Find the directional derivative of f at the given point inthe direction indicated by the angle θ.
Given:
f(x,y) = ye-x
point: (0,4)
θ=2π/3
Answers
To find the directional derivative of f at the point (0,4) in the direction indicated by the angle θ=2π/3, we first need to find the gradient of f at that point.
The gradient of f(x,y) is given by:
∇f(x,y) = ⟨-e^(-x), 1⟩
So at the point (0,4), the gradient of f is:
∇f(0,4) = ⟨-e^0, 1⟩ = ⟨-1, 1⟩
Now, we need to find the component of this gradient in the direction of θ=2π/3. We do this using the dot product:
∇f(0,4) · u
where u is the unit vector in the direction of θ=2π/3.
To find u, we use:
u = ⟨cosθ, sinθ⟩ = ⟨-1/2, sqrt(3)/2⟩
So,
∇f(0,4) · u = ⟨-1, 1⟩ · ⟨-1/2, sqrt(3)/2⟩
= (-1)(-1/2) + (1)(sqrt(3)/2)
= 1/2 + sqrt(3)/2
= sqrt(3)
Therefore, the directional derivative of f at the point (0,4) in the direction indicated by the angle θ=2π/3 is sqrt(3).
To find the directional derivative of f(x, y) = ye^(-x) at the point (0, 4) in the direction indicated by the angle θ = 2π/3, we first need to compute the gradient of f and the unit vector in the direction of θ.
1. Compute the gradient of f (denoted by ∇f):
∂f/∂x = -ye^(-x)
∂f/∂y = e^(-x)
At the point (0, 4), ∇f = (-4, 1).
2. Compute the unit vector in the direction of θ:
u = (cos(θ), sin(θ)) = (cos(2π/3), sin(2π/3)) = (-1/2, √3/2)
3. Compute the directional derivative D_u f:
D_u f = ∇f • u = (-4, 1) • (-1/2, √3/2) = (-4 * -1/2) + (1 * √3/2) = 2 + (√3/2)
The directional derivative of f(x, y) = ye^(-x) at the point (0, 4) in the direction indicated by the angle θ = 2π/3 is 2 + (√3/2).
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Related Questions
A map is shown.
How far is Sandra's house from Johnny's house?
Answers
Answer:
1681 miles
By Pythagoras theoram
6. Casey wants to decorate her dorm room with posters. Posters cost $5 each and Casey
has no more than $35 to spend. What is the greatest amount of posters Casey can buy?p
A <7
Answers
Answer:
7
Step-by-step explanation:
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Franklin National Life Insurance Company purchased new computers for $300,000. If the rate at which the computers' resale value changes is given by the function V'(t) = 5700(t − 10) where t is the length of time since the purchase date and V'(t) is measured in dollars per year, find an expression V(t) that gives the resale value of the computers after t years. V(t) = dollars How much would the computers sell for after 5 years? (Round your answer to the nearest dollar.) $
Answers
To find an expression for V(t), we can integrate V'(t) with respect to t. Doing so, we have:
V(t) = ∫V'(t) dt = ∫5700(t − 10) dt = 5700 ∫(t − 10) dt = 5700 [t^2/2 - 10t] + C
Since V(t) is the resale value of the computers, the constant of integration C should be the initial value of V(t), which is the cost of the computers. Therefore, we have:
V(t) = 5700 [t^2/2 - 10t] + 300000
Now, to find the value of the computers after 5 years, we can substitute t = 5 into the expression for V(t):
V(5) = 5700 [5^2/2 - 10*5] + 300000 = 5700 [25/2 - 50] + 300000 = 5700 [-12.5] + 300000 = -67500 + 300000 = 232500
Thus, the computers would sell for approximately $232,500 after 5 years.
Explanation: The function V'(t) gives the rate at which the resale value of the computers changes with time. In other words, it gives the slope of the function V(t) at any point in time. To find the function V(t) itself, we need to integrate V'(t) with respect to t. The constant of integration C is added to the result of the integration to ensure that the initial value of V(t) is equal to the cost of the computers. Once we have the expression for V(t), we can find the value of the computers at any point in time by substituting the appropriate value for t into the expression. In this case, we found that the value of the computers after 5 years is approximately $232,500.
