Therefore the directional derivative of f at a in the direction of the vector ad is grad F( x, y ) ×ad(u) =64/10
What is directional derivative ?Any function's rate of change at a given location in a fixed direction is known as its directional derivative. Any derivative is thought of in this way: as a vector form. It provides information on the function's immediate rate of variation.
Here,
The terms "directional derivative" and "gradient of a function" must be used in order to respond to this question.
Grad F(x, Y) = 64/10 ad(u)
A function's gradient is a vector with the following definitions:
Grad f(x,y) is equal to f(x,y)/x I + f(x,y)/y j.
where the definition of the directional derivative in the direction of ab is
Grad f(x,y) = Uab(u), where Uab is a unitary vector pointing in the direction of ab.
Consequently, Uab (u) = Uab/|ab|
If f (x,ydirectional )'s derivative in the direction of vector ab is 5, then.
A (7, 3), B (12, 3), and vector ab is then:
ab = [ 12 - 7 , 3 - 3 ] ⇒ ab = [ 5 , 0 ] as well as |ab| = (5)2 (0)2 |ab| = 5
a unitary vector in the direction of ab is:
ab(u) = 5×i/ 5 and according to equation (1)
δf(x,y) / δx × i × 5 × i / |5| = 5
δf(x,y) / δx × i × 5 × i = 25
δf(x,y) / δx = 5 then f( x,y ) = 5 × x + ????
We go on to calculate the component on j of f(x,y)
Following the same procedure
ac = ( 7 , 7 ) - ( 7 , 3 ) ⇒ ac = [ 0 , 4 ] |ac| = √(4)² + (0)²
|ac| = 4
In the direction of ac(u), the unitary vector is:
ac/|ac| = 4 × j / 4
Then :
j / 4 + f(x,y) / y = 4
16 is equal to f(x,y) / y j + 4 j.
both f(x,y) = -4y & f(x,y) / y = - 4
f(x,y) = 5 × I + 4 × j
Finally:
((15 - 7, 9 - 3)) as the vector ad ⇒ ad = ( 8 , 6 ) ( 8 , 6 )
a unitary vector in the direction of
ad(u) = (8 ×i + 6 ×j) / √ (8)² Plus (6)
² ⇒ ad(u) = (8 ×i + 6 ×j) /√ (8)² + (6) ²
ad(u) = (8 ×i + 6 ×j) /10
Currently, we have f (x, y) = 5 I + 4 j and ad(u) = 8 I + 6 j /10.
We can calculate the directional derivative of f(x,y) in the direction of ad with the use of equation (1)
grad F( x, y ) ×ad(u) = ( 5 × i + 4 × j ) × ( 8 ×i + 6 ×j ) /10
grad F( x, y ) ×ad(u) = 4 + ( 24/10)
grad F( x, y ) ×ad(u) =64/10
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How long does it take to travel 150 km?
It takes 3.33 hours of time to travel a distance of 150 km by bus
The problem is related to time, which basically depends on the speed at which the bus is moving, as we knew the formula for time is distance/speed, here we are provided with the distance which is 150km also equal to 150000m. For normal conditions where the speed of the bus is h 45km per hour, therefore
=>Distance = Speed × Time
=>150km = 45 Km/hr × Time
Time = 150/45 hr = 3.33 hr ,Which is almost 3.33 hours
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A Roth IRA receives $6000 per year. How long would it take to reach $1000000 with an interest rate in a mutual fund of 8% compounded monthly
The time taken to reach $1000000 with an interest rate in a mutual fund of 8% compounded monthly is about 64 years and 2 months.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $6000
r = 8%
n = 12
A = $1000000
Now,
1000000 = 6000 [tex](1 + 0.08/12)^{12t}[/tex]
1000/6 = [tex]1.0067^{12t}[/tex]
log on both sides.
log 166.67 = 12t log 1.0067
2.22 = 12t x 0.0029
12t = 2.22 / 0.0029
12t = 765.52
t = 765.52/12
t = 64.163 years
This means,
About 64 years and 2 months.
Thus,
The time taken to reach $1000000 is 64 years and 2 months.
