A vector function, also known as a vector-valued function, is a mathematical function that takes one or more inputs, typically real numbers, and returns a vector as the output
1, (a) The distance from v1 to v2 can be found using the formula:
|~v1 - ~v2| = √[(1 - ⇡)² + (3 - e)² + (4 - 7)²] ≈ 5.68
(b) The dot product of v1 and v2 is:
~v1 · ~v2 = (1)(⇡) + (3)(e) + (4)(7) = 31
The cross product of v1 and v2 is:
~v1 ⇥ ~v2 = |i j k |
|1 3 4 |
|⇡ e 7 |
= (-17i + 3j + πk)
(c) To find the parametric equation for the line through the points (1, 3, 4) and (π, e, 7), we can first find the direction vector of the line by subtracting the coordinates of the two points:
~d = hπ - 1, e - 3, 7 - 4i = hπ - 1, e - 3, 3i
Then we can write the parametric equation as:
~r(t) = h1,3,4i + t(π - 1, e - 3, 3i)
or in component form:
x = 1 + t(π - 1), y = 3 + t(e - 3), z = 4 + 3t
(d) The equation for the plane containing the points (1, 3, 4), (π, e, 7) and the origin can be found by first finding two vectors that lie in the plane. We can use the direction vector of the line from part (c) as one of the vectors, and the vector ~v1 as the other vector. Then the normal vector to the plane is the cross product of these two vectors:
~n = ~v1 ⇥ ~d = |-3 3 2 |
| 1 π-1 0 |
| 3 e-3 3 |
= (6i + 9j + 3k) ≈ (2i + 3j + k)
Thus the equation of the plane can be written in scalar form as:
6x + 9y + 3z = 0
or in vector form as:
~n · (~r - ~p) = 0, where ~p = h1,3,4i is a point in the plane.
Expanding this equation gives:
2x + 3y + z - 7 = 0
2. To calculate the circumference of a circle of radius r, we can parametrize the circle using polar coordinates:
x = r cos(t), y = r sin(t)
where t is the angle that sweeps around the circle. The arc length element is:
ds = √(dx² + dy²) = r dt
The circumference is the integral of ds over one complete revolution (i.e. from t = 0 to t = 2π):
C = ∫₀^(2π) ds = ∫₀^(2π) r dt = 2πr
To learn more about integral visit:
brainly.com/question/18125359
#SPJ11
How do you solve a table of values?
A table of values basically lists the values of y for the given line given the values of x.
Explain the method to solve table of values?A table of values is a graphic organizer or chart that enables you to choose two or more points from which to make your graph.
Here is an illustration of a table of values for the equation y = 2x + 1.
Put x = 0, y = 1
Put x = 1, y = 3
The method to solve table of values are-
Making a table of values allows you to graph a line using a slope-intercept form equation. To determine the coordinate point's corresponding y-values, choose a few x values and enter those values into the equation. Create a graph and plot the points. To draw the line, join the points together.To know more about the table of values, here
https://brainly.com/question/12151322
#SPJ4
Answer:
Table of Values of a Function displays the table of values for the given function.
Step-by-step explanation:
How To solve the table of Values:The procedure to use the table of values of a function calculator is as follows:
Step 1: Making a table of values allows you to graph a line using a slope-intercept form equation.
Step 2: To determine the coordinate point's corresponding y-values.
Step 3: Choose a few x values and enter those values into the equation.
Step 4: Create a graph and plot the points.
To draw the line, join the points together.
To know more about Table Values: https://brainly.com/question/30243714
#SPJ4
A 2 column table with 5 rows. The first column, yards of red fabric, x, has the entries 1, 2, 3, 4. The second column, yards of blue fabric, y, has the entries 27, 26, 25, 24.
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy? Check all that apply.
The answer choices which represent equations which model the total yards of fabric Sophie will buy is; x + y = 28, 28 - x = y and 28 - y = x.
Which equations model the total yards of fabric Sophie will buy?As evident in the attached table, where x represents the yards of red fabric she buys and y represents the yards of blue fabric she buys.
It follows that the following x and y pairs are possible; (1, 27), (2, 26), (3, 25) and (4, 24).
On this note, it can be inferred that in each of the red and blue fabric pairs; x + y = 28.
Consequently, the required equations which model the total yards of of fabric Sophie will buy are; x + y = 28, 28 - x = y and 28 - y = x.
Complete question; The given answer choices are; x+y=28, 28+x=y, x-y=28, 28-x=y and 28-y=x.
Read more on linear equation models;
https://brainly.com/question/28159620
#SPJ1
Answer:
x+y=28
28-x=y
28-y=x
Find the missing values so that the area of the product is equal to the
area of its sum.
Anothony says that the expression abc has three terms because it uses three different variables. Critique Anothony's reasoning and explain whether he is correct.