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Jason considered two similar televisions at a local electronics store. the cheaper version was 12 inches by 24 inches. the more expensive version was \large \frac{8}{3} the size of the cheaper one. what are the dimensions of the expensive television? a 4.5 inches by 9 inches b 28 inches by 56 inches c 7.5 inches by 15 inches d 32 inches by 64 inches
Answers
The dimensions of expensive television is 32 inches through 64 inches.
This trouble may be solved if we understand the idea of fraction and a way to calculate the part of a fragment.
right here it is for the reason that the inexpensive tv is 12 inches by means of 24 inches.
Also it is given that the expensive television is \(\frac{8}{3}\) of the cheaper one.
Now taking the length into consideration the length of the television is
=\(\frac{8}{3}*12\)
= 32 inches
Now taking the width into consideration the width of the television is
=\(\frac{8}{3}*24\)
= 64 inches
So, the dimension of the expensive television is 32 inches by 64 inches.
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Allison works in a department store selling clothing. She makes a guaranteed salary of $350 per week, but is paid a commision on top of her base salary equal to 15% of her total sales for the week. How much would Allison make in a week in which she made $300 in sales? How much would Allison make in a week if she made x dollars in sales?
Answers
Answer: 395
0.15x+350
Step-by-step explanation:
When using a one-sample t-procedure to construct a confidence interval for the mean of a finite population, a condition is that the population size be at least 10 times the sample size. The reason for the condition is to ensure that
a. The sample size large enough
b. The central limit theorem is applicable for the sample mean
c. The sample standar deviation is good apporximation of the population standar deviation
d. The degree dependence among observations is negligible
e. The sampling method is not biased
Answers
The correct answer is (b) The central limit theorem is applicable for the sample mean.
The condition that the population size be at least 10 times the sample size is necessary to ensure that the sample mean follows a normal distribution, as required by the central limit theorem. The central limit theorem states that the sample mean will be approximately normally distributed, regardless of the underlying population distribution, as long as the sample size is large enough. In this case, the condition is necessary to ensure that the sample size is sufficiently large for the central limit theorem to be applicable. Options (a), (c), (d), and (e) are not the correct answers because they do not directly relate to the condition that the population size be at least 10 times the sample size.
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Meadow Dew Corporation currently has an EPS of $4.05, and the benchmark PE for the company is 21. Earnings are expected to grow at 4.9 percent per year. a. What is your estimate of the current stock price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the target stock price in one year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. Assuming the company pays no dividends, what is the implied return on the company’s stock over the next year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Answers
(a)The estimate of the current stock price is $85.05.
(b)The target stock price in one year is $89.05.
(c) The implied return on the company's stock over the next year is 4.70%.
(a) To estimate the current stock price, we'll use the formula for the Price-Earnings (P/E) ratio.
Stock price = EPS ×P/E
Given:
EPS = $4.05
P/E ratio = 21
Substituting these values into the formula:
Stock price =4.05×21
Calculating this expression:
=85.05
Therefore, the estimate of the current stock price is $85.05.
b. To calculate the target stock price in one year, we'll consider the earnings growth rate of 4.9 percent.
The formula for the future stock price is:
Future Stock Price=Current Stock Price×(1+Earnings Growth Rate)
Given:
Current Stock Price = $85.05
Earnings Growth Rate = 4.9%
Substituting these values into the formula:
Future Stock Price=85.05×(1+0.049)
=89.05
Therefore, the target stock price in one year is approximately $89.05.
c. To calculate the implied return on the company's stock over the next year, we'll use the formula:
Implied return = Future Stock Price−Current Stock Price/Current Stock Price × 100
Given:
Current Stock Price = $85.05
Future Stock Price = $89.05
Substituting these values into the formula:
Implied Return=89.05−85.05/85.05×100
=4.70
Therefore, the implied return on the company's stock over the next year is approximately 4.70%.
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Zucchini weights are approximately normally distributed with mean 0.8 pound and standard deviation 0.25 pound. Which of the following shaded regions best represent the probability that a randomly selected zucchini will weigh between 0.55 pound and 1.3 pounds?
Answers
Answer:
0.81859
Step-by-step explanation:
We solve using z score method
The formula for calculating a z-score is is z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
Mean 0.8 pound
Standard deviation 0.25 pound
For x = 0.55 pound
z = 0.55 - 0.8/0.25
= -1
Probability -value from Z-Table:
P(x = 0.55) = 0.15866
For x = 1.3 pounds
Z = 1.3 = 0.8/0.25
= 2
Probability value from Z-Table:
P(x = 1.3) = 0.97725
The probability that a randomly selected zucchini will weigh between 0.55 pound and 1.3 pounds is
P(x = 1.3) - P(x = 0.8)
0.97725 - 0.15866
0.81859.
Answer:
A
Step-by-step explanation:
2 standard deviations away
for the following grouped frequency distribution table, what is the width of each class interval? x f 20-29 2 30-39 5 40-49 4 50-59 1
Answers
The width of each class interval from the given grouped frequency distribution table is 9.
What is a class interval?In a frequency distribution, the numerical width of a class is referred to as the class interval. Data is organised into classes in a grouped frequency distribution. The class interval is determined by the difference between the upper and lower class limits.
The give class intervals are 20-29, 30-39, 40-49 and 50-59.
The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.
So, class width = Upper class - Lower class
29-20=9
39-30=9
Therefore, the width of each class interval is 9.
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Sarah has 5 red balloons,5 blue balloons,10 yellow balloons. Sarah says "One-quarter of the balloons are red
Is Sarah correct Yes or No
Answers
No, Sarah is not correct. There are 5 blue balloons and 10 yellow balloons, which combined make up three-quarters of the total number of balloons.
To determine if Sarah's statement is correct, we need to calculate the fraction of red balloons out of the total number of balloons.
The total number of balloons Sarah has is:
5 (red) + 5 (blue) + 10 (yellow) = 20 balloons
Therefore, the fraction of red balloons out of the total number of balloons is:
5 (red) / 20 (total) = 1/4
This means that one-fourth of the balloons are indeed red. However, this does not mean that all of the other balloons are not red.
Sarah's statement suggests that the remaining three-quarters of the balloons are not red, which is not necessarily true. In fact, we know that there are 5 blue balloons and 10 yellow balloons, which combined make up three-quarters of the total number of balloons.
Therefore, Sarah's statement is not accurate.
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The recursive formula for a geometric sequence is: a = 4 an=an-1×3 What is the 3rd term of this sequence?
Answers
Answer:
36
Step-by-step explanation:
a1 = 4
an=an-1 *3
a2 = a1 *3 = 4*3 = 12
a3 = a2*3 = 12*3 = 36
a variable measured with discrete data means that the data identify participants as belonging to
Answers
A variable measured with discrete data means that the data identify participants as belonging to one of a finite number of categories or groups. Discrete data can only take on certain values and cannot be subdivided any further. For example, the number of siblings a person has is a discrete variable as it can only take on whole numbers (0, 1, 2, 3, etc.).
In contrast, continuous data can take on any value within a range. For example, a person's height is a continuous variable as it can be measured with decimals (5'7.5", 6'2", etc.).
It is important to distinguish between discrete and continuous variables as they require different methods of analysis and interpretation. Understanding the nature of the data is crucial in ensuring accurate and meaningful results in research studies.
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help please! ill mark brainliest!
Answers
Answer:
The answer is 90
Step-by-step explanation:
When HI=GH
Then m<G=m<I= 45
m<H=180-(45+45)=90
If you need any explanation in it or anything on math you can communicate with me on Whats on this number +201557831028 or in email or face or anything
The polygon circumscribes a circle . what is the perimeter of the polygon ?The perimeter of the polygon is _ cm
Answers
The perimeter of the polygon is 76 cm
Explanation:Tangents from the same points are of the same lengths.
Using an illustration:
The points are in Magenta and the lengths with same sides have been indicated
Now we can calculate the perimeter of the polygon:
Perimeter = 8cm + 19cm + 19cm + 6cm + 6cm + 5cm + 5cm + 8cm
Perimeter = 76cm
The perimeter of the polygon is 76 cm
Find the area of the region under the graph of the function f on the interval [4,7]. f(x)= 2/x^2 square units
Answers
The area of the region under the graph of f(x) on the interval [4, 7] is 3/14 square units.
