Please help me with this question

Answer:

a. i. (i + tj + 2tk)/√(1 + 5t²)

ii.  (-5ti + j + 2k)/√[25t² + 5]

b. √5/[√(1 + 5t²)]³

Step-by-step explanation:

a. The unit tangent

The unit tangent T(t) = r'(t)/|r'(t)| where |r'(t)| = magnitude of r'(t)

r(t) = (t, t²/2, t²)

r'(t) = dr(t)/dt = d(t, t²/2, t²)/dt = (1, t, 2t)

|r'(t)| = √[1² + t² + (2t)²] = √[1² + t² + 4t²] = √(1 + 5t²)

So, T(t) = r'(t)/|r'(t)| = (1, t, 2t)/√(1 + 5t²)  = (i + tj + 2tk)/√(1 + 5t²)

ii. The unit normal

The unit normal N(t) = T'(t)/|T'(t)|

T'(t) = dT(t)/dt = d[ (i + tj + 2tk)/√(1 + 5t²)]/dt

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + [-10tk/√(1 + 5t²)⁻³]

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + j/√(1 + 5t²)+ [-10t²k/√(1 + 5t²)⁻³] + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) - 10t²k/[√(1 + 5t²)]⁻³ + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ - 10t²k/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) + 2k/√(1 + 5t²)

= -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + (j + 2k)/√(1 + 5t²)

We multiply by the L.C.M [√(1 + 5t²)]³  to simplify it further

= [√(1 + 5t²)]³ × -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + [√(1 + 5t²)]³ × (j + 2k)/√(1 + 5t²)

= -(i + tj + 2tk)5t + (j + 2k)(1 + 5t²)

= -5ti - 5²tj - 10t²k + j + 5t²j + 2k + 10t²k

= -5ti + j + 2k

So, the magnitude of T'(t) = |T'(t)| = √[(-5t)² + 1² + 2²] = √[25t² + 1 + 4] = √[25t² + 5]

So, the normal vector N(t) = T'(t)/|T'(t)| = (-5ti + j + 2k)/√[25t² + 5]

(b) Use Formula 9 to find the curvature.

The curvature κ = |r'(t) × r"(t)|/|r'(t)|³

since r'(t) = (1, t, 2t), r"(t) = dr'/dt = d(1, t, 2t)/dt  = (0, 1, 2)

r'(t) = i + tj + 2tk and r"(t) = j + 2k

r'(t) × r"(t) =  (i + tj + 2tk) × (j + 2k)

= i × j + i × 2k + tj × j + tj × 2k + 2tk × j + 2tk × k

= k - 2j + 0 + 2ti - 2ti + 0

= -2j + k

So magnitude r'(t) × r"(t) = |r'(t) × r"(t)| = √[(-2)² + 1²] = √(4 + 1) = √5

magnitude of r'(t) = |r'(t)| = √(1 + 5t²)

|r'(t)|³ = [√(1 + 5t²)]³

κ = |r'(t) × r"(t)|/|r'(t)|³ = √5/[√(1 + 5t²)]³

Answer:

A

Step-by-step explanation:

I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.

Answer:

D

Step-by-step explanation:

the end result of a radical can never be negative unless the negative sign shows outside of the radical

Step-by-step explanation:

the answer is in the above image

Answer:

my answer is 225/5 sorry comments for wrong

Answer:

- 54

Step-by-step explanation:

11 c + 5 a - 8

11 × -6 + 5 × 4 - 8 (given :- a = 4 and b = -6)

- 66 + 20 - 8

- 54

Answer:

I hope this helps

the outcomes are the compulsory 6, and 1 or 2

Step-by-step explanation:

[tex] \frac{3}{6} \\ \frac{1}{2} or \: 0.5[/tex]

Answer:

question 19 = no solution because not enough information

question 20 = 18 for volume

Step-by-step explanation:

question 19:

cylinder formula

surface A =2πrh+2πr2

2π times 9 times 7 + 2π times 9 times 2

SA = 508.938009882

volume equals 395.840674352

question 20:

biggest one,

4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4

V=18 IS the volume

Answer:

The last formulas are called

square based pyramid formula

cone formula

sphere formula

Can help with the first two as im short of time

Hope this helps.

Always remember to check the units^3

Step-by-step explanation:

19)   V = π r 2 h  = 1781.28303 ft3  = 1781.3ft^3

20) V = 1/2 b h l = 180m^3

Answer:

Angle a is not the same as angle y

Step-by-step explanation:

I think

Answer:

[tex]\frac{5105}{22}[/tex]

Step-by-step explanation:

Used Python function to get all the numbers and add them, then I divided it by 22, which is the number of numbers in the array.

The mean of the data is 232.045.

To find the mean of the data.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations). Mean is the most commonly used measure of central tendency. There are different types of mean, viz. arithmetic mean, weighted mean, geometric mean (GM) and harmonic mean (HM).

Given that:

The data are:

217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105

=5105 / 22 = 232.045

So, the mean of the data is 232.045.

Learn more about mean here:

https://brainly.com/question/24072290

#SPJ2

The option is missing:

A. 230.811

B. 231.045

C. 232.045

D. 232.811

Answer:

C 0.90

Step-by-step explanation:

Add 0.10 and 0.80=0.90

Answer:

D

Step-by-step explanation:

P(A and B)=P(A)×P(B)=0.80×0.10=0.08

Answer:

we arrive at the conclusion that the new employee installs the vertical blinds faster on average.