According to the mathematical notations, we can say that in this case, Antonhy's reasoning is incorrect, because the expression abc is only one term and not three as he stated.
What are the terms of an expression?It corresponds to a term that has letters and numbers, which are separated only if there is a mathematical sign between them, such as the plus or multiplication sign, for example, to be an expression of three terms, the expression should be like this:
a x b x cTherefore, we can consider that the term abc corresponds to a monomial, as it is only one term in an expression, and not three as supposed by Anthony.
Find out more about monomial term on:
https://brainly.com/question/2279092
#SPJ1
Find Dy/Dx By Implicit Differentiation. x/y +y/x = 3y
The derivative of y with respect to x (Dy/Dx) can be found by using implicit differentiation and is equal to (x/y)(Dx/Dx) / (3y - x - y).
The given equation is x/y + y/x = 3y.
To find the derivative of y with respect to x (Dy/Dx), we will use implicit differentiation.
First, we will take the derivative of both sides of the equation with respect to x:
(1/y) * (Dy/Dx) + (1/x) * (Dy/Dx) + (y/x^2) * (Dx/Dx) = (3)(Dy/Dx)
We can simplify this expression by combining the terms with Dy/Dx and Dx/Dx:
(Dy/Dx)(1/y + 1/x + 3) = (y/x^2)(Dx/Dx)
Now we can solve for Dy/Dx by rearranging the equation:
Dy/Dx = (y/x^2)(Dx/Dx) / (1/y + 1/x + 3)
Finally, we can plug in our known values and solve for Dy/Dx:
Dy/Dx = (x/y)(Dx/Dx) / (3y - x - y)
Therefore, the derivative of y with respect to x (Dy/Dx) can be found by using implicit differentiation and is equal to (x/y)(Dx/Dx) / (3y - x - y).
Learn more about implicit differentiation here:
https://brainly.com/question/11887805
#SPJ4
What comes first in order pairs?
In an ordered pair (x,y), the x-coordinate comes first, followed by the y-coordinate. The x-coordinate represents the horizontal position of the point on a coordinate plane and the y-coordinate represents the vertical position of the point on a coordinate plane.
For example, in the ordered pair (4,3), 4 is the x-coordinate, and it represents the horizontal position, and 3 is the y-coordinate, and it represents the vertical position of the point (4,3) on a coordinate plane.
Your school hope to collect 335 tshirts for the Salvation Army. 134 tshirts were donated the first week and 48 more were donated the second week how many shirt must be donated this week to meet your goal
Answer:
134 + 48 = 182
182 + x = 335
x = 153
Answer:
153
Step-by-step explanation:
335-134=201
201-48=153
Which expression is equivalent to (st)(6)?
s(t(6))
s(x) × t(6)
s(6) × t(6)
6 × s(x) × t(x)
Answer: The expression (st)(6) means to substitute the value of 6 into the function (st) which is the composition of two functions s and t. The order of applying the functions is crucial, so the first function s will be applied to the result of the second function t after being applied to the 6. So the correct equivalent of (st)(6) is s(t(6))
Step-by-step explanation:
NEES ASAP check picture
Answer:
A
Step-by-step explanation:
Your answer was correct.
How do you factor polynomials ?
Answer:I often do is just see how many terms in there if is only have two that will be Binomial, if it was three therm I will just think that probably trinomial, only have one that will be the monomial, more than 3 term i will think it just polynomials.
Please help I’ll give brainliest Write the rule for the linear function in the table
The rule for the linear function in the table include the following: y = 2x.
How to write a rule for the linear function?In order to write a rule for the linear function, we would have to use the point-slope form formula. Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Next, we would determine the linear function representing the relationship between the x-value and y-value in the given table as follows:
y - y₁ = m(x - x₁)
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-4) = (4 - (-4))/(2 - (-2))(x - (-2))
y + 4 = 8/4(x + 2)
y + 4 = 2(x + 2)
y = 2x + 4 - 4
y = 2x
Read more on slope here: brainly.com/question/23086745
#SPJ1
y=5x-9
-2x-3=-7 Please show work
Answer:
Step-by-step explanation:
-2x-3=-7
+3 +3
-2x=-4
/-2 /-2
x=2
Y=5(2)-9
Y=10-9
Y=1
Answer:
Step-by-step explanation:
Given:y = 5x - 9 (eq'n 1)
-2x - 3 = -7 (eq'n 2)
Solution:Solve for x in (eq'n 2)
-2x -3 = -7 (add 3 to both side of the eq'n)
(-2x - 3) + 3 = -7 + 3
-2x = -4 (divide both side by -2)
x = 2
Therefore the value of y is:
From (eq'n 1), Substitute the value of x
y = 5x - 9
y = 5(2) - 9
y = 1
expand and simplify (x+9) (x+3)
The expression (x+9) (x+3) in the simplified expanded form will be x² + 12x + 27.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ (x+9) (x+3)
Simplify the expression, then we have
⇒ (x+9) (x+3)
⇒ x (x+3) + 9(x+3)
⇒ x² + 3x + 9x + 27
⇒ x² + 12x + 27
The expression (x+9) (x+3) in the simplified expanded form will be x² + 12x + 27.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
a box as a volume of 3/4 inches long 1/2 inches wide and 1/4 inches high
The distances between some planets are given below.