To find the area of the region under the graph of the function f(x) = 2/x^2 on the interval [4, 7], we can calculate the definite integral of f(x) over this interval. The definite integral represents the signed area between the curve and the x-axis.
The integral of f(x) with respect to x can be calculated as follows:
∫[4, 7] (2/x^2) dx = -2/x evaluated from 4 to 7.
Substituting the upper and lower limits into the expression, we have:
(-2/7) - (-2/4) = -2/7 + 1/2 = -4/14 + 7/14 = 3/14.
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A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 3 inches above the equilibrium position. Find the equation of motion
Answers
The equation of motion is: x (t) = -0.66 * cos (9.8 * t).
Here, we have,
We have that Newton's second law for a system is:
Knowing m the united mass and k the spring constant
m * (d²x) / (dt²) = -k * x
where x (t) is the displacement from the equilibrium position. The equation can be expressed like this:
(d²x) / (dt²) + (k / m) * x = 0
Weight units should be converted to mass units as follows:
m = W / g = 24 lb / (32 ft / s ^ 2) = 3/4 slug
We also need to convert inches to feet, to know the stretch, we know that 1 foot is twelve inches, therefore:
4 in * 1 ft / 12 in = 0.33 ft
With Hooke's law we proceed to calculate the spring constant k:
k = W / s = 24 lb / 0.33 ft = 72 lb / ft
Knowing then that m is equal to 3/4 and that k is equal to 72, we can replace in the initial equation:
(d²x) / (dt²) + (72 / (3/4)) * x = 0
(d²x) / (dt²) + 96x = 0
We know that the solution of a differential equation of the form a (d²x) / (dt²) + (w²) * x = 0 is equal to:
x (t) = C1 * cos (wt) + C2 * sin (wt)
Let w² = 96, then w = √96= 9.8
Replacing
x (t) = C1 * cos (9.8 * t) + C2 * sin (9.8 * t)
We have that the initial conditions are x (0) = - 8 in, which is equal to -8/12 ft = -0.66 ft
x (0) = -0.66 and x '(0) = 0 ft / s
Replacing we have:
x (t) = -0.66 * cos (9.8 * t) + 0 * sin (9.8 * t)
Then the equation would be
x (t) = -0.66 * cos (9.8 * t)
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Follow the steps to find the product of and 0.55.
Estimate the product of and 0.55.
1/4-
Convert the decimal 0.55 to a fraction.
V55/100
What is the product of the two numbers?
X 110/150 or 11/15
110/300 or 11/30
77/103
Answers
1) Estimate value of the product of 2/3 and 0.55 is, 2/3.
2) The fraction part is, 55 / 100
3) The product of the two numbers is, 11/30
We have to given that,
Estimate the product of 2/3 and 0.55.
And, Convert the decimal 0.55 to a fraction.
And, The product of the two numbers.
Now,
Estimate the product of 2/3 and 0.55,
So, we can round 0.55 to the nearest whole number, which is 1.
Then, multiply 2/3 by 1 to get an estimate of the product.
so, The correct answer is 2/3.
Now, we can convert the decimal 0.55 to a fraction,
= 0.55
= 55/100
= 11/20
Thus, The correct answer is, 55/100.
And, the product of 2/3 and 0.55,
= 2/3 x 55/100
= 110/300
= 11/30.
Hence, The correct answer is, 110/300 or 11/30
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Identify the transformation from ABCD to A'B'C'D'.
Answers
Answer:
C. Reflection across the y-axis
Step-by-step explanation:
Reflection across y axis= (x,y) to (-x,y) so B (1,2) is now B'(-1,2). Hope this helped!
Leah Deposited $7000 in an account that earns 2% interest compounded annually. How much interest will she have earned after 6 years?
Answers
Answer:
840
Step-by-step explanation:
7000×2×6 ÷ 100. since it is 2%
= 840
Which statement about the sketch below is true?
The similar triangles show that the slope of the line is - 1/2.
The similar triangles show that the slope of the line is 1/2.
The similar triangles show that the slope of the line is 2.
The similar triangles show that the slope of the line is -2
Answers
The statement about the sketch below that is true is: The similar triangles show that the slope of the line is -2.
In the given sketch, the presence of similar triangles can provide insights into the slope of the line. When two triangles are similar, their corresponding sides are proportional, meaning their ratios are equal. In the context of slopes, the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line represents the slope.
