The wire in the shape of a helix, described by r(t) = 4 cos(t)i + 4 sin(t)j + 5tk, forms a spiral curve that rotates around the z-axis. It has a radius of 4 units in the x-y plane and extends along the z-axis for a height of 5 units. This periodic and symmetric helix exhibits intriguing geometric properties and finds applications in various fields.
The wire in the shape of a helix is given by the equation r(t) = 4 cos(t)i + 4 sin(t)j + 5tk. This helix is parameterized by the variable t, which represents the angle of rotation around the helix. Let's explore the properties and characteristics of this helix in more detail.
The helix is defined in three-dimensional space by the position vector r(t), where i, j, and k represent the unit vectors along the x, y, and z-axes, respectively. The coefficients 4 and 5 determine the shape and size of the helix. The cosine and sine functions modulate the x and y coordinates, respectively, as t varies.
The helix has a radius of 4 units in the x-y plane, and it extends along the z-axis with a height of 5 units. As t increases, the helix rotates around the z-axis, creating a spiral shape. The period of the helix is 2π, meaning it completes one full rotation around the z-axis in 2π units of t.
To visualize the helix, we can plot points on the curve for different values of t. As t ranges from 0 to 2π, we obtain a complete representation of the helix. The helix starts at the point (4, 0, 0) when t = 0, and as t increases, it gradually winds around the z-axis, reaching its maximum height of 5 units when t = 2π.
One interesting property of this helix is that it is a periodic curve, meaning it repeats itself after one full rotation. This periodicity arises from the periodic nature of the cosine and sine functions. Additionally, the helix is symmetric with respect to the z-axis, as the coefficients of i and j are the same.
The helix can be useful in various applications, such as modeling DNA structures, representing spiral staircases, or describing the paths of certain celestial objects. Its elegant and repetitive nature makes it a fascinating geometric object to study.
In summary, the wire in the shape of a helix, described by r(t) = 4 cos(t)i + 4 sin(t)j + 5tk, forms a spiral curve that rotates around the z-axis. It has a radius of 4 units in the x-y plane and extends along the z-axis for a height of 5 units. This periodic and symmetric helix exhibits intriguing geometric properties and finds applications in various fields.
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Just for curiosity, which ‘high school/secondary school’ education is harder, the UK or USA?
Answer:
UK
Step-by-step explanation:
Triangle PQR has coordinates P (2, 4), Q (-2, 4), R (0,-6).
Write the coordinates of the vertices of the image of a
triangle after a dilation of 2.5.
Select 3 coordinates only.
A) P' (5, 10)
B) P' (0.8, 1.6)
C) Q' (-5, 10)
D) Q' (-0.8, 1.6)
E) R' (-6,0)
F) R' (0, -15)
Answer: P’ (5,10) , Q’ (-5,10) , R’ ( 0,-15)
Step-by-step explanation:
Just multiply 2.5 by the x,y
Answer:dec I think
Step-by-step explanation:
Is 1 + 4(3x – 10) – 12x equivalent to -9?
Answer:
No.
Step-by-step explanation:
Remove parenthesis:
1+12x-40-12x
Combine like terms:
-39+0x = -39. -39 is NOT equal to -9.
I need help it's geometry
Step-by-step explanation:
[tex] \sin(45) = \frac{x}{5} \\ \frac{1}{ \sqrt{2} } = \frac{x}{5} \\ x = \frac{5}{ \sqrt{2} } = 3.535[/tex]
[tex] \sin(45) = \frac{y}{5} \\ y = \frac{5}{ \sqrt{2} } = 3.535[/tex]
Answer:
[tex]\frac{5\sqrt{2} }{2 }[/tex]
Step-by-step explanation:
x=y
45-45-90 equation is x-x- x square root of 2
What is the domain of all of these points?
(8, 2), (12,9), (16, 16), (20, 23)
Answer:
8, 12, 16, 20
Step-by-step explanation:
those are the domains
The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 27 text messages is taken and results in a sample mean of 25 characters, find a 95% confidence interval for the population mean. Round your answers to two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576 You may use a calculator or the common z-values above.
Answer:
(22.74 ; 27.26)
Step-by-step explanation:
The confidence interval relation is stated as :
Mean ± Zcritical * σ/sqrt(n)
Mean = 25
σ = 6
The Zcritical at 95% = 1.96
Hence,
25 ± 1.96 * (6/sqrt(27))
25 ± 1.96 * 1.1547005
Lower boundary :
25 - (1.96 * 1.1547005) = 22.73678702
Upper boundary :
25 + (1.96 * 1.1547005) = 27.26321298
(22.74 ; 27.26)
3 x (5 + 7)
What two words can describe (5 + 7) in the expression above?
O A. quotient and factor
OB.
difference and factor
OC. sum and factor
OD. sum and quotient
The expression contain sum and factor.
The correct option is (C).
What is Expression?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Given:
3 x(5+7)
In the Above Expression we have two operation Multiplication and Addition.
Also, the Multiplication is also termed as factor.
Hence, the expression contain sum and factor.
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Which of the following nets is for a pyramid?
2nd one
hope it helps you
The net of the pyramid is given by figure B
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
A net is a two-dimensional representation of a three-dimensional shape that, when folded along the edges, forms the shape of the solid.
In the case of a pyramid, the net consists of a polygonal base and triangular faces that meet at a common vertex.
The number of triangular faces depends on the type of pyramid (triangular, square, pentagonal, etc.).
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What will be the cost of the paving if cement costs $26.50 per square metre?
Answer:
hey
Step-by-step explanation:
4k squared = 100 solve for k
Answer:
k = 5
Step-by-step explanation:
4k^2 = 100
4k^2/4 = 100/4
k^2 = 25
k=5
(−3⋅10^3 )⋅(4⋅10^6)=???
Answer:
-1.19164 x 10^8
Step-by-step explanation:
pls help me it is inportant
Answer:
(5.x)+(5.2)
Step-by-step explanation:
Hope it helps you......
Answer:
nah
Step-by-step explanation:
f(x) = -3x + 3
f(-2) = [?]
Help
is this the answer you're looking for? I'm sorry I'm confused
can somebody help with this please dont put fake answers i really need to pass this test
Step-by-step explanation:
by using Pythagoras theorem,
h^2= p^2+b^2
or, b^2=h^2- p^2
Answer:
it's 24 cm
30²-18²=
b²=900-324= 576
b²=576
b=24
What is the volume of the cylinder below?
Answer:
11253.76
Step-by-step explanation:
We know that the formula for the volume of a cylinder is pi(r^2)(h) and we have both the radius (8 yards) and the height (56 yards) given to us. Given this, we can plug those numbers into the equation and do pi x (8)^2 x 56 which is simplified to 3.14 x 64 x 56, and when we solve this out we can get a final answer of 11253.76
workout the value of (2^3)^2
Answer:
64
Step-by-step explanation:
(2^3)^2 = (8)^2 = 64
The heights of tomato plants are Normally distributed with Calculate the Z-score for a tomato plant that has a a mean of 3.56 feet and a standard deviation of 0.25 feet height of 4.07 feet. Use the z-lable to answer the question. The Z-score, rounded to 2 decimal places, for a tomato plant that has a height of 4.07 feet is About what percent of tomato plants have a height less than 4.07 feet? Round the percent to 2 decimal places, if necessary About % of tomato plants have a height less thah 4.07 feet
the answers are for the first 2.04% and the second tis 97.93% trust bb :>
Answer:
97.03
Step-by-step explanation:
it is the answer
if it is not then I am sorry
In Normal distribution(z) tomato plants have height less than 4.07 feet is 97.93 %.
What is normal distribution?Normal distribution is a "continuous probability distribution that its symmetrical around its mean with most values near the central peak".
According to the question,
The heights of tomato plants are Normally distributed.
Mean(μ) = 3.56
Standard deviation (σ) = 0.25
For a tomato plants that has a height of 4.07 feet
In order to find Percentage of tomato plants have a height less than 4.07 feet
Standard Normal Distribution Formula,
z = (x-μ)/σ where X~(μ,σ).
