find all points at which the direction of fastest change of the function f(x, y) = x2 y2 − 4x − 6y is i j. (enter your answer as an equation.)
Answers
The points where the direction of the fastest change of the function is in i j is (1, 1) and (-1, -1).
In order to find the direction of the fastest change, we need to find the gradient of the given function. The gradient is a vector that points in the direction of the steepest ascent, which is also the direction of the fastest change. Let's take the partial derivative of f(x, y) with respect to x and y.
f(x, y) = x²y² − 4x − 6y∂f/∂x = 2xy² − 4∂f/∂y = 2x²y − 6
The gradient of f(x, y) is given by:
∇f(x, y) = <2xy² − 4, 2x²y − 6>
Now we need to find the values of x and y such that the direction of the gradient vector is i j. We know that the direction of the gradient vector is given by: ∇f/|∇f|
Therefore, we need to solve the following equations for x and y.
<2xy² − 4, 2x²y − 6> = k
where k is a constant and is the unit vector in the i j direction. Now we have to solve the following system of equations.
2xy² − 4 = ki2x²y − 6 = kj
By solving the above two equations, we get, x=±1 and y=±1
Substitute these values in the first equation, we get, k=√(8/9)
Hence, the answer is (x, y) = (1, 1), (-1, -1).
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Related Questions
3[(x^3 -7x+1) - (x+4)]
О А. 3х³ - 24х-9
О B. х-8х-3
0 С. 3x²-5x-6
O D. 3x²-6x+15
Answers
Answer:
A
Step-by-step explanation:
You have to simplify the brackets in turn.
3 times x^3- 7x+1 = 3x^3- 21x+ 3
then do 3 times x + 4= 3x + 12
you then add them all together, if they have a power add them, if they just have an x add them, and if they are just a number add them.
So it goes to 3x^3- 24x - 9,
this is because 3x^3 cant be added/ subtracted by anything, -24x is made from -21x- 3x, and -9 is made from 3 - + 12, so this means 3 - 12 = -9.
I hope this helps, have a lovely day.
4 – x2 If f(x2) = find: 9 5 + x2 f'(x) =
Answers
The derivative of the function f(x) = x³+5x²-2x+1 is f'(x) = 3x² + 10x - 2.
In calculus, the derivative of a function represents the rate at which the function is changing at any given point. It is defined as the limit of the rate of change of the function as the change in the independent variable approaches zero
To find the derivative of the function f(x) = x³+5x²-2x+1, we can use the power rule, which states that if f(x) = x^n, then f'(x) = n × x^(n-1). Using this rule, we can find the derivative of each term in the function f(x) and add them up to get the derivative of the entire function
f'(x) = d/dx(x³) + d/dx(5x²) - d/dx(2x) + d/dx(1)
Using the power rule, we get
f'(x) = 3x² + 10x - 2
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The given question is incomplete, the complete question is:
If f(x) = x³+5x²-2x+1 , find f'(x) ?
Write the equation of the line through (5,3) prep to y=1/2x+3
Answers
Answer: -2x+13
Hope this helps :)
56,000 is what percent of 70,000?
Answers
Answer:
39200000
Step by step explanation is in the photo
What is the value of Z?
Answers
Answer:
2
Step-by-step explanation:
2(z)+2 = 4
2z = 2 x 2 = 4
You are considering purchasing a consol that promises annual payments of $4. a. If the current interest rate is 3 percent, what is the price of the consol? Instructions: Round your answer to the nearest penny (2 decimal places). The price of the consol is $ b. You are concerned that the interest rate may rise to 4 percent. Compute the percentage change in the price of the consol and the percentage change in the interest rate. Compare them. Instructions: Round your answer for dollar amounts to the nearest penny (2 decimal places ) and answers for percentages to the nearest tenth (1 decimal place) The new price of the consol would be $ The price of the consol falls by 7% and the interest rises by 7% c. Your investment horizon is one year. You purchase the consol when the interest rate is 5 percent and sell it a year later, following a rise in the interest rate to 6 percent. What is your holding period return? Instructions: Round your answer to the nearest tenth (1 decimal place) Your holding period return is %
Answers
a. The price of the consol is approximately $133.33.
b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.
c. Your holding period return is approximately -49.99%.
a. The price of the consol can be calculated using the formula for the present value of a perpetuity:
Price = Annual Payment / Interest Rate
In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:
Price = $4 / 0.03 ≈ $133.33
Therefore, the price of the consol is approximately $133.33.
b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:
New Price = Annual Payment / New Interest Rate
Substituting the values, we get:
New Price = $4 / 0.04 = $100
The percentage change in the price of the consol can be calculated using the formula:
Percentage Change = (New Price - Old Price) / Old Price * 100
Substituting the values, we have:
Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%
The percentage change in the interest rate is simply the difference between the old and new interest rates:
Percentage Change in Interest Rate = (4% - 3%) = 1%
Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.
c. The holding period return can be calculated using the formula:
Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100
The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:
Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67
Substituting the values into the holding period return formula:
Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%
Therefore, the holding period return is approximately -49.99%.