In the given sketch, if the similar triangles indicate a ratio of 1:2 between the vertical and horizontal sides, it means that for every 1 unit increase in the vertical direction, there is a 2 unit increase in the horizontal direction. Since slope is calculated as the ratio of rise to run, this indicates a slope of -2 (negative because the line is downward sloping).
Therefore, the true statement is that the similar triangles show that the slope of the line is -2.
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n general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (you must first specify a coordinate system in order to find the components of each arrow.) this problem gives you some practice with the components. let vectors a⃗
Answers
The result for a) \(A⃗ - B⃗\) is (3, -5, -4), b) \(B⃗ - C⃗\) is (-5, 4, 0), c) \(-A⃗ + B⃗ - C⃗\) is (-6, 4, 3), d) \(3A⃗ - 2C⃗\) is (-3, -2, -11), e) \(-2A⃗ + 3B⃗ - C⃗\) is (-11, 14, 8) and the result for f) \(2A⃗ - 3(B⃗ - C⃗)\) is (17, -12, -6).
Let's calculate the given expressions using the given vectors:
Given vectors:
\(A⃗\) = (1, 0, -3)
\(B⃗\) = (-2, 5, 1)
\(C⃗\) = (3, 1, 1)
a) \(A⃗ - B⃗\)
(1, 0, -3) - (-2, 5, 1)
= (1 + 2, 0 - 5, -3 - 1)
= (3, -5, -4)
b) \(B⃗ - C⃗\)
(-2, 5, 1) - (3, 1, 1)
= (-2 - 3, 5 - 1, 1 - 1)
= (-5, 4, 0)
c) \(-A⃗ + B⃗ - C⃗\)
-(1, 0, -3) + (-2, 5, 1) - (3, 1, 1)
= (-1, 0, 3) + (-2, 5, 1) - (3, 1, 1)
= (-1 - 2 - 3, 0 + 5 - 1, 3 + 1 - 1)
= (-6, 4, 3)
d) \(3A⃗ - 2C⃗\)
3(1, 0, -3) - 2(3, 1, 1)
= (3, 0, -9) - (6, 2, 2)
= (3 - 6, 0 - 2, -9 - 2)
= (-3, -2, -11)
e) \(-2A⃗ + 3B⃗ - C⃗\)
-2(1, 0, -3) + 3(-2, 5, 1) - (3, 1, 1)
= (-2, 0, 6) + (-6, 15, 3) - (3, 1, 1)
= (-2 - 6 - 3, 0 + 15 - 1, 6 + 3 - 1)
= (-11, 14, 8)
f) \(2A⃗ - 3(B⃗ - C⃗)\)
2(1, 0, -3) - 3[(-2, 5, 1) - (3, 1, 1)]
= (2, 0, -6) - 3[(-2 - 3, 5 - 1, 1 - 1)]
= (2, 0, -6) - 3(-5, 4, 0)
= (2, 0, -6) - (-15, 12, 0)
= (2 + 15, 0 - 12, -6 - 0)
= (17, -12, -6)
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In general, it is best to conceptualize vectors as arrows in space and then make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A⃗ =(1,0,−3), B⃗ =(−2,5,1), and C⃗ =(3,1,1). Calculate the following and express your answers as ordered triplets of values separated by commas. a) A-B b) B-C c) -A+B-C d) 3A-2C e) -2A+3B-C f) 2A-3(B-C)
The figures above are examples of
Answers
Have a good day.
For f(x)= 2x-15 ,find f(x) when x=-4
I just need some help on this question.
Answers
Cual es el area de un semicírculo que se diámetro es 14
Answers
The area of a circle is given by:
\(A_C=\frac{1}{4}\cdot\pi\cdot d^2.\)Where π ≅ 3.14 and d is the diameter of the circle.
Now, a semi-circle is a half of a circle, so its area is half of the area of the complete circle:
\(A_{SC}=\frac{1}{2}\cdot A_C=\frac{1}{2}\cdot(\frac{1}{4}\cdot\pi\cdot d^2)=\frac{1}{8}\cdot\pi\cdot d^2\text{.}\)Replacing the value d = 14 in the last formula, we get:
\(A_{SC}=\frac{1}{8}\cdot\pi\cdot(14units)^2=24.5\cdot\pi\cdot units^2\cong76.97units^2.\)Answer
The area of a semicircle with a diameter d =14 is approximately 76.97 units square.