= [tex]\frac{4.07-3.56}{0.25}[/tex]
= [tex]\frac{0.51}{0.25}[/tex] = 2.04.
P ( x < 4.05) = P( z < 2.04 )
= 0.9793 ( Using standard Normal distribution table)
To find the percentage of tomato plants have height less than 4.07 feet is
multiply 0.9793 by 100
= 97.93%
Hence, Using Standard Normal distribution we find tomato plants have height less than 4.07 feet is 97.93 %
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Help fast please. I will give brainliest.
Answer:
Q5 ) A 80 UNITS²
pls give me brainliest
Find the ratio of 580 ml to 1.12 I to 104 ml
Answer:
580 : 1120 : 104
Step-by-step explanation:
1.12 ml -> 1120 ml
hence,
580 : 1120 : 104
solve the equation 3(x + 1) + 6 = 33.
Answer:
155
Step-by-step explanation:
How many liters of 30% salt solution must be added to 6 L of an 80% salt solution to obtain a 50% salt solution
Answer:
9 Liters
Step-by-step explanation:
Let us represent:
The number of liters of the 30% salt solution = x
Number of liters for the 80% solution = 6 Liters
Number of liters for the 50% solution = x + 6 Liters
Hence:
x × 30% + 6 × 80% = (x + 6)50%
0.3x + 4.8 = 0.5x + 3
Collect like terms
4.8 - 3 = 0.5x - 0.3x
1.8 = 0.2x
x = 1.8/0.2
x = 9 Liters
Therefore, the number of liters for the 30% Salt solution = 9 Liters
What is the slope between
(2,5) (4, 13)
Answer:
m=4..............
Answer:
The slope is: 4.
Step-by-step explanation:
Slope formula:
y2-y1
--------
x2-x1
Plug in the numbers
13 - 5
--------
4-2
Simplify
8
---
2
Simplify again
4
This is your slope.
here you can get free question answer things, so
1+0 = ?
u can get free “helped people”by this
Answer:
the answer is 1
........
1+0=1
Because anything plus zero equals itself (Example) :
3+0=3, 4+0=4, etc
Therefore
1+0=1
Have a good day!
If the mean of 5 numbers is 10 and the mean of other 15 numbers is 20 , what is the combined mean of both 20 numbers
9514 1404 393
Answer:
17.5
Step-by-step explanation:
The sum of the 5 numbers is 5·10 = 50.
The sum of the 15 numbers is 15·20 = 300.
The sum of all 20 numbers is then 50+300 = 350, so their mean is ...
mean = sum/number = 350/20 = 17.5
The combined mean of the 20 numbers is 17.5.
For George’s party, his dad bought an ice cream cake. After the party, 1/3 of the cake was left. The next day, George ate half of what was left. Choose the model that shows what fraction of cake George ate
Answer :
1/3 ÷ 2 = 1/6 left
12 (X + 2) - 4x = 4( 2X + 11 ) -20
Solve for X
Answer:
Step-by-step explanation:
12 (x + 2) - 4x = 4 (2x + 11) - 20
12 + 24 - 4x = 8x + 44 - 20
36 - 4x = 8x + 24
36 - 24 = 8x - 4x
12 = 4x
---- ----
4 4
3 = x
-x = -3
x = 3
Please Help! Ill give brainliest no fakes PLEASE!!
Answer:
4 and then 15
Step-by-step explanation:
second one: 6:4
last one: 15:10
-8= -4+x
Solve for x
Answer:
-4 + x = - 8
x = - 8 +4
x = - 4
hope it helps :-
Answer:
-4=x or x=-4
Step-by-step explanation:
Move -4 to the other side by adding 4 on both sides:
-8+4=4-4+x
-4=x or x=-4
Hope this helps!
what is the decimal word form of 120.95?
x y
0 -6
1 -4
2 -2
3 0
The table above represents what type of function?
A.
neither linear nor nonlinear
B.
nonlinear
C.
linear and nonlinear
D.
linear
Answer: let me check
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
0 -6 is a linear and a nonlinear and it keeps on going