Mathematics High School

Find parametric equations for the tangent line at the point (cos(3pi/6),sin(3pi/6), (3pi/6))
on the curve x=cost, y= sint, z=t
x(t)=?
y(t)=?
z(t)=?

Answers

Answer 1
[tex]r(t)=(\cos{t},\sin{t},t) \\r'(t)=(-\sin{t},\cos{t},1) \\t= \frac{3\pi}{6} = \frac{\pi}{2} \\ r'(t)=(-\sin{\frac{\pi}{2}},\cos{\frac{\pi}{2}},1) \\ r'(t)=(-1,0,1) \\ \\x=0+t(-1)=-t \\y=1+t\times 0=1 \\z= \frac{\pi}{2} +t[/tex]

Related Questions

A surveyor, standing 100 ft. from the base of a building, measures the angle of elevation to the top of the building to be 75 degrees. How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?

Answers

right well height = 100tan75
= 373.205 Ft

dH/da = 100sec^2(a)

Fractional change in height = dH/H = 0.04

0.04 = 100 sec^2 a da/H
da = 0.04 H / 100 sec^2a
da = 0.01

Hope this helps

How are mc091-2.jpg and mc091-3.jpg related?

Answers

check what u wrote cause its not numbers fix it so i can help you
its 1 image and doesnt show anything

Kurt johnson delivers packages for a delivery company. he receives $7.50 for every package delivered. what does kurt earn in a week if he delivers 48 packages? 360.00 405.00 555.00 640.00

Answers

y = 7.50x.....y = earnings per week , x = number of packages delivered

48 packages.....so x = 48
y = 7.50(48)
y = 360.....so if he delivers 48 packages, he earns $ 360

Answer:

He earned $ 360.00.

Step-by-step explanation:

Given,

The amount he gets for a package of delivery = $ 7.50

The number of packages he delivered in a week = 48,

Hence, the amount he earned in the week = The amount he gets for a package of delivery × The number of packages he delivered

= 7.50 × 48

= $ 360.00

A vehicle travels on a highway at a rate of 65 mi/h how long does it take the vehical to travel 25 mi?

Answers

use the velocity formula and solve for time.v=d/t
t=d/v

Substitute your variables and solve.
65 mi/hr = 65 / 3600 mi/second
25 mi / ( 65/3600) = 1384.6 seconds

Answer:

Step-by-step explanation:

A vehicle travels at a rate of 65 m/h, How long does it take the vehicle to travel at 25 miles?

Apply the "distance formula":

d = rt

25 = 65t

25/65 = t

5/13 hour = t

or

0.385 hour = t

or

23.08 minutes = t

Miss fernandez built two rectangular gardens the length of garden a is 2 feet longer than twice its width the list of garden b is 1 foot less than the width of garden a the length of garden b is 2.5 times its width the two gardens have the same perimeter what are the dimensions of the gardens

Answers

For garden A, let width = w, length = L
For garden B, let width = x, length = y

So we are given the following:
L = 2+2w
x = w - 1
y = 2.5x
2w+2L = 2x+2y   ------> w+L = x+y

Ok lets do some substituting into the perimeter equation
[tex]w + (2+2w) = (w-1) + 2.5(w-1)[/tex]
adding like terms...
0.5w = 5.5
w = 11

This means that:
L = 2+2(11) = 24

x = 11-1 = 10
y = 2.5x = 2.5(10) = 25

Final solution:
Garden A is 11 by 24
Garden B is 10 by 25

A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal parts of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?

Answers

Final answer:

To maximize profit, the candy manufacturer should use mathematical linear programming. The decision variables are the amounts of Candy A (x) and Candy B (y). The profit function P = 285x + 260y is to be maximized subject to constraints arising from available stock of dark chocolate, caramel, and walnuts, leading to a typical linear programming problem.

Explanation:

To solve this problem, we need to use Linear Programming, a mathematical model that helps in making optimal decisions. The candies are what we call decision variables. Our decision variables here are Candy A and Candy B.

Candy A: x kilograms (dark chocolate and caramel in equal parts).

Candy B: y kilograms (two parts of dark chocolate and one part of walnut).

We want to maximize the profit function P = 285x + 260y subject to constraints arising from the available stock of dark chocolate (DC), caramel (C), and walnuts (W).

DC constraint: A uses DC in equal parts, and B uses two parts DC. Therefore, x + 2y ≤ 360.C constraint: A uses equal parts C, x ≤ 430 (as B doesn't use C).W constraint: B uses one part W, y ≤ 210 (as A doesn't use W).

The next step is to solve these inequalities graphically or using mathematical methods to get values of x and y that maximize P while respecting constraints. This case, where we want to optimize a certain function with respect to constraints, is a typical linear programming problem in mathematics.