Step-by-step explanation:

null hypothesis; m₁-m₂ =0

alternative hypothesis; m₁-m₂<0

Given the information in this question, we first have to solve for the t statistic

[tex]t=\frac{22-24.8}{\sqrt{\frac{0.90^{2} }{10}+\frac{0.75^{2} }{10} } }[/tex]

[tex]t=\frac{-2.6}{\sqrt{o.081+0.05625} }[/tex]

[tex]t=\frac{-2.6}{0.37047}[/tex]

t = -7.018

the degree of freedom = n₁+n₂-2

= 10+10-2

= 18

Alpha α = 0.05

from these results the t critical value = -1.734

because the test statistic -7.018 < -1.734,

at 0.05 level of testing, we arrive at the conclusion that the new employee installs the vertical blinds faster on average than the veteran.

Answer:

Letter B

Step-by-step explanation:

I used a graphing calculator,

Hope this helps

Answer:

32.25

Step-by-step explanation:

1 quart = 32 fluid ounces

12 months = 1 year

86 quarts/1 month = 1032 quarts/12 months

1032/32 = 32.25 fluid ounces

Hope this might help you (•.•) :)

Answer:

83 or a

Step-by-step explanation:

if angle 6 is 97 then the total would be 180 meaning that 83 would be the answer to 5s angle

"83 degrees" is correct.

On a line, it can be assumed that all the angles must add up to 180 degrees. If you have two angle on a line and don't know the value of one of them, you can subtract that angle from 180 to find the missing angle. Considering this, 180 - 97 = 83.

Answer:

∅ = 83.9º

Step-by-step explanation:

tan = opp/adj

opp = 15 - 1 = 14

tan∅ = 14/1.5

∅ = arctan 14/1.5

use calculator

∅ = 83.884496433714593º

Rounded

∅ = 83.9º

Answer:

Step-by-step explanation:

              Steps                                Justifications

1). -2x = 28 - 6x                               1). Given

2). -2x + 6x = 28 - 6x + 6x              2). Addition property of equality

3). 4x = 28                                       3). Simplification

4). [tex]\frac{4x}{4}=\frac{28}{4}[/tex]                                        4). Division property of equality

5). x = 7                                            5). Simplification

Answer:

37

Step-by-step explanation:

296÷8=37

Hope this helps! :)

Answer:

37 apples will be in 9 boxes

Step-by-step explanation:

296 ÷ 8 = 37

Notice how points T and Z are vertically aligned, or vertically lined up. This is where the graph fails the vertical line test.

The input x = 2 leads to the outputs y = 3 and y = 5 (which are the y coordinates of points Z and T in that order).

A function is only possible when any given input leads to exactly one output only. It would be like saying "the conversion function from Celsius to Fahrenheit has 0 degrees C convert to both 32 degrees F and 50 degrees F at the same time". But such a statement makes no sense and it's not useful. So this is one example of why having one output makes sense for a function.

In short, we need one output for any given input. But the input x = 2 leads to more than one output. That's why we don't have a function.

Answer:

The radius is 10

Step-by-step explanation:

Given

[tex]x^2 + y^2 + 21 = 40 + 18y.[/tex]

Required

The radius

Rewrite as:

[tex]x^2 + y^2 - 18y = 40-21[/tex]

Subtract 81 from both sides

[tex]x^2 + y^2 - 18y +81= 40-21+81[/tex]

Expand

[tex]x^2 + y^2 - 9y - 9y +81= 40-21+81[/tex]

Factorize

[tex]x^2 + y( y- 9) - 9(y -9)= 40-21+81[/tex]

Factor out y - 9

[tex]x^2 + (y- 9) (y -9)= 40-21+81[/tex]

Express as squares

[tex]x^2 + (y- 9)^2= 100[/tex]

[tex]x^2 + (y- 9)= 10^2[/tex]

The equation of a circle is:

[tex](x - a)^2 + (y- b)= r^2[/tex]

By comparison:

[tex]r^2=10^2[/tex]

[tex]r = 10[/tex]

Answer:

first and fourth options

x = pi/6

x= 11pi/6

Step-by-step explanation:

cos(30 degrees) = sqrt(3)/2

as pi stands for a half circle of 180 degrees

30 degrees = pi/6

cos(30) = cos(-30) = cos (330) =

cos(pi/6) = cos(-pi/6) = cos(11×pi/6)

Answer:

A and d

Step-by-step explanation:

Edge:)

Answer:

[tex] \frac{8}{5} = \frac{4}{x} \\ 8x = 20 \\ x = 2.5[/tex]

Answer:

here the resize factor is 5/8

so we need to calculate

x = 4 *5/8

= 20/8

= 2.5

I assume you get the basic idea from the other question you posted.

9514 1404 393

Answer:

  3 units left

Step-by-step explanation:

Replacing x in a function with (x-h) translates the graph to the right by h units. Here, you have h = -3, so the graph is translated left 3 units.

Answer:

30 I suppose

Step-by-step explanation:

Answer:

x = 2 ± [tex]\frac{\sqrt{2} }{2}[/tex]

Step-by-step explanation: