Looks like f(x, y) = cot⁻¹(xy), as in the inverse cotangent.
If you're like me and you don't remember the derivative of the inverse trig functions, we can derive it as follows. Let y = cot⁻¹(x), so that for appropriate x we can write cot(y) = x. By the chain rule, differentiating both sides gives
-csc²(y) y' = 1
y' = -sin²(y) = -sin²(cot⁻¹(x)) = - 1 / (x² + 1)
Next, recall that the derivative of a function f(x, y) at a point (a, b) in the direction of a vector v is given by
∇ f(a, b) • v
Compute the gradient ∇ f(x, y) :
∇ f(x, y) = - y / ((xy)² + 1) i - x / ((xy)² + 1) j
At the point P, we have
∇ f(x, y) = - 8/17 i - 8/17 j
So, the derivative of f at P along v = - 4 i + 5 j is
(- 8/17 i - 8/17 j) • (- 4 i + 5 j) = - 8/17
Two numbers, both greater than 23, have HCF 23 and LCM 644. The sum of the numbers is:
Answer: 253
Step-by-step explanation:
First, we have two numbers A and B.
We know that all numbers can be written as a product of prime numbers.
And the HCF of A and B is 23
Then we can write:
A = 23*a
B = 23*b
(remember that 23 is a prime number)
Where a and b are larger than 1.
Now we know that the least common multiple between them is 644.
Notice that the primes that conform a can not be the same as the ones for b, because in that case, the HCF would not be 23.
Now to find a and b we can compute:
644/23 = 28.
28 = a*b
Now let's write 28 as a product of prime numbers:
a*b = 28 = 4*7 = 2*2*7
Then we can define:
a = 2*2
b = 7.
Our two numbers are:
A = 23*2*2 = 92
B = 23*7 = 161
A + B = 92 + 161 = 253
The sum of the two numbers would be:
253
Assume the two numbers be [tex]x[/tex] and [tex]y[/tex]
Given that,
HCF of [tex]x[/tex] and [tex]y[/tex] = 23
so,
The numbers could be written as:
23[tex]x[/tex] and 23[tex]y[/tex]
We know that,
LCM of 23[tex]x[/tex] and 23[tex]y[/tex] = 644
We also know that,
LCM × HCF = The product of two numbers
∵ 644 × 23 = 23[tex]x[/tex] × 23[tex]y[/tex]
So, by solving them we get;
14812/529 = [tex]x[/tex] × [tex]y[/tex]
∵ [tex]x[/tex] × [tex]y[/tex] = 28
If we prime factorize 28, we get
28 = 2 × 2 × 7
This gives us,
[tex]x =[/tex]23 × 2 × 2 = 92
[tex]y =[/tex] 23 × 7 = 161
Thus, the sum of the two numbers = 92 + 161 = 253
Learn more about "HCF" here:
brainly.com/question/13070189
write down two prime numbers that have a sum of 32
Answer:
3 and 29
OR
13 and 19
Step-by-step explanation:
3+29=32
OR
13+19=32
Note: Prime numbers are those that can only be divided by one or itself!
Which of the following is a situation in which a quadratic equation cannot be
solved using the quadratic formula?
Answer:
the a
Step-by-step explanation:
zzzzz
I WILL GIVE BRAINLIEST HELPPP
1. 3/10 = 12/50 true or false
2. 1/2=6/12 true or false
3.5/6=10/12 true or false
4.5/7=15/21 True or false
5.3/8=6/15 true or false
PLeASE HELP
Answer:
1. False
2. True
3. True
4. True
5. False
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. False 3/10 x 5 = 15/50 not 12/50
2. True 1/2 x 2 = 6/12
3. True 5/6 x 2 = 10/12
4. True 5/7 x 3 = 15/21
5. False 3/8 x 2 = 6/16 not 6/15
In New York the temperature was -4 Fahrenheit in the morning if the temperature dropped eight Fahrenheit what is the temperature now
Answer:
-12 Fahrenheit.
Step-by-step explanation:
(100 POINTS) Write the particular equation of this transformed cosine graph. (Hint: Try to find the best point to center the sinusoidal axis.)
Answer:
y= - 3cosx - 2
Step-by-step explanation:
Our max here is at 1, and the minimum is at - 5
The distance between the x-axis and these points are 1 and 5. 5 + 1/2 = 6/2 = 3, our amplitude. But let's double check. Our middle point is - 2 so...
- 5 - (- 2) = - 5 + 2 = - 3
The amplitude is rather - 3.
f(x) = Acos(Bx + C) + D
Using this we know B = 0, D = - 2 (the middle point), C = 0, and A = - 3 (amplitude). B = 0, and C = 0, as there is no horizontal/vertical shift
f(x) = Acos(Bx + C) + D
f(x) = - 3cosx + (- 2)
f(x) = - 3cosx - 2
Answer:
y= - 3cosx - 2
Step-by-step explanation:
Just Answered on A P E X Practice Assignment
why my bawls itch so much its annoying
Answer:
is this a joke
Step-by-step explanation:
Answer:
scrath
Step-by-step explanation:
reach down. give itch, happ.y
Complete the statements.
8.703 dekagrams =_____
kilograms
100.3
_____= 10.03 hectometers
909.9
_____= 90,990 centiliters
Step-by-step explanation:
1. 0.08703 killograms
2. Decameters
3. Liters
Answer:1. 0.08703 killograms
2. Decameters
3. Liters
Step-by-step explanation:
2. Add 62 to the difference of
90 and 36.
Answer:
116
Step-by-step explanation:
(difference = subtract)
90 - 36 = 54
adding 62 to 54 = 116
answer
62+(90-36)
62+54
116
Which of the following equations can be used to model the number of meals someone will eat over a period of time if they eat three meals a day?
Answer:
1
Step-by-step explanation:
Answer:
3t + 5 = 32
and
3t+ 2 = 20
Step-by-step explanation:
i got it right :)
how many fifths are there in 8 3/5?
Answer:
43 becuase 8 3/5 times 5
Step-by-step explanation:
Helppppppppppppppppp
You are rock climbing and descending a cliff at a rate of 9 feet per minute. The cliff is about 360 feet high. How long until you are at a height of 234 feet?
How long until you are halfway down the cliff?
Five pounds is equal to 2.268 kilograms. How many kilograms is 2 pounds?
0.4536
0.9072
1.8144
4.536
Answer:
B) 0.9072
Step-by-step explanation:
If Kim reduces the weekly number of hours she works by one-fourth and her current weekly income is $520.00, what is her new weekly income?
Answer:
$390 you divide 520 by 4 so 520/4=130 now we subtract 130 from 520, 520-130=390
Step-by-step explanation:
Solving this question requires basic arithmetic formula and fractions.
New weekly income = $390
Let's call the number of hours kim works weekly as "x"
If she reduces this number of hours by one-fourth and her current weekly income is $520, then it means the amount to be deducted is;
[tex]\frac{1}{4}[/tex] × $520 = $130
Thus, her new weekly income will be;
$520 - $130 = $390
Read more at; brainly.com/question/11407386
Find the perimeter and area of a rectangle of cardboard measuring 15.9 cm by 11.7cm
Write the inequality.
A number k plus 5 is greater than or equal to
8.
Ak +5> 8
k+5 <8
k+5 <8
k+528
y = 7x^3 - 4x^2 + 3x - 12
find the domain step plz
Answer:
The domain is -oo < x < oo or (-oo,oo)
Step-by-step explanation:
Sometimes it helps if you draw this out on a number line or graph the equation! :)
Domain is how far x goes. As in this case x is infinite both ways.
what is the measure of an angle that is linear pair with 10 degrees
Answer:
170 degree bcause 180 -10 = 170 ( linear pair )
Answer:
170 degree bcause 180 -10 = 170 ( linear pair )
Step-by-step explanation:
The sum of 2 numbers is 25. The sum of their reciprocals os 1/4. Determine the two numbers.
Answer:
5, and 20
Step-by-step explanation:
5+20=25
reciprocal of 5 is 1/5 and reciprocal of 20 is 1/20 so 1/5=4/20 and 4/20 + 1/20 = 5/20. 5/20 = 1/4
Will give brainliest and thanks and please explain
Answer:
(65-5) / 2.5 = d
Step-by-step explanation:
100% sure
Answer:
d=65/2-5
26days
Step-by-step explanation:
(WILL GIVE BRAINLIEST)
What is 3/5 written as a percent?
A. 6%
B. 30%
C. 60%
D. 167%
Answer:
60%
Step-by-step explanation:
1/5 equals 20 % and thus 3/5 is 20 % multiplied by 3 so 60 %
Answer: "Percent" or "%" means "out of 100" or "per 100", Therefore x% can be written as
x/100
.
We can then rewrite this as: 60%.
HELP ASAP!!!WILL GIVE BRANLIST
Answer:
See photo below
I hope this helps!
Answer:
you see the top u take a line and put it right through the 2 top coners and put a line there.
Step-by-step explanation:
Help. What is the slope of the line in the graph?
Hello,
As you have not provided the graph, I can teach you how to answer the question.
You are solving for the slope of the line. The slope can be found by using the following equation:
slope (signified by the variable m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Note that the numbers does not exactly matter, only that what you set as variable [tex]x_1[/tex], the y inside that coordinate will also be [tex]y_1[/tex], and likewise for point 2.
For example, let us say your points for your line is (3 , 6) and (10 , 4)
Let:
[tex](x_1 , y_1)[/tex] [tex]= ( 3 , 6)[/tex]
[tex](x_2 , y_2) = (10 , 4)[/tex]
Plug in the corresponding numbers to the corresponding variables:
slope [tex]m = \frac{4 - 6}{10 - 3} = - \frac{2}{7}[/tex]
The given points will result in a [tex]-\frac{2 }{7}[/tex] slope.
Hope this helps!
A government might try to reduce unemployment in order to:
A. Allow businesses to invest money more freely.
B. set limits on its own economic growth.
C. keep inflation from rising too quickly
D. make sure its people can find jobs
If you get it correct will give brainly
Answer:
Make sure people can find jobs
Step-by-step explanation:
Answer: D, Make sure it’s people can Find job’s.
Step-by-step explanation: it’s the Answer I just did the quiz.
Which equation represents a line with a slope of zero?
O y= 2x
O y=-3x+
O y=4
O x=-5
Answer:
y = 4
Step-by-step explanation:
In y =mx+b (slope -intercept form ),
We have m to be the slope
The first and the second equations contains the slope (coefficient of x)
The fourth option clearly states the slope is -5
That leaves with the third option with only a y-intercept.
Answer:
y=4
Step-by-step explanation:
y=4 on the graph would look like this -------------------------- and it would have a slope of zero. It's not x = -5 because that would have an undefined slope |.
And the first two the slope is the number in front of the x.
Hope this helped!!!
what is 8,526 divide by 9
Answer:
Use a calculator but otherwise it is 947.3333
Step-by-step explanation:
first 8000 divided by nine which is 888.8888
second is 500 wich is 55.5555
third is 20 divided by nine wich is 2.2222222
fourth is 6 divided by nine wich is 0.66666667
fith add all of them which is around 947.3333
Alright, I need help!
Answer:side B middle length!
Step-by-step explanation:
create an equation from the model that describes the relationship between the weights on each side of the scale into the correct answer in the Box
Answer:
2y+3=4y+2
Step-by-step explanation:
Answer:
2y+3=4y+2
Step-by-step explanation:
cause i got it right
3. If (5,5) is the endpoint of a line with the midpoint at (0,0), where is the
other endpoint?