Learn more about Linear Programming here:

https://brainly.com/question/34674455

#SPJ12

Mr. Shaw graphs the function f(x) = –5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?

a.) y – 12 = –5(x + 2)
b.) y – 12 = 2(x + 2)
c.) y + 12 = 2(x – 2)
d.) y + 12 = –5(x – 2)

Answers

I hope this helps you
Point slope formula has fallowing shape:
y-y1=m(x-x1)

where x1 and y1 are coordinates of the given point.

in f(x) = -5x + 2 we can see that slope is -5
m = -5

if we exchange all of this in point slope formula we get:

y - 12 = -5(x - (-2)) = -5(x+2

Answer is a)

A furniture company misprinted a sales ad for a living room set but honors the advertised price. For each customer who purchases the living room set, the company suffers a loss of $125. Write a function to represent the company's total loss. What is the value of the function for an input of 50, and what does it represent? ...?

Answers

We can say that there are x customers.
So,
f (x) = 125x
To get how much money the company loses, we can make x equal to 50.
f (50) = 125(50) = 6250
The company loses $6,250 when 50 customers purchase the furniture.

Which of the following is not a way to prove a quadrilateral is a parallelogram?

Answers

I think it's the second answer choice.

The way to not prove a quadrilateral is a parallelogram is; Show one set of opposite sides of the quadrilateral is congruent.

Parallelogram and Congruence

A parallelogram is a quadrilateral which has opposite sides to be congruent and parallel as the name implies and hence, opposite angles of the parallelogram are congruent.

However, showing one set of opposite sides of the quadrilateral is congruent is not a confirmatory test for a parallelogram, as it evades the parallel law of opposite sides of the Parallelogram.

Read more on parallelogram;

https://brainly.com/question/17167464

What times what equals 80.73

Answers

80.98498747 is your answer

PLEASE HELP!!
Oscar entered y=−0.4^x+3y=−0.4^x+3 into an online graphing tool.

What function did he graph?

y=(−0.4)x+3y=(−0.4)x+3

y=(−0.4)x+3y=(−0.4)x+3

y=−(0.4)x+3y=−(0.4)x+3

y=−(0.4)x+3

Answers

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions. 
Among the choices provided above the function the Oscar graph is 
y=(−0.4)x+3y=(−0.4)x+3

solve for X. y=1/4 (x)+3

Answers

The answer is:
____________________
x = 4y - 12 ; (Assuming the problem meant to solve for "x"; "in terms of "y").
_______________________
{Otherwise, the question might be "incomplete".}.
______________________________________________
The question seems incomplete; how can we solve for "x" when we do not know what "y" equals?
__________________________
However, it could be possible to "solve for x" in terms of "y".  To so this, we need to isolate ""x" on one side of the equation:
_______________________________
Given: y=1/4 (x) + 3 ; Let us multiply the ENTIRE EQUATION (both sides) by "4", to get rid of the "1/4" (fraction coefficent) of "x", and to "cancel out" the "1/4" fraction cofficient of "x" to the implied "1"; to help solve for "x" :
________________________________________
4 *{ y= 1/4 (x) + 3} ;
______________________
4y = x + 12 ; Now we can subtract "12" from EACH SIDE of the equation;                       to isolate "x" on one side of the equation; and to solve for "x":
_______________________
4y - 12 = x + 12 - 12 ;
________________________
4y - 12 = x ; This is our answer:
___________________________
x = 4y - 12 ; (Assuming the problem meant to solve for "x"; "in terms of "y").

What is the best approximation of the sine of 50°?

A. 0.2624

B. 0.6428

C. 0.7660

D. 1.1918

Answers

The best and most correct answer among the choices provided by your question is the first choice or letter A.

As I calculated it, sine 50 is equivalent to 0.2623748537.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Solve for x. Enter your answer in interval notation using grouping symbols.

x^2+4x<45 ...?

Answers

Solving for x we get 2 values...
-9,5

Simplify (8j3 + 5j2 – 3) – (5j3 + 7j2 – 12j + 7) ...?

Answers

The answer to the problem is:

8j^3 + 5j^2 - 3 - 5j^3 - 7j^2 + 12j - 7
 
3j^3 - 2j^2 + 12j - 10 


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!


Answer:

3j^3 - 2j^2 + 12j - 10

Step-by-step explanation:

I took the test and got a 100%

Which of the following is a result of shifting a circle with equation (x + 3)² + (y - 2)² = 36 left 3 units?

Answers

The x's make the graph go left or right. to make it go left you add 3 to the existing 3. If you wanted it to go right you would subtract 3.


(x + 6)^2 + (y - 2)^2 = 36 

Answer:

The answer is [The x-coordinate of the center of the circle decreases by 3.]

Step-by-step explanation:

Wendy wants $15,000 saved in 6 years to make a down payment on a house. How much money should she invest now at 4.65% compounded annually in order to meet her goal?

Answers

A=P(1+R/100)^n
A=$15000, n=6 years, R=4.65
Therefore,
15000=P(1+4.65/100)^6
15000=P(1.3135)
P=15000/1.3135
  =$11420 (to the nearest dollars)

Help With Number 8 Please?

