The velocity vector of the given path r(t) = (9cos2(t), 3t - t^3, 2t) is [tex]v = 9sint\hat{i}+(3-3t^{2} )\hat{j} +2\hat{k}[/tex].
According to the given question.
We have a path
r(t) = (9cos2(t), 3t - t^3, 2t)
So, the vector form of the above vector form can be written as
[tex]r(t) = 9cos2(t)\hat{i}+ (3t - t^{3} )\hat{j} + 2t\hat{k}[/tex]
As, we know that the rate of change of position of an object is called velocity vector.
Therefore, the velocity vector of the given path r(t) = (9cos2(t), 3t - t^3, 2t) is given by
[tex]v = \frac{d(r(t))}{dt}[/tex]
[tex]\implies v = \frac{d(9cost\hat{i}+(3t-t^{3})\hat{j}+2t\hat{k} }{dt}[/tex]
[tex]\implies v = \frac{d(9cost\hat{i})}{dt} +\frac{d(3t-t^{3})\hat{j} }{dt} +\frac{d(2t)}{d(t)}[/tex]
[tex]\implies v = 9sint\hat{i}+(3-3t^{2} )\hat{j} +2\hat{k}[/tex]
Hence, the velocity vector of the given path r(t) = (9cos2(t), 3t - t^3, 2t) is [tex]v = 9sint\hat{i}+(3-3t^{2} )\hat{j} +2\hat{k}[/tex].
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help me with this please
Answer:
48
Step-by-step explanation:
The area of this circle is
[tex]\pi( {4}^{2} ) = 16\pi = 50.27[/tex]
about 50.27 square centimeters. So 48 square centimeters seems reasonable here since 3 is used for π.
Marcus had $50 in the bank and deposited
$x a week. At the end of 15 weeks, he had
$1,010 in the bank. Write and solve an
equation to determine how much money he
deposited each week.
13)
Answer:
$64
Step-by-step explanation:
Equation: 50 + 15x = 1010
x = (1010 - 50) ÷ 15 = 64
Since x is the total amount of money deposited in the bank per week, the answer is $64.
Russell has $38 and is saving $2 per day. cornelius has $64 and is spending $2 per day. after how many days will russell have more money than cornelius?
The equation be 38 + 2x - (64 - 2x) = 0 then the value of x = 6.5.
How to find the value of x?To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Let the day be x
38 + 2x - (64 - 2x) = 0
Subtract 38 from both sides
38 + 2x - (64 - 2x) - 38 = 0 - 38
Simplifying the above equation, we get
2x - (64 - 2 x) = -38
Expanding the above equation, 2x - (64 - 2x) = 4x - 64
4x - 64 = -38
Add 64 to both sides
4x - 64 + 64 = -38 + 64
Simplify
4x = 26
Divide both sides by 4
[tex]$\frac{4 x}{4}=\frac{26}{4}[/tex]
Simplifying the equation
[tex]$x=\frac{13}{2}[/tex]
The value of x = 6.5.
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Evaluate the line integral
6 integral yzcosx ds x = t, y = cost, z = sint 0 < t < pi
It looks like the integral is
[tex]\displaystyle 6 \int yz\cos(x) \, ds[/tex]
With [tex]x=t[/tex], [tex]y=\cos(t)[/tex], and [tex]z=\sin(t)[/tex], the line element is
[tex]ds = \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt}\right)^2 + \left(\dfrac{dz}{dt}\right)^2} \, dt = \sqrt2 \, dt[/tex]
and so
[tex]\displaystyle 6 \int yz\cos(x) \, ds = 6\sqrt2 \int_0^\pi \cos^2(t) \sin(t) \, dt[/tex]
Substitute [tex]u = \cos(t)[/tex] and [tex]du=-\sin(t)\,dt[/tex], then
[tex]\displaystyle 6 \int yz\cos(x) \, ds = -6\sqrt2 \int_1^{-1} u^2 \, du = 12\sqrt2 \int_0^1 u^2 \, du = \boxed{4\sqrt2}[/tex]
where in the second-to-last equality, we have
[tex]\displaystyle -\int_1^{-1} = \int_{-1}^1[/tex]
and
[tex]\displaystyle \int_{-1}^1 u^2 \, du = 2 \int_0^1 u^2\,du[/tex]
by symmetry.
algebra 2: graph question
what is the value of a?
what is the value of b?
(graph attached)
Answer:
a = 3.14
b = 6.28
Step-by-step explanation:
The interval where the function is decreasing is where increasing x values result in decreasing y values. The y values peak at the point (3.14, 2) and decrease until the point (6.28, 0) where the function starts increasing again.
A video game shop is analyzing its sales performance using matrices. matrix a contains the unit sales data for each product category (horizontally) per week (vertically). matrix b contains the unit sales data for weekends for each category (horizontally) per week (vertically). to find the number of games in each product category that were sold each week only on weekdays, which matrix operation must be performed? a. add matrix a to the inverse of matrix b. b. more data is needed to calculate the sales during weekdays. c. subtract matrix b from matrix a. d. add matrix b to matrix a.
Answer:
Matrix B should be subtracted from Matrix A.
Step-by-step explanation:
Identify the inequality
that describes this graph.
y≤x + 5
y>x+5
The inequality that describes this graph is y ≥ x+5
How to determine the inequality?From the given graph, we have the following highlights:
The line of the graph is a closed lineThe upper part is shadedThe first highlight above implies, the inequality can be any of ≥ and ≤
While the second highlight above implies, the inequality is ≥
Hence, the inequality that describes this graph is y ≥ x+5
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Find the absolute maximum and minimum values of the function, subject to the given constraints. k(x,y)=−x2−y2 4x 4y; 0≤x≤3, y≥0, and x y≤6
For function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
For given question,
We have been given a function k(x, y) = -x² - y² + 4x + 4y
We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
First we find the partial derivative of function k(x, y) with respect to x.
⇒ [tex]k_x=-2x+4[/tex]
Now, we find the partial derivative of function k(x, y) with respect to y.
[tex]\Rightarrow k_y=-2y+4[/tex]
To find the critical point:
consider [tex]k_x=0[/tex] and [tex]k_y=0[/tex]
⇒ -2x + 4 = 0 and -2y + 4 = 0
⇒ x = 2 and y = 2
This means, the critical point of function is (2, 2)
We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
Consider k(0, 0)
⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)
⇒ k(0, 0) = 0
Consider k(3, 3)
⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)
⇒ k(3, 3) = -9 - 9 + 12 + 12
⇒ k(3, 3) = -18 + 24
⇒ k(3, 3) = 6
Therefore, for function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
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Calling out to anyone who knows this. Seeking assistance!
Answer: someone already answered this check the link out
Step-by-step explanation. https://brainly.com/question/11711784
What is the value of y?
Z
Y
60 degrees
70 degrees
50 degrees
Using proportions, the value of y is of 100º.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In a circle, the measure of an arc is twice the measure of it's equivalent internal angle. The internal angle is of 50º, hence the measure of the arc, given by y, is found as follows:
y = 2 x 50º = 100º.
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which relation is a function?
The relation that is a function is:
b. y = 2x² - 3x + 7
When a relation is a function?A relation is a function if each value of the input is mapped to only one value of the output.
Hence, when both x and y are squared, we have that [tex]x = \pm ay[/tex], hence it is not a function. This is the case for items a and c.
For item d, we have that the relation can be simplified as follows:
x = -y² + 3y
x = y(-y + 3)
The solution above, is associated to two values of y, hence it is also not a function. Then the function is given by:
b. y = 2x² - 3x + 7
In the solution, it can be seen that for each input x, only one value of y can be generated.
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Select the correct answer.
Which equation represents the vertical line passing through (14.-16)?
OA
OB. y=-16
OC
X= 14
OD.
y=14
X=-16
Check the picture below.
find the missing length 25 and 65
Answer: 60.
Step-by-step explanation:
Let in a right triangle one of the legs is 25, and the hypotenuse is 65.
Hence, the other leg is: [tex]\sqrt{65^2-25^2}=\sqrt{4225-625}=\sqrt{3600}=60.[/tex]
60. In the given figure, PTR is tangent of a circle. If AT=PT and ZAPT=20°, what is the value of ZABT?
The value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that:
A circle is shown in the picture.
PTR is the tangent of a circle.
AT=PT
Angle APT=20°
Let O is the center of the circle:
Angle BOT = 2 Angle PAT = 40 degrees
BO = TO = r
Angle BOT = Angle TBO = (1/2)(180 - 40) = 70 degrees
RTP is the tangent
OT ⊥ PTR
Angle OTA = 90 - Angle ATR = 50 degrees
Angle ABT = 180 - Angle PAT - Angle BTA
= 180 - 20 - (170 + 50)
= 40 degrees
Thus, the value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
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please answer this question I f0ll0w u and mark brainiest and give many thanks
Answer:
look above
Step-by-step explanation:
hope it helps
While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2. 4 m/s relative to the surface of the walkway, you decide to try to determine the speed of the walkway itself. You watch the child run on the entire 18-m walkway in one direction, immediately turn around, and run back to his starting point. The entire trip takes a total elapsed time of 32 s. Given this information, what is the speed of the moving walkway relative to the airport terminal?.
The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.
How to estimate the speed of the moving walkway relative to the airport terminal?Let x be the speed of the walkway.
(2.8 + x) = speed of child moving in direction of the walkway
(2.8 - x) = speed of child moving against the direction of the walkway
Travel time = distance/speed
Travel time of child moving in direction of walkway = 23/(2.8+x)
Total elapsed time given = 29s
23/(2.8 + x)+ 23 / (2.8-x) = 29
LCD = (2.8 + x)(2.8 - x)
[tex]23(2.8 - x) + 23(2.8 + x) = 29(2.8 + x)(2.8 -x)[/tex]
simplifying the equation, we get
[tex]23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)[/tex]
[tex]23(2.8+2.8)/29=2.8^2-x^2[/tex]
[tex]x^2=(2.8)^2-(23*5.6)/29)=3.4[/tex]
[tex]x=\sqrt{3.4}=1.84m/s[/tex]
Speed of walkway = 1.84 m/s
The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.
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Build Your Math Skills 2A, Round decimals to the nearest hundredth (0.01): 42.988
Answer: 42.99
Step-by-step explanation:
42.988. Since 8 is close to ten and is in the hundredth we round it hence 42.99.
Is there anyone who help me in my math work
Answer:
LCM=72
Step-by-step explanation:
l.c.m by prime factorization
a)18,24
factor of 18=2*3*3
factor of 24=2*2*2*3
common and remaining factor=2*3*3*2*2= 72
I need help asap please help me
Answer:
8
Step-by-step explanation:
I belive what they mean is how many dots thier are i am not complety sure though but just by counting them up i came up with 8.
hope this helped
the sides of each square have a length of 3 inches. what is the perimeter of Edgar's check boar
Answer:
(b) 96 inches
Step-by-step explanation:
The perimeter of the board is the sum of its four edge lengths.
Edge lengthEach edge of the board is indicated as being 8 squares long. Each square is 3 inches on a side, so the edge of the board is ...
8 × (3 in) = 24 in . . . . board edge length
PerimeterThe perimeter of the board is 4 times the length of one edge, so is ...
P =4s = 4(24 in) = 96 in
The perimeter of Edgar's checkerboard is 96 inches.
__
Scaled geometry (alternate solution)The perimeter of one small square on the board is ...
P = 4s = 4(3 in) = 12 in
The whole board is a dilation of one square by a factor of 8. Its perimeter will be ...
P' = (scale factor) × P
P' = 8×(12 in) = 96 in
The perimeter of Edgar's checkerboard is 96 inches.
Briefly describe each of the eight guidelines for evaluating statistical studies.
8 Guidelines for Critically Evaluating a Statistical Study
1. Identify the Goal, Population, and Type of Study
2. Consider the Source
3. Examine the Sampling Method
4. Look for Problems in Defining or Measuring the Variables of
Interest
5. Watch Out for Confounding Variables
6. Consider the Setting and Wording of Any Survey
7. Check That Results Are Fairly Represented in Graphics or
Concluding Statements
8. Stand Back and Consider the Conclusions
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When navigating the maze, the robot will only need to go north, south, east, and west. it can be useful to use the complex plane to represent these directions. when using the complex plane this way, we use numbers such that their magnitude is equal to 1. if we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?
The values represent the robot facing east, south, and west are 1, -i, -1.
What was the meaning of puzzle?To offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve : challenge mentally also : to exert (oneself, one's mind, etc.) over such a problem or situation they puzzled their wits to find a solution.
given that,
The robot can only go north, south, east and west.
Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.
Now,
It is provided that the ' i ' represent that robot is facing north.
So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.
Since, the values on y-axis are negative in that direction.
Hence, South will be represented by ' - i ' .
Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.
So, the value that represents East will be 1.
(as it is on the positive x-axis ).
Since, west is in the opposite direction of east.
So, West will be represented by -1.
Hence,The values represent the robot facing east, south, and west are 1, -i, -1.
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What is the range of the data? 6 7 9 10
Answer:
4
Step-by-step explanation:
10 - 6 = 4
find the exepted value of the random varible with the following probability distribution x=2,3,4,5,6,7,8,9,10,11,12 Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36
The expected value of the random variable is 7
How to determine the expected value of the random variable?The probability distribution is given as:
x=2,3,4,5,6,7,8,9,10,11,12
Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36
The expected value of the random variable is calculated using
E(X) = ∑xP(x)
Using the above formula, we have
E(x) = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9+ 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18+ 12 * 1/36
Evaluate the sum of products
E(x) = 7
Hence, the expected value of the random variable is 7
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Find a power series representation for the function
Recall the power series expansions of [tex]\sin(x)[/tex] and [tex]e^x[/tex].
[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1}[/tex]
[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{1}{n!} x^n[/tex]
By substituting [tex]3x[/tex] for [tex]x[/tex] in the latter series, we have
[tex]\displaystyle e^{3x} = \sum_{n=0}^\infty \frac{1}{n!} (3x)^n = \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]
Then the series expansion of [tex]f(x)[/tex] is
[tex]\displaystyle f(x) = x^3 \sin(x) + e^{3x+2} \\\\ ~~~~~~~~ = x^3 \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2(n+2)} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]
[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.
Find the power series representation for the function:In the question the given function is,
⇒ f(x) = x³sin(x) + e³ˣ⁺²
We know that series representation of sin x and eˣ are:
[tex]sin x = \sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1}[/tex][tex]e^{x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]⇒ [tex]e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]
= [tex]\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
Substituting the series representation in the function we get,
⇒ f(x) = x³sin(x) + e³ˣ⁺²
⇒ [tex]f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
Hence [tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².
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What is the value of x in the equation7x+2y=48 , when y = 3?
Answer:
x = 6
Step-by-step explanation:
put '3' in where 'y' is :
7x + 2(3) = 48
7x + 6 = 48 subtract 6 from both sides of the equation
7x = 42 divide both sides by 7
x = 6
a) Solve
4(x-7)= 14
(2)
Answer:
x=14
Step-by-step explanation:
4(x-7)= 14(2)
4x - 28 = 28
4x = 56
x = 14
solve for x in x²+8x+15=0 in factorisation method
Answer: [tex]x=-5, -3[/tex]
Step-by-step explanation:
[tex]x^2 +8x+15=0\\\\(x+5)(x+3)=0\\\\x=-5, -3[/tex]
Select the correct answer.
Graph the following system of inequalities.
y ≥x-2
y ≤-4x - 2
y
-6-5
6
0 1 2 3 4
X
9
5
2
F
6
12 RE
NUE
F
4 5 6
Answer:
I don't understand the formatting after the first two equations.
Step-by-step explanation:
See attached graph.
Elijah has a flower box in shape of a rectangular prism with injector dimensions that are 15 inches in length, 8 inches in width height. elijah will flower box 3/4 full of soil. how many cubic inches of soil will be in flower box?
720 cubic inches of soil will be in the flower box.
Cuboid Definition: Cuboid shaped objects surround us in our day-to-day life. From television sets, books, carton boxes to bricks, mattresses, and shoeboxes, cuboid objects are all around us. In Geometry, a cuboid is a three-dimensional figure with six rectangular faces, twelve edges, and eight vertices.
Volume of Cuboid = Length x Width x Height
∴ The volume of the soil box = 15 x 8 x 8 = 960 inch³
Since 3/4 is occupied by the soil, the volume of the soil becomes
= 3/4 x 960
= 720 inch³
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