Planet Q
Planet Q is 3.5 × 10° km from planet P.
Planet R is 1.2 × 10? km from planet P.
The shortest distance between planet Q and planet R is 1.64 * 10⁷ km
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:
hypotenuse² = adjacent² + opposite²
From the diagram, QR is the shortest distance between planet Q and planet R. Hence using Pythagoras:
QR² = QP² + PR²
QR² = (3.6 * 10⁶)² + (1.6 * 10⁷)²
QR = 1.64 * 10⁷ km
The shortest distance is 1.64 * 10⁷ km
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
What is the exponent 3 called?
The exponent 3 is called the power or index. It is the number that indicates how many times the base number (in this case 3) is multiplied by itself.
To determine this
For example, 3³ means 3 multiplied by itself 3 times, or 3 x 3 x 3 = 27. So 3 is the base number and 3 is the exponent or power.
In mathematical notation, the exponent is written as a small number or variable above and to the right of the base number, with a caret symbol (^) separating them. For example, 3³ is written as 3³, and x² is written as x².
Additionally, in mathematics, exponents are also used to represent the number of times a number is multiplied by itself, the exponent number represents how many times the number is being multiplied.
To learn more about the exponent, visit:
brainly.com/question/30066987
#SPJ4
Need the answers am having trouble with this last question help me pls
Answer:
A, B, C, and G
Step-by-step explanation:
f(0)=75 is true because that's the y-intercept
f(30)=100 is true
f(20)=175 is true
f(0)=0 is not true because we already identified f(0) as 75
f(x)=100 when x=20 is not true because we already identified f(20) as 175
f(10)<f(5) is not true because looking at the graph, f(10)>f(5)
f(10)=f(15) is true because the graph is constant between the two points
A savings account is opened with an initial deposit of $425.00. determine the account balance after 9 years if the account earns 2.7% simple interest annually. $3,928.28 $1,457.75 $528.28 $103.28
The account balance after 9 years is $528.28. The result is obtained by adding the interest to the initial deposit.
How to count the simple interest?
The simple interest of an amount of money can be counted by the following formula.
I = P₁ - P
I = P × r × t
Where
I = simple interestP = principal amount (initial balance)P₁ = final balancer = simple interest ratet = time periodWe have
Initial deposit, P = $425.00.Time period, t = 9 years.Simple interest rate, r = 2.7% per year.Find the final account balance!
After 9 years, the simple interest of the savings is
I = P × r × t
I = $425.00 × 2.7% × 9 years
I = $3,825.00 × 0.027
I = $103.28
The final account balance would be
I = P₁ - P
$103.28 = P₁ - $425.00
P₁ = $425.00 + $103.28
P₁ = $528.28
Hence, after 9 years, the account balance would be $528.28.
Learn more about simple interest here:
brainly.com/question/29800198
#SPJ4
What do you observe about the end behavior tails of the graphs of the polynomial functions?
The end behavior of the graphs of polynomial functions is determined by the highest degree of the polynomial.
For example, a polynomial with degree n will eventually approach infinity as x increases or decreases without bound. This can be expressed mathematically as:
f(x) = axn -> lim x->∞ f(x) = ∞
and
f(x) = axn -> lim x->-∞ f(x) = ∞
where a is a constant.
For a polynomial of degree n, the graph will have n-1 turning points. As the degree increases, the graph approaches a smooth curve. Additionally, the graph will have either one up-turn or one down-turn depending on the sign of the leading coefficient. If the leading coefficient is positive, the graph will have an up-turn; if the leading coefficient is negative, the graph will have a down-turn.
For example, the end behavior of the graphs of the polynomial f(x) = 2x3 + 2x2 - 2x - 1 has degree 3, so it will have 2 turning points and will have an up-turn as the leading coefficient is positive.
Learn more about end behavior of the graphs here:
https://brainly.com/question/11808280
#SPJ4
What two numbers multiply to give you 16 and add up to give you negative 8
Answer:
-4 and -4
Step-by-step explanation:
A train will travel 300300300 kilometer at a contant rate. 1. Write an equation that repreent the train' rate in kilometer per hour (rrr) baed on how many hour the trip take (ttt)
The equation that represents how many hours it will take if train travel at a constant rate of r kilometers per hour speed is t = 300/r
Define Speed :This is defined as the ratio of distance to time taken usually in kilometers per hour, miles per hour.
