(x)=Lx]; -3
if a 30 foot rope is divided into 1/4 of a foot pieces how many pieces of rope are there
Answer:
7.5 is the answer to this
Choose Yes or No to tell if the number 3 will make each equation true. 2 ÷ □ = 3 2 Choose... 2 ÷ 6 = □ Choose... 2 ÷ □ = 2 3 Choose... □ ÷ 8 = 3 8 Choose...
Answer:
1 no
2 yes
3 no
4 no
Step-by-step explanation:
2 ÷ □ =2/3, □ ÷ 8 = 3/8 is true for x is true which equation choose is yes.
What is Division?A division is a process of splitting a specific amount into equal parts.
We have to choose yes or no to tell if the number 3 will make each equation true.
2÷□=3/2
To get 3/2 we have to divide two by three.
2/3=3/2
These are not equivalent so it is not yes.
The other expression 2 ÷ 6 = □
2 ÷ 6=1/3 which is not 3, so it is no.
The third expression
2 ÷ □ = 2/3
When we put 3 in the blank place we get two divided by three.
2 ÷ 3=2/3
Which is true so answer is yes for 3.
□ ÷ 8 = 3/8
When we put three in the blank we get three divided eight which is true.
3÷ 8 = 3/8 which is yes for 3.
Hence, 2 ÷ □ =2/3, □ ÷ 8 = 3/8 is true for x is true which choose is yes.
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Give the Domain and Range of the following function.
2
2
4
6
O Domain: 2 < X < 6, Range: 4
o Domain: 1 <3 < 6, Range: 1
O Domain: 0 < x < 7, Range: 1
O Domain: 1 < x < 7, Range: 1
Answer:
Domain: 1 ≤ x ≤ 6, Range: 1 ≤ y ≤ 7
cómo se calcula la probabilidad de que salga el número 5 lanzando un dado 20 veces
The diagonals of square ABCD intersect at point E. If BE = 2x + 1, and AC = 3(6x - 4), find BD.
1
3
6
9
Answer:
Step-by-step explanation:
Answer:
It is 6
Step-by-step explanation:
I did the problem already
What is the slope of the line represented by the equation y = -1/2x+1/4
Answer: m=-1/2 which is the slope
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
in an equation, the number with the x is always the slope. thx
Hello! May Someone Kindly help me with this? its worht 13 points!
Determine if the triangles are similar. If they are similar state why they are similar and
complete the similarity statement. If the triangles are not similar, select "N/A" for the last
two dropdowns.
R
Q
11
14
U
V
22
28
S
[ Select)
The triangles are
vby
[ Select]
.Δ
SUV-A [Select]
listen to cooties by melanie martinez and tell me what u think
Answer:
Okie doki
Step-by-step explanation:
Answer:
or ask something school related or get off of here
Step-by-step explanation:
Linda bought 14 souvenirs during 7 days of vacation. How many days will Linda have to
spend on vacation before she will have bought a total of 20 souvenirs? Assume the
relationship is directly proportional.
days
Answer:
10
Step-by-step explanation: