Find the maximum rate of change of f at the given point and the direction in which it occurs. f(p, q) = 8qe−p + 4pe−q, (0, 0) maximum rate of change $$ Correct: Your answer is correct. direction $$
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]
If I save 10$ at the end of every month for 12 years how much will I have ?
Answer:
1440
Step-by-step explanation:
theres 144 months in 12 years and I just multiplied it by 10
A rectangle has an area of (x2 − 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw, what could be the length and width of the rectangle?
Answer:
b
Step-by-step explanation:
edge
what isnithegdierhfdirhfduidhfvuc
hi, im chelsea. whats your favorite dinner food?
Answer:
it's cuvfhdiudfhridfhreidgehtinsi tahw
Step-by-step explanation:
have a good day
HELP PLEASE PLEASEEEEEE
Answer:
I think the area is 9 ft square
China and the United States are playing each other in the championship match of the 1999 Women's World Cup soccer tournament. Brandi Chastain of the U.S. team is about to take a penalty kick against the Chinese team's goalkeeper, Gao Hong. Chastain will kick the ball from 18 yards away from the goal at 120 miles per hour. How many seconds does the goalkeeper have to react, dive, and reach the ball before it crosses the goal line
Answer:
The goalkeeper has 0.306 seconds to react, dive, and reach the ball before it crosses the goal line.
Step-by-step explanation:
We use the following relation to solve this question:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
Chastain will kick the ball from 18 yards away from the goal at 120 miles per hour.
Since the velocity is in miles per hour, the distance has to be in yards.
Each yard has 0.000568182 miles, so the ball will be kicked from 18*0.000568182 = 0.0102 miles.
This means that [tex]v = 120, d = 0.0102[/tex]
How many seconds does the goalkeeper have to react, dive, and reach the ball before it crosses the goal line?
We have to find t, first in hours. So
[tex]v = \frac{d}{t}[/tex]
[tex]120 = \frac{0.0102}{t}[/tex]
[tex]120t = 0.0102[/tex]
[tex]t = \frac{0.0102}{120}[/tex]
[tex]t = 0.000085[/tex]
An hour has 3600 seconds. So
3600*0.000085 = 0.306.
The goalkeeper has 0.306 seconds to react, dive, and reach the ball before it crosses the goal line.
Entomologists estimate that an average person consumed almost a pound of bug parts each year. There are that many insect eggs, larvae, and miscellaneous body pieces in the food we eat and the liquids we drink. The Food and Drug Administration (FDA) sets a Food Defect Action Level (FDAL) for each product. For example, the legal limit for peanut butter is 30 insect fragments per 100 grams. You just bought the crackers with 25 grams of peanut butter. What is the probability that the snack will include at least 3 crunchy critters
Answer:
0.9797
Step-by-step explanation:
We have X = number of insects in the 25bgrams of butter
Then the legal limit of concentration in peanut butter = 30 fragments/ 100 grams
Then insect amount in 25 grams =
E(X) = 30/100 x 25
= 0.3 x 25
= 7.5 fragments of insects
Using the poisson function in Excel, the probability of at least 3 crunchy critters
1 - p(X<=2)
p(X<=2) = POISSON (2, 7.5, TRUE) = 0.020156715
1 - 0.020156715
= 0.9797
for many years the number of rainy days in March has been recorded in the towns Riverton and waterview Riverton has a mean of 11 rainy days in march with a standard deviation of three days Waterview has a mean of 13 rainy days in march with a standard deviation of 2 days brainly
Answer:
peak farther to the RIGHT
peak will be NARROWER
Step-by-step explanation:
hope this helps !! :)
Easter game idea's please!
my neighborhood always throws an Easter egg hunt but this year we wanted to spice things up and add some cool game with cool prizes and snacks! any ideas?? (dont worry we wear mask at the small neighborhood party's we have)
Mr. Johnson sold a new tv that was $450. If he earns 7% commission, how much money will he make in commission?
Answer:
$31.50
Step-by-step explanation:
Find the missing side. Round to the nearest tenth.
Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
1)
Hyp =40
∠48
x = Adj
use CAH since it's got these pieces in it
Cos(48) = x / 40
40* Cos(48) = x
26.76522 = x
x = 26.8 ( rounded to nearest 10th)
2)
∠29
Hyp = 35
Opp = x
use SOH since this problem has those pieces in it
Sin(29) = x / 35
35*Sin(29) = x
16.9683 = x
x = 17.0 (rounded to nearest 10th)
3)
40 = Adj
∠16
Hyp = x
use CAH again
Cos(16) = 40 / x
x = 40 / Cos(16)
x = 41.611
x = 41.6 (rounded to nearest 10th )
4)
∠55
Opp = 35
x = Adj
use TOA
Tan(55) =35/x
x = 35/Tan(55)
x = 24.5072
X = 24.5 ( rounded to nearest 10th)
What is the answer for this question? The quotient of r and 6 is equal to 42
can someone send me a random receipt you have you gotten recently. it can be anything at all pls
whats 2+7 because i really need help
Answer:
9 LOL-
Step-by-step explanation:
Choose all that apply!! i’ll give a brainly!!
Step-by-step explanation:
The answer is A
PLEASE FOLLOW ME
pls help!due very soon.ill pick brainliest for the answer that helps me the most.(I can only pick brainliest if there's two answers)
2. A local t-shirt company sold 2000 t-shirts two weeks ago when they charged $10 for each shirt. The following week they sold 1120 t-shirts when they raised the price to $19 per shirt. Assuming that this rate of change continues find the following: a. Find a linear function S(p) that models the number of shirts sold as a function of the price p. b. Explain the meaning of the slope In terms of the problem. c. Predict the number of shirts the store would sell if they charged $25 for each shirt. d. If the store would like to maintain a weekly sales level of 1450 shirts how much should they charge per shirt?
9514 1404 393
Answer:
a) S(p) = -97.78p +2977.78
b) about 98 fewer shirts per week will be sold for each $1 increase in price
c) 533 shirts per week
d) $15.63
Step-by-step explanation:
a) You are given two ordered pairs: (p, s) = (10, 2000) and (19, 1120). The two-point form of the equation for a line can be used.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
s = (1120 -2000)/(19 -10)(p -10) +2000
s = -97.78(p -10) +2000
S(p) = -97.78p +2977.78
__
b) The slope is shirts/dollar, meaning about 98 fewer shirts will be sold for each dollar increase in price.
__
c) S(25) ≈ 533
At a price of $25, the store would sell about 533 shirts per week.
__
d) 1450 = S(p) = -97.78p +2977.78
-1527.78 = -97.78p
15.625 = p ≈ 15.63
The store should charge $15.63 per shirt to maintain sales of 1450 shirts per week.
the equation y=ax describes the graph of a line if the value of a is negative the line
Answer:
Goes up and to the left
Step-by-step explanation:
Find X please help me with test corrections due midnight tonight!
If HBN is congruent to LYR.
Answer:
the answer is
x=22..........
1) You have three- fourths yards of pipe. How many pieces can you cut the pipe into if each piece is one-eighth yard?
Answer:
Step-by-step explanation:
(3/4)/(1/8)
(3/4)(8/1)
24/4
6 pieces of pipe
help me please anyone here? will mark brainliest of correct but report if nonsense
Step-by-step explanation:
1/(1 - p + p²) - 1/(1 + p + p²) - 2p/(1 - p² + p⁴) =
[ (1 + p + p²)-(1 - p + p²)/(1 - p + p²)(1 + p + p²) ] - 2p/(1 - p² + p⁴) =
2p/(1 + p + p² - p - p² - p³ + p² + p³ + p⁴) - 2p/(1 - p² + p⁴) =
2p/(1 + p² + p⁴) - 2p/(1 - p² + p⁴) =
[ 2p(1 - p² + p⁴) - 2p( 1 + p² + p⁴) ]/(1 + p² + p⁴)(1 - p² + p⁴) =
(2p - 2p³ + 2p⁵ - 2p - 2p³- 2p⁵) / (1 - p² + p⁴ + p² - p⁴ + p⁶ + p⁴ - p⁶ + p⁸) =
-4p³ / (1 + p⁴ + p⁸)
I WILL MARK BRAINLIEST PLEASE ANSWER ( NO LINKS I WILL REPORT YOU IF YOU GIVE ME A LINK)
Answer: B
Step-by-step explanation:
Find the circumference of the circle.
Answer:
the 3rd one 72.22 is the answer
Answer:
the formula for it is 2*3.14*r
so to get the radius you divide the diameter by two, so 23 divided by 2 is 11.50
so then we do 2*3.14*11.50= 77.22
there u go!
Step-by-step explanation:
what is the slope line
Answer:
In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run. To find the slope of the line, pick two points on the line.
Answer:
Uphill slopes are positive slopes.
The slope will be a positive number like 5 or 2/3.
Downhill slopes are negative slopes.
The slope will be a negative number like -7 or -1/3.
Step-by-step explanation:
The equation of a line is shown.
6x – 3y = 5
A dilation centered at the origin with a scale factor of 6 is applied to this line.
A. What is the slope of the line after the dilation?
B. What is the value of the y-intercept of the line after the dilation?
Answer:
my guess would have to be
A. slope= 4
B. y-intercept= 23/3 or 7 2/3(simplified)
Step-by-step explanation:
im not sure how accurate my answer would be but what i did was put the equation in slope intercept form and added 6 for the dilatation to all factors of the equation.
The slope is 2/3.
The y-intercept is -5/3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line.
6x - 3y = 5
Now,
To apply a dilation with a scale factor of 6 centered at the origin.
We multiply both sides by 6.
So,
6 (6x - 3y) = 6 x 5
Now,
Simplifying.
36x - 18y = 30
Dividing both sides by 18.
2x - y = 30/18
2x - y = 5/3
Now,
Writing in slope-intercept form.
y = mx + c
So,
y = 2x - 5/3
This means,
Slope m = 2
y-intercept c = -5/3
Thus,
The slope is 2/3.
The y-intercept is -5/3.
Learn more about equation of a line here:
https://brainly.com/question/23087740
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Is the relationship between the number of days and the number of hours proportional?
Answer:
yes because no matter what 24 hrs will equal a day
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
(Urgent) Worth 15 points 7.3
Answer: 20790
Step-by-step explanation:
Leon older brother is 4 and 3/4 feet tall Leon is 1/3 foot shorter than his brother how tall is Leon
Answer:
4 5/12 feet tall
Step-by-step explanation:
All you have to do is subtract 1/3 from 4 and 3/4 in order to get this answer.
Answer:
Leon is 53/12 feet or 4 & 5/12 or 4.4167 (same answer different forms)
Step-by-step explanation:
Leon older brother is 19/4 feet tall or 57/12.
Leon is 1/3 or 4/12 foot shorter than his brother.
57/12-4/12= 53/12
The ratio of a model building's dimensions to the building's actual dimensions is 1/20. If the height of the model is 18 inches, what is the height of the actual building in feet?
36 ft
30 ft
38 ft
360 ft
Answer:
30 ft
Step-by-step explanation:
18 in=1.5 ft
20*1.5=30
How many more people studied for 0-30 minutes than people who studied for 121-150 minutes?
Answer:
5 more people studied more in 0-30 minutes than people who studied 121-120 minutes.
Step-by-step explanation: