To derive the properties of R2 for the model m Ji = Σβ,tij + u; j=1, we need to first understand what R2 represents. R2, also known as the coefficient of determination, is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a regression model.
In the given model, the dependent variable is m Ji and the independent variable is tij. The coefficient β represents the slope of the regression line and u represents the error term.
To derive the properties of R2, we can use the formula:
R2 = 1 - (SSres/SStot)
Where SSres is the sum of squared residuals and SStot is the total sum of squares.
SSres = Σ(m Ji - ŷi)2
SStot = Σ(m Ji - ȳ)2
Where ŷi is the predicted value of m Ji and ȳ is the mean of m Ji.
By substituting the values of SSres and SStot into the formula for R2, we can derive the properties of R2 for the given model.
R2 = 1 - (Σ(m Ji - ŷi)2/Σ(m Ji - ȳ)2)
The properties of R2 for the given model are:
1) R2 is always between 0 and 1. A value of 0 indicates that the independent variable(s) do not explain any of the variance in the dependent variable, while a value of 1 indicates that the independent variable(s) explain all of the variance in the dependent variable.
2) R2 is a measure of the strength of the relationship between the independent variable(s) and the dependent variable. The closer R2 is to 1, the stronger the relationship.
3) R2 is affected by the number of independent variables in the model. The more independent variables there are, the higher the R2 value will be.
4) R2 does not indicate causation. It only measures the strength of the relationship between the independent variable(s) and the dependent variable.
To know more about variance refer here:
https://brainly.com/question/14116780
#SPJ11
Convert this rational number to its decimal form and round to the nearest thousandth. 1/7=__√[?] First, let's convert the fraction into a long division problem. Hint: First enter the number on the inside of the division box. This number should be the numerator of the fraction.
0.142857.
To convert the rational number 1/7 to its decimal form and round to the nearest thousandth, let's start by converting the fraction into a long division problem.
Enter the numerator of the fraction, 1, into the division box, and then divide it by the denominator of the fraction, 7.
The result of this long division is 0.142857. Finally, round this decimal to the nearest thousandth, which gives us 0.143.
Learn more about decimal form
brainly.com/question/16361602
#SPJ11
In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. A regression analysis was completed and the value for s was found to be 3.05.
Which of the following is the best interpretation of s?
The average residual is about 3.05 pretzels.
The average residual is about 3.05 centimeters.
The average handspan of a student is 3.05 centimeters.
The average number of pretzels a student could grab is 3.05 pretzels.
6) Two ships leave a port at the same. The first ship sails on a bearing of 83° at 30 knots
(nautical miles per hour) and the second on a bearing of 173° at 20 knots. How far apart are they after
2 hours? Provide the exact simplified answer only. (Abbreviation for nautical miles is NM.)
Include a complete, fully labeled diagram and SHOW ALL STEPS.
Sketch it.
The first ship sails on a bearing of 83° at 30 knots while the second on a bearing of 173° at 20 knots. After two hours, the distance between the ships is 72 NM
The two ships are travelling on different bearings and at different speeds. To calculate the distance between them after two hours, we need to use the formula:
Distance = Speed x Time
The distance the first ship has travelled after two hours:
Distance 1st ship = 30 knots x 2 hours = 60 nautical miles (NM)
The distance the second ship has travelled after two hours:
Distance 2nd ship = 20 knots x 2 hours = 40 nautical miles (NM)
The angle difference = 173° - 83° = 90°
Since the port, the first ship, and the second ship form a right triangle, we can find the total distance between the two ships using the Pythagorean Theorem.
Distance² = (60 NM)² + (40 NM)²
Distance = √ (3600 + 1600) = √ 5200 = 72 NM
Therefore, after two hours, the two ships will be 72 NM apart.
Learn more about Pythagorean Theorem here:
https://brainly.com/question/24761611
#SPJ11
On a coordinate plane, how are the locations of the points (9 , -5) and (9 , 5) related?
A.
locations unrelated
B.
reflection across the x-axis
C.
reflection across the y-axis
D.
reflection across both axes
Option B, On a coordinate plane, the locations of the points (9, -5) and (9, 5) related reflection across the x-axis.
The two locations (9, -5) and (9, 5) have the same x-coordinate, but their y-coordinates are different. We need to see how the coordinates of two points change as they undergo various transformations to understand their relationship.
If points are not linked, their coordinates cannot become one because they have no relation to each other. The x coordinates of the points remain the same, but if they are reflected on the x-axis, their y coordinates are reversed. The point (9, -5) in this case will be reflected to (9, 5) and vice versa.The y coordinates of these points remain the same, but if they are reflected on the y-axis, their x coordinates are reversed. In this case, point (9, -5) will reflect towards (-9, -5) and point (9, 5) will reflect towards (-9, 5).Negative if the x and y coordinates of the point are reflected on both the x-axis and the y-axis. In this case, point (9, -5) will reflect towards (-9, 5) and point (9, 5) will reflect towards (-9, -5).Learn more about the coordinate plane at
https://brainly.com/question/24134413
#SPJ4
1. Use substitution to determine which ordered pairs lie on the graph of the exponential function. f(x) = 3(4)2x
Ordered pair (0, 3), (1, 48) and many more lies on the graph of the function.
What are Functions?
A function in math is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. It can be represented using an equation, graph, or table of values.
The exponential function [tex]f(x) = 3(4)^(2x)[/tex] can be evaluated for any value of x to get the corresponding value of y. To find ordered pairs that lie on the graph of this function, we can substitute different values of x into the function and calculate the corresponding values of y.
For example, if we substitute x = 0 into the function, we get:
[tex]f(0) = 3(4)^(2(0)) = 3(4)^0 = 3(1) = 3[/tex]
So the ordered pair (0, 3) lies on the graph of the function.
Similarly, if we substitute x = 1 into the function, we get:
[tex]f(1) = 3(4)^(2(1)) = 3(4)^2 = 3(16) = 48[/tex]
So the ordered pair (1, 48) also lies on the graph of the function.
We can repeat this process for other values of x to find more ordered pairs that lie on the graph of the function.
To learn more about Functions from the given link
https://brainly.com/question/22340031
#SPJ1
What am I missing to get full marks
The required cost of the cans of weedkiller needed to cover lawn are £ 47.4.
What is Trapezoid and formula for area?The formula A = 12 (a Plus b) h is used to calculate the area of a trapezoid, where a and b are the bases (parallel sides) and h is the height (the angle between the bases).
According to Question:We have;
Dimensions of Trapezoid; a = 20, b = 12, Height = h
So;
[tex]$Area = \frac{(a+b)h}{2}$[/tex]
For h, Using Pythagoras theorem;
17² = 8² + h²
h = 15 m
Then,
[tex]$Area = \frac{(12+20)15}{2}$[/tex]
Area = 240 Sq meter
Then,
100 Sq meter = £19.75
For 240 Sq meter
= £19.75(2.4)
= £ 47.4
Thus, required cost is £ 47.4.
To know more about Trapezoid visit:
brainly.com/question/8643562
#SPJ1
Minimize the objective function 9x+3y subject to the constraints. ⎩⎨⎧y≥−2x+11y≤−x+10y≤−31x+6y≥−41x+4The minimum value is The minimum occurs atx=andy=.
The minimum value of the objective function is 16 and it occurs at x = 1 and y = 5.
The given objective function is 9x+3y. The given constraints are y≥−2x+11, y≤−x+10, y≤−3, x+6y≥−4, and x+4.
To minimize this objective function, we need to set up the Lagrangian function:
L(x,y,λ1,λ2,λ3) = 9x+3y - λ1(y+2x-11) - λ2(y-x+10) - λ3(y+3) - λ4(x+6y-4) - λ5(x+4)
We can then find the critical points of this function by taking the partial derivatives of the Lagrangian with respect to x, y, λ1, λ2, and λ3, and setting them equal to zero:
∂L/∂x = 9 - λ2 + 6λ4 = 0
∂L/∂y = 3 - λ1 - λ2 - λ3 - 6λ4 = 0
∂L/∂λ1 = -(y+2x-11) = 0
∂L/∂λ2 = -(y-x+10) = 0
∂L/∂λ3 = -(y+3) = 0
∂L/∂λ4 = -(x+6y-4) = 0
∂L/∂λ5 = -(x+4) = 0
Solving these equations, we get the solution x = 1, y = 5, λ1 = 4, λ2 = -3, λ3 = 8, λ4 = -3, and λ5 = -1.
To know more about Lagrangian function click on below link:
https://brainly.com/question/30426461#
#SPJ11
Find the length of YZ.
V
35
N
YZ =
W 44
36
X
When we square the two sides, we obtain: Z = square (82) , YZ thus has a length of about 9.06 units.
what is Pythagoras theorem ?The connection among all three opposites of a right triangle is a key idea in geometry known as Pythagoras' theorem. According to this rule, the square of the hypotenuse's length—the side that faces the right angle—in a right triangle is the product of the squares of the dimensions of the other two sides. You can write this as follows: [tex]a^2 + b^2 = c^2[/tex] where a and b are the sizes of the other two right triangle sides and c has been the angle of the hypotenuse. The theorem is named after Pythagoras, an ancient Greek mathematician who is credited with finding it and creating its mathematical proof.
given
We may apply the Pythagorean theorem to determine the length of YZ.
Triangle VYZ is a right-angled triangle with the legs VY and VZ and the hypotenuse YZ, as may be seen. From the information provided, we can determine the lengths of VY and VZ.
VY = 35 - 36 = -1 (we can see from the diagram that V is to the left of Y, hence VY is negative) (we can see from the diagram that V is to the left of Y, so VY is negative)
VZ = 44 - 35 = 9 (we can see from the graphic that Z is below V, hence VZ is positive) (we can see from the diagram that Z is below V, so VZ is positive)
Using the Pythagorean theorem, we have the following:
[tex]VY^2 + VZ^2 = YZ^2\\YZ^2 = (-1) (-1)^2 + 9^2 \\YZ^2 = 1 + 81 \\YZ^2 = 82[/tex]
When we square the two sides, we obtain: Z = square (82) , YZ thus has a length of about 9.06 units.
To know more about Pythagoras theorem visit :-
https://brainly.com/question/14461977
#SPJ1
DOES ANYONE KNOW THE ANSWER PLEASE
Answer:
Step-by-step explanation:
45 points for signing up.
2.5 points for each visit [tex]=2.5v[/tex]
Needs to total 75 points.
So [tex]45+2.5v=75[/tex] is the solution.
This is shown by option [tex](D)[/tex].
Create an exponential function (y=ab^x) that passes through the points (1960,19.005) and (2010,19.548). Round (a) and (b) to three decimal places.
The equation of exponential function=y = 0.054 × [tex]1.028^{x}[/tex]
What are exponential functions?As the name implies, exponents are utilised in exponential functions. But remember that a variable serves as the exponent instead of a constant as the basis of an exponential function.
A function is a power function rather than an exponential function if its base is a variable and its exponent is a constant.
If the graph of exponential function passes through the points (1960,19.005) and (2010,19.548), then the coordinates of these points satisfy the equation, y = [tex]ab^{x}[/tex]
Now, 19.005 = a × [tex]b^{1960}[/tex]
⇒ [tex]b^{1960}[/tex] = 19.005/a
Similarly, 19.548 = a × [tex]b^{2010}[/tex]
⇒ [tex]b^{2010}[/tex] = 19.548/a
⇒ [tex]b^{1960}[/tex] × [tex]b^{50}[/tex] = 19.548/a
⇒ [tex]b^{50}[/tex] = 19.548/a × a/19.005
= 1.028
Putting this value to find a,
we get a = 0.054
So, the equation of exponential function=
y = 0.054 × [tex]1.028^{x}[/tex]
To know more about exponential function, visit:
https://brainly.com/question/14355665
#SPJ1
The diameter of a circle is 9 in. Find its area to the nearest tenth.
schoology
The probability that a person will be helped by a certain medicine is .75. Our facility will be seeing 30 patients today. Let X count the number of patients, of those 30, that are helped by the medicine. Determine the following:
a) P (20 < or = X)
b) P (18 < or = X < 25)
c) P ( X < 16)
a) P (20 < or = X) = 0.8617: This is the probability that 20 or more of the 30 patients will be helped by the medicine.
b) P (18 < or = X < 25) = 0.8557: This is the probability that between 18 and 25 of the 30 patients will be helped by the medicine.
c) P ( X < 16) = 0.0266: This is the probability that less than 16 of the 30 patients will be helped by the medicine.
The given situation can be modeled using a binomial distribution, where the number of trials is 30, and the probability of success is 0.75. We can use the binomial probability formula to find the probabilities for each of the given conditions. The binomial probability formula is:
P(X = x) = (n choose x) * p^x * (1-p)^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success, and (n choose x) is the binomial coefficient.
a) P (20 < or = X) = 1 - P (X < or = 19) = 1 - sum_{x=0}^{19} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8617
b) P (18 < or = X < 25) = P (X < or = 24) - P (X < or = 17) = sum_{x=18}^{24} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8557
c) P ( X < 16) = sum_{x=0}^{15} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.0266
Therefore, the probabilities are 0.8617, 0.8557, and 0.0266 for the conditions a), b), and c) respectively.
You can learn more about probability at
brainly.com/question/24756209
#SPJ11
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!
The simplified fraction is given as follows:
(2x - a)/(2x + a).
How to simplify the fraction?At the numerator, the fraction is simplified applying the least common factor as follows:
2 - (a/x) = (2x - a)/x.
At the denominator, the fraction is also simplified applying the common factor as follows:
2 + (a/x) = (2x + a)/x.
x is a common denominator to both of the fractions, hence it can be simplified, and then the simplified fraction is given as follows:
(2x - a)/(2x + a).
More can be learned about simplification of fractions at https://brainly.com/question/78672
#SPJ1
How far is the mall from the pet shop? Explain how you know
The distance of the mall from the pet shop, based on the graphic given, is 2 miles.
How to find the distance?The distance between the Pet Shop, the School, the Mall and the Park are all shown on the graphic. The intervals between the distance given is shown to be 1 / 2 miles.
The number of distance marks between the Pet Shop and the Mall is 4 marks which means that distance between the Pet Shop and the Mall would be :
= 4 x 1 / 2
= 4 / 2
= 2 miles
Find out more on distance at https://brainly.com/question/22444331
#SPJ1
What is the answer? I don't quite get it.
(3x + 1/2) + (7x - 4 1/2)
Answer:
To simplify the expression, we can combine the like terms.
(3x + 1/2) + (7x - 4 1/2)
= 3x + 7x + 1/2 - 4 1/2 (distributing the addition)
= 10x - 4 (combining the like terms)
Therefore, (3x + 1/2) + (7x - 4 1/2) simplifies to 10x - 4.
Michael, a farmer, wants to buy a Mex tractor .the price of the tractor is R160 000,VAT excluded.he can afford a deposit of R20 000.he decides to buy the tractor on hire purchase over a period of 60 months and simple interest of 10%.what would he pay in total after 60 months?
Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.
How to calculate the total interest he will need to pay over the months ?First, let's calculate the total amount he will need to finance:
Total amount to finance = R160,000 + 0.15 x R160,000 (VAT at 15%) = R184,000
Next, let's calculate the total interest he will need to pay over the 60 months:
Total interest = (principal x rate x time) / 100
where
principal = R184,000 (the total amount financed)rate = 10% (the annual interest rate)time = 5 years (60 months)Total interest = (R184,000 x 10% x 5) / 100 = R92,000
Therefore, the total amount Michael will need to pay over the 60 months is the sum of the total amount financed and the total interest:
Total amount to pay = Total amount to finance + Total interest = R184,000 + R92,000 = R276,000
So, Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.
Learn more about interest here : brainly.com/question/20690803
#SPJ1
Rewrite the following statement using a number in scientific notation. The diameter of a certain atom is about \( 0.54 \) nanometers. (Recall that nano- means "billionth.")
This as \( 5.4 \times 10^{-10} \) meters, or \( 5.4 \times 10^{-9} \) centimeters
The diameter of a certain atom is about \( 0.54 \) nanometers, which can be rewritten in scientific notation as \( 5.4 \times 10^{-1} \) nanometers. This is because scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. In this case, we move the decimal point one place to the left and multiply by \( 10^{1} \) to get the number in scientific notation. Since nano- means "billionth," we can also write this as \( 5.4 \times 10^{-10} \) meters, or \( 5.4 \times 10^{-9} \) centimeters.
Learn more about Diameter
brainly.com/question/5501950
#SPJ11
22+ what + 32 equals 81?
3
x
+
7
(
3
x
+
4
)
3
x
+
7
×
3
x
+
7
×
4
3
x
+
21
x
+
28
24
x
+
28
Julia is a salesperson. She sold a chandelier for $66 and earned 5% commission .How much commission didJulia earn?
Answer:
$3.30
Step-by-step explanation:
66 times 0.05
What is JL? aaaaaaaaaaaaaaaaaa
Given the function f(x)=x+3/x-8 aind the following. (a) the
average rate of change of f on [−3,1]: (b) the average rate of
change of f on [x,x+h]:
(a) The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1
(b) The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)
The average rate of change of a function is the slope of the line that passes through two points on the graph of the function. It is calculated by the difference in the y-values of the two points divided by the difference in the x-values of the two points.
The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1
The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)
Therefore, the average rate of change of f on [x,x+h] is (x^2-5x-8h-11)/(x^2-8x-8h+64).
Learn more about Average rate
brainly.com/question/12395856
#SPJ11
What is the scale factor in the dilation?
One-sixth
One-third
3
6
The scale factor of the preimage to image is 3. Then the correct option is C.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The picture rectangle has points on coordinates (0, 0), (0, 8), (9, 8), and (9, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).
The scale factor is given as,
SF = 9 / 3
SF = 3
The scale factor of the preimage to image is 3. Then the correct option is C.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
The complete question is given below.
What is the scale factor in the dilation?
On a coordinate plane, the image rectangle has points (0, 0), (0, 8), (9, 8), and (8, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).
a) One-sixth
b) One-third
c) 3
d) 6
Answer:
Step-by-step explanation: C !!!!!! / 3
Edge 2023
1/6
1/3
3 <--------------- correct
6
Math question 13 help
Answer:
This is an odd function
Step-by-step explanation:
Given a function f(x),
if f(-x) = f(x) then the f(x) is even
If f(-x) = -f(x0 then the function is odd
If neither of the above is true then the function is neither odd nor even
We are given
[tex]f(x) = 4x^3 - x^5 + 5x\\f(-x) = 4(-x)^3 -(x)^5 + 5(-x)\\\\(-x)^3 = - x^3\\(-x)^5 = -x^5\\\\\\\therefore\\f(-x) = 4(-x^3) - (-x^5) + 5 (-x)\\\\= -4x^3 + x^5 - 5x\\\\= -(4x^3 -x^5 + 5x)\\\\= -f(x)[/tex]
So the function is odd
PLEASE HELP!! I don’t even know how to type that
The value of [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given equation is [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex]
[tex]\sum \:a_n+b_n=\sum \:a_n+\sum \:b_n[/tex]
By Applying the sum rule
[tex]=\sum \:_{n=1}^{400}2n-\sum \:_{n=1}^{400}1[/tex]
=2×2(400+1)/2 -400
=2×200×401−400
=16000
Hence, the value of [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.
To learn more on Sequence click:
https://brainly.com/question/21961097
#SPJ1
common help me with this pls
Answer:
See image attached for complete answer
Step-by-step explanation:
The attached image shows the calculation of probabilities for each branch
I believe it is self-explanatory
Since P(bus to shops) = 0.4, P(walk to shops ) = 1- 0.4 = 0.6
Since P(bus from shops) = 0.7, P(walk from shops) = 1- 0.7 = 0.3
The probabilities at the leaves of the tree(rightmost entries) show the combined probabilities of to and from
For example if she takes a bus to the shops and takes a bus from the shops, the combined probability = 0.4 x 0.7 = 0.28
If she walks to the shops and takes a bus from the shops the combined probability = 0.6 x 0.7 = 0.42
The other two probabilities can be computed the same way
The probability that she walks at least one way
= P(walking to shop) or P(walking from shop)
= sum of the probabilities in the yellow shaded boxes
= 0.12 + 0.42 + 0.18
= 0.72
Ils Practice 3 Simplify the expression. Make all exponents pos ((-8x^(5))(x^(-3)))/(20x^(2))
The expression ((-8x⁵)(x⁻³))/(20x²) when simplified, making all exponents positive, will become -2/5.
To simplify the expression ((-8x⁵)(x⁻³))/(20x²), we need to apply the rules of exponents and simplify the coefficients.
First, let's simplify the coefficients:
-8/20 = -2/5
Next, let's apply the rules of exponents:
Product Rule: When multiplying two exponential expressions with the same base, you can add the exponents. That is, xᵃ · xᵇ = xᵃ⁺ᵇ
Quotient Rule: When dividing two exponential expressions with the same base, you can subtract the exponents. That is, xᵃ / xᵇ = xᵃ⁻ᵇ
(x⁵)(x⁻³) = x⁵⁺⁽⁻³⁾ = x²
x²/x² = x²⁻² = x⁰ = 1
So the expression simplifies to:
(-2/5)(1) = -2/5
Therefore, the simplified expression is -2/5.
Learn more about rules of exponents here: https://brainly.com/question/11975096.
#SPJ11
Let r (t) = sin t i+ e^t j + ln ( t + 1 ) k
be a space curve. Which of the following vectors is perpendicular to the tangent vector of the curve at ( 0, 1, 0)?
a. < 0, 1, 0 >
b. < -1, 0, -1 >
c. < 1, 0, -1 >
d. < 1, - 1, 1>
e. <1, 0, 1 >
The vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c
The space curve given is r(t) = sin t i + e^t j + ln(t+1) k. To find the tangent vector of the curve at a given point, we need to take the derivative of the curve with respect to t. The derivative of the curve is r'(t) = cos t i + e^t j + (1/(t+1)) k.
At the point (0, 1, 0), t = 0. So, the tangent vector at this point is r'(0) = cos 0 i + e^0 j + (1/(0+1)) k = <1, 1, 1>.
Now, we need to find which of the given vectors is perpendicular to the tangent vector. Two vectors are perpendicular if their dot product is equal to 0. So, we need to find the dot product of the tangent vector with each of the given vectors and see which one is equal to 0.
a. <1, 1, 1> • <0, 1, 0> = 0 + 1 + 0 = 1 (not perpendicular)
b. <1, 1, 1> • <-1, 0, -1> = -1 + 0 - 1 = -2 (not perpendicular)
c. <1, 1, 1> • <1, 0, -1> = 1 + 0 - 1 = 0 (perpendicular)
d. <1, 1, 1> • <1, -1, 1> = 1 - 1 + 1 = 1 (not perpendicular)
e. <1, 1, 1> • <1, 0, 1> = 1 + 0 + 1 = 2 (not perpendicular)
Therefore, the vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c.
Learn more about Vector
brainly.com/question/29740341
#SPJ11
Indigo built a toy box in the shape of a rectangular prism with an open top. The diagram below shows the toy box and a net of the toy box. What is the surface area, in square centimeters, of the toy box? (Lengths are 9cm, 5cm and 10cm)
The surface area, in square centimeters, of the toy box is 370 cm²
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area. Surface area is measured in cm².
Given, the lengths are 9 cm, 5 cm, and 10 cm.
To calculate the surface area, the formula is2(h × W) + 2(h × L) + 2(W × L)
2 x 9 x 5 + 2 x 9 x 10 + 2 x 5 x 10
90 + 180 + 100
370
Therefore, the surface area of the box is 370 cm²
Learn more about surface area, here:
https://brainly.com/question/29298005
#SPJ1
The question is incomplete, the image of the box is attached below:
If
sinα=− 4
3
,π⩽α⩽ 2
3π
, find the exact value of: a
cosα
b
sin2α
c
cos2α
d
tan2αcos 2
α
sin 2
α
The exact values are:
cosα = -√7/3
sin2α = 8√7/9
cos2α = -7/9
tan2αcos2α/sin2α = 1
If sinα = −4/3, π⩽α⩽2π/3, we can find the exact value of cosα, sin2α, cos2α, and tan2αcos2α/sin2α by using the trigonometric identities.
cosα = √(1 - sin²α) = √(1 - (-4/3)²) = √(1 - 16/9) = √(-7/9) = -√7/3
sin2α = 2sinαcosα = 2(-4/3)(-√7/3) = 8√7/9
cos2α = 1 - sin²α = 1 - (-4/3)² = 1 - 16/9 = -7/9
tan2αcos2α/sin2α = (sin2α/cos2α)(cos2α/sin2α) = 1
Therefore, the exact values are:
cosα = -√7/3
sin2α = 8√7/9
cos2α = -7/9
tan2αcos2α/sin2α = 1
Learn more about Trigonometric identities
brainly.com/question/24377281
#SPJ11
Use the long division method to find the result when x^(4)-6x^(2)-x-19 is divided by x-3
The result obtained when x^(4)-6x^(2)-x-19 is divided by x-3 using long division method is x3 - 18x2 - 9x - 57 + 19/x-3.
The question is, "Use the long division method to find the result when x^(4)-6x^(2)-x-19 is divided by x-3".
To solve this problem using long division, we need to set up the division like this:
x4 - 6x2 - x - 19
___________________ (x-3)
0
-3x3 - 18x2 - 9x - 57
Now, divide the first term of the numerator by the first term of the denominator, x4/x = x3, and write it above the division. Next, multiply the result x3 by the denominator (x-3) to get -3x3.
Now subtract -3x3 from the numerator (x4 - 6x2 - x - 19) to get -6x2 - x - 19. Divide this by the denominator (x-3) to get -18x2 - 9x - 57, and write it below the division. Now multiply the result -18x2 by the denominator (x-3) to get -54x2 - 27x - 171.
Finally, subtract -54x2 - 27x - 171 from -6x2 - x - 19 to get the remainder, -19.
To know more about long division click on below link:
https://brainly.com/question/28824872#
#SPJ11