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PLEASE HELP I NEED IT ASAP
Answer: 1 13/ 20
Step-by-step explanation:
first multiply 2 1/5 and 1 3/4 you will get 3 17/20then subtract from 3 17/20 - 2 1/5 you will get 1 13/20
In a city, there are 16 swimming pools. On weekends, 6 of the pools are open.
George says the ratio of pools open on weekends to the total number of pools is 6:16.
Emma says the ratio of pools open on weekends to the total number of pools is 6:10.
Which student is correct? PLEASE....... Explain.
The student that is correct is George as the ratio of pools open on weekends to the total number of pools is 6:16.
What is the ratio?Ratio is the relationship between two or more numbers. It is the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.
In order to determine the ratio between the number of pools open on the weekend to the total number of pools express the numbers that represent each value as ratios.
This will be:
= number of pools open on weekends: total number of pools
= 6 : 16
George is correct.
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I dont know this problem(please help)
I need help with please
Solving the word problems, Sandy has 1.5 more bucket of apple than Keith and Jayson has saved 15/4 month of worth pay
This is often a mathematical problem expressed entirely in words typically used as an educational tool.
To solve this type of problem, we have to translate the words into algebraic expressions or equations and solve for the unknown variables.
1)
Keith = 2 5/6 bucket of apples
Sandy = 4 1/3 bucket of apples
We have to convert this from mixed fractions into improper fraction
Keith = 2 5/6 = 17/6 bucket of apples
Sandy = 4 1/3 = 13/3 bucket of apples
To determine how many more bucket of apples Sandy picked than Keith, we simply need to subtract the fractions from one another.
13/3 - 17 / 6 = 3/2 = 1.5
Sandy picked 1.5 more than Keith
2)
To determine how much Jayson has, we simply need to sum up all his money which will be
2 1/2 + 1 1/4
Let's convert the mixed fractions into an improper fraction
2 1/2 + 1 1/4 = 5/2 + 5/4 = 15/4
Jayson saved 15/4 months worth of pay
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Question 1 Please Help Me!!
Answer:
Step-by-step explanation:
the answer is b the arrow BD make angels equal in both sides
Please help!! Thank you!!
Answer:
The cellular plan allows you to use 4 gigabytes and charges you a flat $90. After 4 gigabytes have been used then, every gigabyte after that is an extra $20.
a. Make a scatter plot and draw a line of fit on a separate sheet of paper.
b. Use the data from 2009 and 2017 to write the equation of the line of fit in slope-intercept form where x is the number of years since 2005.
Explain your process.
a) The scatter plot and the line of fit are given on the second image shown at the end of the answer.
b) The linear function is defined as follows: y = 1.75x + 168.
How to define the linear function?The linear function is defined in the slope-intercept format, as follows:
y = mx + b.
In which:
m is the slope.b is the y-intercept.Considering the data for 2009 and for 2017 from the table, taking x as the number of years since 2005, two points are given as follows:
(4,175) and (12, 189).
The slope, given two points, is calculated as the division of the change in y divided by the change in x, hence:
m = (189 - 175)/(12 - 4) = 14/8 = 1.75.
Hence:
y = 1.75x + b.
When x = 4, y = 175, hence the intercept b is calculated as follows:
175 = 1.75(4) + b
b = 168.
Then the line of fit is:
y = 1.75x + 168.
The scatter plot is composed by all the points of the data-set, considering x as the number of years since 2005, hence:
(0, 169), (2, 175), ... (12, 189).
Missing InformationThe table is given by the first image at the end of the answer.
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A lion weighs 7 times as much as a leopard. The combined weight of the cats is 480 pounds. What is the weight of each cat?
Answer:
Leopard: 60 lb
Lion: 420 lb
Step-by-step explanation:
Let x = weight of leopard.
Weight of lion = 7x.