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Need a bit of help with this question:
Answers
Firstly let's find hypotenuse(let it will be "n" of smaller triangle
Let use Pythagorean theorem
\(a^{2} + {b}^{2} = {n}^{2} \\ {20}^{2} + {10}^{2} = {n}^{2} \\ n = \sqrt{500} \)
Now we need to find hypotenuse(x) of bigger triangle
\( {c}^{2} + {n}^{2} = {x}^{2} \\ {9}^{2} + { \sqrt{500} }^{2} = {x}^{2} \\ x = \sqrt{581} \)
The value of x must be rounded to 1 DP, so
\( \sqrt{581} = 24.1039... \\ \sqrt{581} \simeq \: 24.1\)
Answer: x=24.1
Find the value of x that makes m
||
m
150°
(3x – 15)°
n
5
Answers
Answer:
Step-by-step explanation:
3x - 15 = 150
3x = 165
x = 55
3(55) - 15 = 150
165 - 15 = 150
150 = 150
The point where two lines meet is known as an angle. The value of c that makes m parallel to n is 15
From the given diagram, we can see that line m is parallel to line n.
The sum of the interior angles given in the diagram is supplementary, i.e
3x - 15 + 150 = 180
3x + 135 = 180
3x = 180 - 135
3x = 45
x = 45/3
x = 15
Hence the value of c that makes m parallel to n is 15
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Write the equation of the circle centered at ( – 3, (-3, – 10) with radius 2.
Answers
Step-by-step explanation:
the equation of the circle centered at (-3, – 10)
=> (x+3)²+(y+10)²=2²
<=> x²+6x+9+y²+20y+100=4
x²+y²+6x+20y+105=0
Let's see
\(\\ \rm\dashrightarrow (x-h)^2+(y-k)^2=r^2\)
(h,k)=(-3,-10)\(\\ \rm\dashrightarrow (x+3)^2+(y+10)^2=2^2\)
\(\\ \rm\dashrightarrow (x+3)^2+(y+10)^2=4\)
\(\\ \rm\dashrightarrow x^2+y^2+6x+20y+105=0\)
What is the solution to the inequality 7x - 26>3 (3x-2)
Answers
Answer:
the solution to the inequality is x<-10
Answer:
x<−10
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
7x−26>9x−6
Step 2: Subtract 9x from both sides.
7x−26−9x>9x−6−9x
−2x−26>−6
Step 3: Add 26 to both sides.
−2x−26+26>−6+26
−2x>20
Step 4: Divide both sides by -2.
-2x/-2 > 20/-2
x<−10
Enter the number that makes the equation true
Answers
Answer:
67
Step-by-step explanation:
0.71=71%.
2/100+2/100=4/100/4%
So we can subtract 71-4=67.
That tells us that the missing number is 67. Add it all up and you will get 0.71 or 71%
Answer:
71
Step-by-step explanation:
.71 + 2/100 = x/100 +2/100
We need to change the decimal to a fraction
.71 means 71 out of 100
71/100 +2/100 = x/100 + 2/100
x is 71
Based on the table, which function models this situation?
Answers
Answer:
F(n) =-3n+24
Step-by-step explanation:
(Chapter 14) fy(a,b) = limit as y approches b f(a,y)- f(a, b)/(y-b)
Answers
In summary, fy(a,b) is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.
The given expression represents the partial derivative of f(x, y) with respect to y, evaluated at (a, b):
fy(a,b) = lim┬(y→b)〖[f(a,y) - f(a,b)]/(y - b)〗
Geometrically, this partial derivative represents the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.
To see why this is the case, consider the following argument:
Let L be the limit in the expression given above.
Let h = y - b be the change in the y-coordinate from b to y.
Then, we can rewrite the limit as:
fy(a,b) = lim┬(h→0)〖[f(a,b + h) - f(a,b)]/h〗
This expression represents the average rate of change of f(x, y) with respect to y over the interval [b, b + h].
As h approaches 0, this average rate of change approaches the instantaneous rate of change, which is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.
Therefore, fy(a,b) is the partial derivative of f(x, y) with respect to y, evaluated at (a, b).
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What’s the answer????
Answers
Step-by-step explanation:
Q7) 10% of 30=3
40% of 30 =3×4=12
30-12=18
the sale price of radio is 18
q8)purchase lose lemmons:0.99÷2=0.495
Bag of 6=2.50÷6=0.4166666667
so the better value is the bag of 6 for 2.50.
Please help me with this question
Answers
Answer:
pt A' is (2, 4)
Step-by-step explanation:
does this table represent a function? why or why not x:2,2,3,4,5 y:1,4,4,2,5
Answers
Answer:
No, the table does not represent a function.
Step-by-step explanation:
By definition, a function will not have 2 or more results for the same input.
The table shows two values of y for the same x: (2,1) and (2,4). The same input, 2, results in two different values, 1 and 4.
See attached image.
h(j + i) - k5 + h
when h = 3, i = 4, j = 2, and k = 1
pls put how you did it
Answers
Answer:
16
Step-by-step explanation:
First you want to plug in all the numbers where the letters are
h ( j + i )- k(5) + h
3 ( 2 + 4 )- 1(5) + 3
After this step you will have to distribute the 3 outside the parenthesis. Which you do by multiplying everything in side the parenthesis by the outside number which is three.
6 + 12 - 1(5) + 3
Then you just follow PEMDAS to solve for the rest
6 + 12 - 5 + 3
18 - 5 + 3
13 + 3
16
Members of a softball team raised $1158.25 to go to a tournament. They rented a bus
for $836.50 and budgeted $24.75 per player for meals. Write and solve an equation
which can be used to determine p, the number of players the team can bring to the
tournament.
Equation:
Answer: p =
Submit Answer
attempt out of
Type here to search
O
Ü
E
69°F
Answers
Answer:
1518.25=836.50+24.75p;
p=(1518.25-836.50)/24.75=681.75/24.75
Step-by-step explanation:
24.75 is about 25, so 681.75 is about 700, so that's about 28 people. If you don't have an option, do the math
Answer:
Equation: 24.75p+836.5=1158.25
Answer: p = 13
Step-by-step explanation:
Cost per player = 24.75
number of players = p
cost of bus = 836.50
total raised = 1158.25
the total cost to take the ferry to green island is $12 fee for the car plus $3 for each passenger in the car
Answers
Answer:I think it’s 15 dollar
Step-by-step explanation:
which is bigger 2/5 or 2/8
Answers
Answer:
2/5 is bigger
Step-by-step explanation:
if you have a pie with 8 slices and you eat 2, and have a pie containing 5 slices and eat 2 which empty space will be larger? think of it that way and i hope that helps
Since the numerators are the same, focus on the denominators. ( Denominators are the numbers below the fraction
Whichever denominator is smaller means that the fraction is bigger.
2/5 and 2/8. 5 is smaller than 8.
This means that 2/5 is a larger fraction.
The distances traveled by car A car Afx x hours. are. represented by the graph and table below.
Answers
Answer: b
Step-by-step explanation:
The speed of car B is twice the speed of car A.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
For car A,
Time= 5 hours
Distance = 200 miles.
speed= 200/5
speed= 40 mph
and, In car B
Time= 6 hours
Distance= 480 miles
speed= 480/6
speed= 80 mph
Hence, the speed of car B is twice the speed of car A.
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Plz help me I’m struggling
Answers
Answer:
Therefore,
The Area of the container is: A = 1152 square feet.
Therefore, option B is correct.
Step-by-step explanation:
Given
Width w = 8 feetHeight h = 12 feetLength l = 24 feetTo determine
Area of the container in square feet
Using the formula to calculate the Area of the container
\(A\:=\:2\left(lw+hw+lh\right)\)
substituting \(\:w=8,\:h=12,\:l=24\) in the formula
\(A=2\left(24\left(8\right)+\left(12\right)\left(8\right)+\left(24\right)\left(12\right)\right)\)
remove the parentheses and multiply the numbers
\(A=2\left(192+96+288\right)\)
\(A=2\times 576\)
\(A=1152\) square feet.
Therefore,
The Area of the container is: A = 1152 square feet.
Therefore, option B is correct.
for the polynomial 7x3 3x2 - 15x - 5 which represents the dimensions of the tv, find the degree of each term. then find the degree of the polynomial.
Answers
The degree of the polynomial is 3.
Here we are given a polynomial 7\(x^{3}\) + 3\(x^{2}\) - 15x - 5 which represents the dimensions of a TV.
There are 4 terms in the polynomial. Let us evaluate each term one by one.
1. 7\(x^{3}\) - the degree of this term is 3 since the power of x is 3
2. 3\(x^{2}\) - the degree of this term is 2 since the power of x is 2
3. -15x - the degree of this term is 1 since the power of x is 1
4. -5 - this is a constant term and hence its degree is 0.