Part 6
Passes through (-6, 10) & (-3, -2)
Slope:
Y-Intercept:
Equation of the line:

Answers
Hey there! I'm happy to help!
SLOPE
To find the slope, you divide the difference of the y values by the difference in the x values.
10-(-2)=10+2=12
-6-(-3)=-6+3=-3
12/-3=-4
So, our slope is -4.
Y- INTERCEPT
To find the y-intercept, we plug our slope and one of our points into the slope intercept equation (y=mx+b) and solve for b, which is the y-intercept. We will use the point (-6,10).
10=-4(-6)+b
Flip the equation so b is on the left.
-4(-6)+b=10
24+b=10
Subtract 24 from both sides.
b=-14
Our y-intercept is -14.
EQUATION
The slope intercept equation is y=mx+b, where m is the slope and b is the y-intercept. Therefore, we have the following answers.
Slope: -4
y-Intercept: -14
Equation of the Line: y=-4x-14
Have a wonderful day! :D
On a number line, A is at 5 and B is at 50. Point X is the midpoint. Point T is 2/3 of the way from X to B. Determine the coordinate of point T.
Coordinate of X = ________
Distance of XB = ________
Fractional distance 2/3(XB) = _________
Coordinate of T = ________
Answers
\(x = \frac{b + a}{2} = \frac{50 + 5}{2} = \frac{55}{2} = 27.5\)
Part 2\(xb = b - x = 50 - 27.5 = 27.5\)
Part 3\( \frac{2}{3} xb = \frac{2}{3} (27.5) \approx18.34\)
Part 4\(t = \frac{2}{3} ab = \frac{2}{3} (b - a) = \frac{2}{3} (45) =15 \\ \)
Which of the following lines is parallel to the line that goes through the points (5, 8) and (3, 6)? Please help me!!!!!!
Answers
Answer:
Any line with the slope 1 or y = x + b
Step-by-step explanation:
Parallel lines by definition have the same slope
Value of the y-intercept or b doesn't matter in this case
You have to find the slope of the line through (3,6) and (5,8)
Slope equation is
\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)Plug in values given
\(\frac{8-6}{5-3}\)
Evaluate
\(\frac{2}{2} =1\)
Any line with the slope of 1 (or no co-efficient in front of x) would be parallel to the line through (3,6) and (5,8)
helpppppppppppp meeeeeeeeeeee pleaseee!!!
Answers
Based on the vertical line test, y is not a function of x in the given graph because the line drawn intercepts the graph at two points.
What is the Vertical Line Test?The vertical line test is used to test whether a relation that is graphed is a function or not.
To conduct the vertical line test, a vertical line is drawn to cut through the graph that represents a relation. If the line intersects the graph at exactly one point, then it is a function. If the line intersects the graph at more than one point, then the graph does not represent a function.
The image attached below shows the vertical line test. The line intercepts the graph at two points, therefore, the relation that is represented by the graph is not a function.
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the scatter plot shows the results of a survey in which 10 people were asked how many e-mail accounts and how many credit cards they have. how many credit cards does the person with 3 e-mail accounts have?
Answers
In the scatter plot, the person with 3 e-mail accounts have 1 credit card.
Define scatter plot.Typically, the relationship between variables is observed and visually displayed using a scatter plot, a type of chart. Dots are used to indicate the variable values. Scatter plots employ Cartesian coordinates to show the values of the variables in a data set because the placement of the dots on the vertical and horizontal axes will reveal the value of each individual data point. Other names for scatter plots are scattergram, scatter graphs, and scatter charts.
The association between two numerical variables measured for the same individuals is displayed in a scatterplot. The values of one variable are plotted on the horizontal axis, and the values of the other variable are plotted on the vertical axis. On the graph, each individual in the data is represented by a point.
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let f(x) = x + 5 and g(x) = x – 4.
Find (f + g)(x)
Answers
(f∘g)(x)=5x (g∘f)(x)=5x+165. Explanation: Finding (f∘g)(x) means finding f(x) when it is composed with g(x) , or f(g(x)) .