Sum of the weights = x + 7x = 8x
Total weight = 480 lb
8x = 480
x = 60
7x = 7 × 60 = 420
Answer:
Leopard: 60 lb
Lion: 420 lb
Answer: shown below
Step-by-step explanation:
x = 7y
x+y+ 480
7y+y = 480
8y = 480
y = 480/8 = 60 pounds for the leopard
x = 7(60) = 420 pounds for the lion
I need help please! I’m struggling
Answer:
24
Step-by-step explanation:
Clara builds 3 parts of the fence per hour--
if she works for 8 hours-- we know she built 3 fences each hour-- you would multiply,
8(hours) x 3 (fences) = 24
we know this is right because 3 parts are built for every hour
(3+3+3+3+3+3+3+3 = 24)
she worked for 8 hours and built 3 parts of the fence every hour
in total, she built 24 parts of the fence.
Inequality (please check the attached image)
Let the number of pens be p and number of pencil cases be c.
Each pen costs php 20 and all pens cost 20p.Each pencil case costs php 40 and all pencil cases cost 40c.Total amount Dona needs to make is at least 2000.Use given information and set inequality:
20p + 40c ≥ 2000Simplify it by dividing all terms by 20:
p + 2c ≥ 100If number of pens is more than 100, we get:
p > 100Substitute this into inequality:
100 + 2c ≥ 100 Subtract 100 from both sides2c ≥ 0 Divide both sides by 2c ≥ 0If Dona sells more than 100 pens then she will exceed php 2000 regardless the number of pencil cases sold.
Lin has two small baking pans, each shaped like a rectangular prism. For each question, explain or show your reasoning. \text{Area} = l \cdot wArea=l⋅w \text{Volume} = l \cdot w \cdot hVolume=l⋅w⋅h
a) Lin lines the bottom of her first pan with aluminum foil. The area of the rectangular piece of foil is 11\frac{1}{4}11
4
1
square inches. Its length is 4\frac{1}{2}4
2
1
inches. What is the width of the foil?
The solution is
The width of the rectangular aluminum foil whose area is 11 1/4 inches is
2 1/2 inches
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the width of the aluminum foil be represented as = W
Now , the equation will be
The area of the aluminum foil is A = 11 1/4 inches²
The value of A = 11 1/4 inches²
The value of A = 45/4 inches²
Now ,
The length of the aluminum foil L = 4 1/2 inches
The value of L = 4 1/2 inches
The value of L = 9/2 inches
Now , from the equation of area of rectangle
Width of the rectangle W = Area of rectangle A / Length of rectangle L
Substituting the values in the equation , we get
Width of the aluminum foil W = ( 45/4 ) / ( 9/2 )
Width of the aluminum foil W = ( 45/4 ) x ( 2 / 9 )
Width of the aluminum foil W = 5 / 2 inches
Width of the aluminum foil W = 2 1/2 inches
Therefore , the value of W is 2 1/2 inches or 5/2 inches
Hence , The width of the rectangular aluminum foil is 2 1/2 inches
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which one is the answer
What happens to the area of a figure when a scale factor is applied?
The area of figure will change quadratically in proportion to length squared when a scale factor is applied
A scale factor is simply a number that multiplies a shape's dimensions. This can enlarge a shape. The scale factor for larger shapes will be greater than one. So, if the scale factor is three, the new shape's dimensions will be three times larger than the original.
A scale factor can also reduce the size of a shape. Smaller shapes have a scale factor that is less than one.
When you dilate a figure, it becomes larger or smaller
With a certain factor, the length of its sides either increases or decreases.
As a result, a change in length will affect the total area of the figure with that scale factor.
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Please help meeeee……..
I honestly do not know???
how many nonzero terms of the maclaurin series for ln(1 x) do you need to use to estimate ln(1.4) to within 0.000001?
We need to use 7 terms to estimate the value of ln(1.4) to within 0.0001.
What is the Maclaurin series?A Maclaurin series is a function that is used to estimate the values functions, evaluate the sum, or determine the value of the anti-derivative of a function.