The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
How to write equation
Distance Saul biked = 300 kilometers
Number of hours it takes train travel = t
Speed of train travel (kilometers per hour) = r
Speed = Total distance travelled / Time taken
r = 300 / t
Equation that represents how many hours
Make t the subject of formula
r = 300 / t
cross product
r × t = 300
t = 300/r
Therefore,
The equation that represents how many hours it will take if train travel at a constant rate of r kilometers per hour speed is t = 300/r
To learn more about Speed problems visit :
brainly.com/question/28416040
#SPJ4
How do you calculate 2 + 3 x 7?
a. 2+3 x 7 = 2+21= 23
b. 2+7x7 = 2 + 21 = 35
C. 2+7x3 = 2 + 21 = 23
Answer:
A
Step-by-step explanation:
using BODMAS
3×7=21+2=23
Find the 10th term in this
quadratic sequence.
2n² + 3
A.5
B.43
C. 105
D. 203
Answer:
D
Step-by-step explanation:
to find the 10th term substitute n = 10 into the rule, that is
2(10)² + 3
= 2(100) + 3
= 200 + 3
= 203
the 10th term is 203
If f(x) = 2x2 - 7x - 7, find f(6)
Step-by-step explanation:
f(x) = 2x² - 7x - 7
f(6) = 2(6)² - 7(6) - 7
f(6) = 72 - 42 - 7
f(6) = 23
the hieghts of the people if the plant Ixx are normally distributed with a mean of 40 inches and a standard deviation of 5 inches. [ they are vertically diverse people.]
The percentage and the z-scores for specific heights of the given normal distributions are as detailed below.
How to Interpret normal distribution?
The first step is to draw the Normal curve with 8 regions, and then we now label the 7 vertical dividing lines with the mean plus/minus one/two/three standard deviations:
By adding the percentage values in the areas indicated in the question, we will arrive at;
The percentage of Ixxians that are;
i) Over 30 inches tall = 100% - (2.35% + 0.15%) = 97.5%
ii) Over 45 inches tall = 13.5% + 2.35% + 0.15% = 16%
iii) Under 50 inches tall = 100% - (2.35% + 0.15%) = 97.5%
iv) under 40 inches tall = 34% + 13.5% + 2.35% + 0.15% = 50%
v) between 35 and 55 inches tall = 34% + 34% + 13.5% + 2.35% = 83.85%
vi) between 25 and 35 inches tall = 13.5% + 2.35% 15.85%
The z-score is defined as the number of standard deviations above the mean corresponding to the given value. Thus;
i. For a height of 32 inches, the z-score is;
z = [32-40]/5
z = -1.6
ii. For a height of 47 inches, the z-score is;
z = [47 - 40]/5
z = 1.4
iii. For a height of 51 inches, the z-score is;
z = [51 - 40]/5
z = 2.2
Read more about Normal Distribution at; https://brainly.com/question/4079902
#SPJ1
Complete question is;
The hieghts of the people if the plant Ixx are normally distributed with a mean of 40 inches and a standard deviation of 5 inches. [ they are vertically diverse people.]
a) What percentage of Ixxians are
i over 30 inches tall?
ii over 45 inches tall?
iii under 50 inches tall?
iv under 40 inches tall?
v between 35 and 55 inches tall?
vi between 25 and 35 inches tall?
b) What is the z-score for an Ixxian of height?
i. 32 inches?
ii. 47 inches
iii. 51 inches
Determine whether each function is linear. write yes or no. explain.
can someone please help me with this question?
Answer:
yes, it is linear
Step-by-step explanation:
the x is +3 to each one, and the y is -1 to each one, this keeps it linear
The graph of g(x) is transformed from its parent function, ). Apply concepts involved in determining the key features of
1
X-6
a rational function to determine the domain and range of the function, g(x)=
A. What is the domain of the function, g(x)?
B. What is the range of the function, g(x)?
Answer:
X = 10
Step-by-step explanation:
I need help with these questions. Please help.
Does (0, 5) make the equation y = x + 5 true?
What is the volume of this cylinder?
Use 7 = 3.14 and round your answer to the nearest hundredth if necessary.
15 cm
cubic centimeters
18 cm
On solving the provided question, we can say that volume of cylinder = [tex]\pi r^2h[/tex] = 13564.8
what is cylinder?One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.
volume of cylinder = [tex]\pi r^2h[/tex]
[tex]\pi[/tex] = 3.14
r = 15 cm\
h = 18 cm
V = [tex]3.14*15*16*18[/tex] = 13564.8
To know more about cylinder visit:
https://brainly.com/question/16134180
#SPJ1