The degree of a polynomial is the degree of the term with highest power in the polynomial. In this case, the 1st term, that is, 7\(x^{3}\) has the highest power and hence the degree of 7\(x^{3}\) will be the degree of the polynomial.
Thus, the degree of the polynomial is 3.
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PLEASE HELP I REALLY NEED THIS ANSWERED, I NEED THE VOLUME OF BOTH CYLINDERS PLZ DONT USE AN ONLINE CALCULATOR THEY GIVE THE WRONG ANSWER
Answers
Answer:
\(\large\fbox{\green{\underline{Cylinder P :- \blue{ 794.0275 in ³}}}}\)
\(\large\fbox{\green{\underline{Cylinder Q :- \blue{1,307.81 in³}}}}\)
Step-by-step explanation:
Volume of cylinder = π × ( radius ) ² × h
1.) Here, radius = 4.25 in and height = 14 in.
Volume of cylinder = π × ( radius ) ² × height
substitute the values
Volume of cylinder P = 3.14 × ( 4.25 in ) ²×14 in.
now, simplify
= 3.14 × 18.0625 in²× 14 in.
= 3.14 × 252.875 in³
multiplying the value
= 794.0275 in³
\( \small \: \: \sf \: \fbox{ cirumference \: of \: cylinder \: P \: = {794.0275 in³}}\)
2.) Here, radius = 7 in. and height = 8.5 in.
Volume of cylinder Q = π × ( radius ) ² × height
substitute the values
Volume of cylinder Q = 3.14 × ( 7 in )² × 8.5 in.
Simplify
= 3.14 × 49 in² × 8.5 in.
multiply the values
= 3.14 × 416.5 in³
\( \small \sf \fbox{Volume of cylinder Q = 1,307.81 in ³}\)
Irene knows her blood type is A, but William does not know his blood type. However, William knows that his mother and father both had blood type B. Irene and William's first child is a boy with type O blood. Based on this information, William's blood type could be
Answers
Based on this information, William's blood type could be either B or O.
What is Segregation of alleles?
Allele pairs (several features of the same gene) are segregated during meiosis so that they can be transferred selectively to different gametes.During meiosis, maternal and paternal alleles separate.What is genotype vs phenotype ?
Genotype: An organism's genetic makeup. Phenotype. physical characteristic that arises within an organism as a result of its genotype. Probability law.Genotype - the set of alleles that make up an organism.How does genotype influence phenotype ?
The alleles you have for a specific gene or collection of genes are referred to as your genotype. The physical attribute itself, or phenotype, can be affected by both genotype and environmental variables.Learn more about Genotype
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A sector with an area of 54πcm² has a radius of 9 cm. What is the central angle measure of the sector in radians?
Choices:
A: 2/3
B: 4/3
C: 2π/3
D: 4π/3
Answers
Answer:
D.4pi/3
Step-by-step explanation:
This is a Lesson 11 problem.
We know that 83.97% of Cecil students drink alcohol.
Determine:
P(Everyone drinks in your n = 18 person English class) = ___________.
Round your answer to four decimals.
Use the multiplication rule for independent events.
Answers
The probability that everyone in the class of 18 students drinks alcohol is approximately 0.2723. This assumes that each student's drinking behavior is independent of the others.
To determine the probability that everyone in a class of 18 students drinks alcohol, we can use the multiplication rule for independent events.
Given that 83.97% (or 0.8397) of Cecil students drink alcohol, we can assume that each student's drinking behavior is independent of the others in the class.
The probability that a single student in the class drinks alcohol is 0.8397.
To find the probability that all 18 students in the class drink alcohol, we multiply the individual probabilities together:
P(Everyone drinks) = P(Student 1 drinks) * P(Student 2 drinks) * ... * P(Student 18 drinks)
P(Everyone drinks) = 0.8397 * 0.8397 * ... * 0.8397 (18 times)
P(Everyone drinks) ≈ 0.8397¹⁸ ≈ 0.2723
Rounded to four decimal places, the probability that everyone in the class drinks alcohol is approximately 0.2723.
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How many solutions does the system have?
5y = 152 – 40
y = 3r – 8
Answers
question #10. The question is in the picture. I'd like a bit of help, please. I will give 15 points to whoever can help out.
Answers
What is m∠1?
answer choices:
50,
105,
60,
100
Answers
Explaination
The side angles in the bottom right triangle has 2 sides that are 50 degrees, wich means the other side is 80 since a triangle equals 180 degrees.
50+ 50 + 80 is 180 so this is correct.
A straight line is also 180.
Since this straight line is being intersected, and one side of the intersection is 80, we can subtract 180 by 80
180-80= 100
100 is your answer
Answer:
105
Step-by-step explanation:
180-75=105