We have:
f(x)=ln(1+x)
Expansion of In(1+x) up to seven terms is:
In(1+x) = x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - x^6/6+ x^7/7
Where it is known that -1 <= x <= 1
Put x=0.4 in the above series:
ln(1.4) = 0.4 - 0.4^2/2 + 0.4^3/3 - 0.4^4/4 + 0.4^5/5 - 0.4^6/6+ 0.4^7/7
We get:
ln(1+4) = 0.3365333
Therefore, we need 7 terms to estimate the value of ln 1.4 to within 0.0001.
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Write a fact family for each set of numbers.
1. 2, 5, 10
2. 5, 8, 40
3. 4, 9, 36
4. 6,9, 54
Answer: in every case, the first two number multiplied equal the third number, I don't quit understand if that's the answer you were looking for,
but that's the first thing that occurred to me
the shipping clerk packs cube with side lengths of 8 inches into a box with side lengths of 10 inches what is the volume of he space left in the larger box for packing materials ?
Answer:
the volume of the space left in the larger box for packing materials is 1000 - 512 = 488 cubic inches.
Step-by-step explanation:
To find the volume of the space left in the larger box for packing materials, we first need to calculate the volume of the smaller cube and then subtract it from the volume of the larger box. The volume of a cube with side length s is given by s^3, so the volume of the smaller cube with side lengths of 8 inches is 8^3 = 512 cubic inches. The volume of the larger box with side lengths of 10 inches is 10^3 = 1000 cubic inches
Give the equation of the circle centered at the origin and passing through the point (12,0)
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Question 4
Yellow Taxi service charges a $15 flat fee plus $2.50 per mile traveled. The charges for
Black and White Taxi service are shown in the graph, where x is the number of miles
and y is the total cost.
18
16
14
12
10
8
6
2
O1 2 3 4 5 6 7 8 9 x
Johnny needs to travel 5 miles. How much will it cost Johnny if he pays the least
amount possible?
Part B
How far does Johnny need to travel so that the cost is the same for both taxi services?
miles
9
The least amount possible is $25 and the number of miles is 25 miles
How much will it cost Johnny if he pays the least amount possible?From the question, we have the following parameters that can be used in our computation:
Yellow Taxi service charges a $15 flat fee plus $2.50
This means that
Yellow Taxi: y = 15 + 2.5x
For the graph, we have
y-intercept = 10
(x, y) = (0, 10) and (2, 16)
So, the slope is
slope = (y₂ - y₁)/(x₂ - x₁) = (16 - 10)/(2 - 0) = 3
So, we have
Black and White Taxi service: y = 10 + 3x
Yellow Taxi: y = 15 + 2.5x
When he travels for 5 miles, we have
Black and White Taxi service: y = 10 + 3 * 5 = 25
Yellow Taxi: y = 15 + 2.5 * 5 = 27.5
Hence, the least amount possible is $25
Distance so that the cost is the same for both taxi servicesThis means that we equate the above equations
So, we have
15 + 2.5x = 10 + 3x
Evaluate the like terms
0.5x = 5
Divide
x = 25
Hence, the distance is 25 miles
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In triangle ABC, m∠B = (12x − 26)° and the measure of the exterior angle to ∠B is (7x − 22)°. Find m∠B. 34° 12° 118° 62°
The angle B for the triangle ABC has a measure of 118° so the correct option is 118°.
How to solve for the angle BThe angle B and its exterior angle lie on a straight line, thus their sum is equal to 180°
From the question, we are given that;
m∠B = (12x − 26)° and the exterior angle = (7x − 22)°
so;
12x - 26 + 7x - 22 = 180° {collect like terms}
19x - 48 = 180°
19x = 180° + 48° {add 48° to both sides}
19x = 228°
x = 228°/19 {divide through by 19}
x = 12
Therefore, by putting the value 12 for x in m∠B = (12x − 26) we get the angle B as;
B = 12(12) - 26
B = 144 - 26
B = 118°
In conclusion, the triangle ABC, with m∠B = (12x − 26)° and the measure of the exterior angle to ∠B is (7x − 22) have the angle B equal to 118°.
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I need help please, it’s asap
The interquartile range of the given data set is 2.16.
The given data is 2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22 and 3.26.
What is the interquartile range?The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.
Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1
The order of the given data is 1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.02.
Here,
Q1= 1/4 (n+1) = 11/4= 2.75
= 2.22
Q3 = 3/4 (n+1) = 8.25
= 4.38
Q2 =4.38-2.22
= 2.16
Therefore, the interquartile range of the given data set is 2.16.
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How do you find the coordinates of a dilation?
In order to dilate something on a coordinate plane, multiply the coordinate with the scale factor. This process is known as mapping.
What is a dilation?
Dilation is a process of altering a thing. It is a process of renewal that to make the objects smaller or larger, with the use of specific scale factor.
The new figure that is the result of dilation is known as the image. Initial figure is referred to as the pre-image.
What is a center of dilation?
Center of dilation is the resizing that happens from a point. The objects/figures are expanded or contracted from the center of dilation.
Scale factor is a figure by which the size of any geometrical figure can be resized, with respect to its original size. The scale factor is multiplied to get image.
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What equation is graphed in this figure?
A: y−4=−13(x+2)
B: y−3=13(x+1)
C: y+2=−3(x−1)
D: y−5=3(x−1)
Answer: D
Step-by-step explanation:
The line is positive and not very steep. For slope, 13 is too steep, -13 and -3 are negative. It must be y-5=3(x-1), which has an accurate slope of 3.
How do i solve for DG?
Answer:
25.9
Step-by-step explanation:
Tangents drawn from a common external point are equal.
[tex]10x-31=2x+17 \\ \\ 8x-31=17 \\ \\ 8x=48 \\ \\ x=6 \\ \\ \implies GE=29 \\ \\ DG=\sqrt{29^2-13^2} \approx 25.9[/tex]
why might you consider using raw scores for as long as possible before assigning a letter grade to a student
The final scores will be dependent on the prior ones.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
raw scores for as long as possible before assigning a letter grade to a student.
Because the final scores will be dependent on the prior ones.
Hence The final scores will be dependent on the prior ones.
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please helppp!!!
Solve for x.
3 1/2≥1.4x
x ≥ 2 1/2
x ≤ 2 1/2
x ≥ 4 9/10
x ≤ 4 9/10
The value of the inequality will be;
⇒ x ≤ 2 1/2
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 3 1/2 ≥ 1.4x
Now,
Since, The inequality is,
⇒ 3 1/2 ≥ 1.4x
Hence, Solve for x as;
⇒ 7/2 ≥ 1.4x
⇒ 3.5 ≥ 1.4x
⇒ 3.5/1.4 ≥ x
⇒ 35/14 ≥ x
⇒ 5/2 ≥ x
⇒ x ≤ 2 1/2
Thus, The value of the inequality for x is;
⇒ x ≤ 2 1/2
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Solve the system of linear equations by graphing. y = –y equals negative StartFraction 5 over 2 EndFraction minus 7.x – 7 x + 2y = 4 What is the solution to the system of linear equations?
x=-9/2 and y=17/4 are the solution to the system of linear equations.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of linear equations are:
y=-5/2x-7..(1)
x+2y=4...(2)
x=4-2y
Subtract x value in equation 1.
y=-5/2(4-2y)-7
y=-20/2+5y-7
y=-10+5y-7
y=5y-17
Subtract both sides by 5y
y-5y=-17
-4y=-17
Divide both sides by 4
y=17/4
Now add y value in equation 2.
x+2(17/4)=4
x+17/2-4=0
x+9/2=0
x=-9/2
Hence, x=-9/2 and y=17/4 are the solution to the system of linear equations.
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If np is greater than mp, which must be true?segment op is longer than segment mq. Segment mn has the same length as segment mp. The measure of angle q equals the measure of angle o. Angle o is larger than angle q.
The side opposite the larger angle is larger and you know that MN>NP, so the angle O's measure is more than the angle Q's measure.
Describe angle.
Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles.
Here,
Greater is the side that is on the other side of the greater angle.
MN>NP.
Consequently, the measure of angle O is greater than angle Q's measure.
Option D is correct since MN>NP is true and the side that opposes the bigger angle is larger. The measure of angle O is therefore greater than the measure of angle Q.
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