Answers

The answer is about 8.14 years :) 

Because,  ↓ 

Unit Rate =  [tex] \frac{I}{1300 * 0.0425 } [/tex]  which is equal to → [tex] \frac{450}{1300 * . 0425} [/tex] 

and that's how I found out that my answer is 8.14 years 
I = p r t First subtract 1750-1300 to find out how much interest was earned. 450=1300(.0425)t ; solve by multiplying 1300*.0425 then divide 450 by that number. You get approx 8.14 years.

Oscar Montez’s savings account has a principal of $7,201. It earns 6% interest compounded quarterly. What is the amount of interest he earned by the end of the second quarter?

Answers

compounded quarterly means that one quarter of the interest is added to the account each quarter one quarter of 6% is 1.5% x = 7201 (1 + .06/4)^2 ___ .06/4 is the interest per compounding , and 2 is the number of compoundings

find all the zeros of the function y=x^3+6x^2+x+6

Answers

Final answer:

The zeros of a function are the values of x for which the function equals zero. The function given here is a cubic function, and finding its zeros can be complex, often requiring numerical methods or advanced mathematical approaches like the cubic formula.

Explanation:

This problem deals with finding the zeros of the cubic function y=x^3+6x^2+x+6. A zero of a function is a value of x for which the function equals zero. You can find the zeros of this function by setting the equation equal to zero and solving for x.

Unfortunately, this particular cubic equation does not have an easy solution using basic algebraic methods. We can't factor it in an easy and straightforward manner. However, you can use numerical methods, or online calculator tools, to get an approximate value for the zeros. Alternatively, you can use the cubic formula (somewhat similar to the quadratic formula), but this requires knowledge of more advanced mathematics.

Please consult your teacher or textbook for more detailed instructions on how to use higher level methods to solve cubic equations. Remember that each method has its own level of accuracy and complexity, so choose the method that best suits your abilities and the requirements of your task.

Learn more about Zeros of Function here:

https://brainly.com/question/31654173

#SPJ12

What is d if p equals 15 in d=-3p^2+168p-315

Answers

so first you will substitute p for 15
so your equation will look like d=3(15)^2+168(15)-315
then you will simplify
to get d= 2025+2520-315
simplify again 
to get d=4230

 
sub
-3(15^2)+168(15)-315=
-3(225)+2520-315=
-675+2205=
1530

d=1530 when p=15

Find the missing length. The triangle in each pair are similar.

Answers

The answer is 39.
B/c 27/45=.6
.6*65=39

Answer:

39 UNIT

Step-by-step explanation:

According to similar triangle.

Let's call NG "X"

45/27 = 65/x

X=( 65*27)/45

X= 1755/45

X = 39

An Antique vase is projected to be worth $1000 in 2 years and $1,300 after 5 years. If the value continues to appreciate at the same rate, what will it be worth in 8 years?

Answers

The value of the antique vase after 8 years with a consistent appreciation rate, it would amount to $1,600.

An antique vase:

Value after 2 years: $1,000

Value after 5 years: $1,300

To find the value after 8 years, we can assume a constant rate of appreciation:

In 8 years, the value will be: $1,000 + ($1,300 - $1,000) = $1,300 + ($1,300 - $1,000) = $1,600

What is the solution to the equation? 
 
5(8 + 7) = 5 • x + 5 • 7



 
A.
x = 1


 
B.
x = 5


 
C.
x = 7


 
D.
x = 8

Answers

D. X=8 distribute the 5 to the 8 and 7 which is 40 + 35 = 5 times x + 5 times 7 Multiply 5 times x and 5 and 7. Add left side to equal 75. Subtract 35 from both sides. Divide by 5 on both sides. Get x = 8 5(8+7) =5x+35 40+ 35 = 5x + 35 75= 5x +35 40= 5x X=8


Six times the sum of a number and twelve is forty.

Which equation represents this?


6N + 12N = 40
6N + 12 = 40
6(N + 12) = 40

Answers

The last one
6(N+12)= 40
Depends if number twelve is multiplied by six as well. In other words, it depends if the text means:
six times the sum of (a number and twelve) or six times the sum of a number and than plus 12 equal 40.

In first case answer is:
6(N + 12) = 40 and in second
in second:
6N + 12 = 40

Which of the following statements is true?

A.A radius is always a chord.
B.A tangent is always a secant.
C.A diameter is always a chord.
D.A chord is always a diameter.
Please help

Answers

A isnt correct because radius goes from center of circle to any point on circle. Chord on the other hand connects 2 points on circle...

B is also false. Secant goes through circle while tangent only touches it in one point. 

C is correct. Chord connects as said before 2 points on circle and in some cases it can connect 2 points in such way that it goes through center which is diameter.

D is not correct because chord doesnt have to pass trought center of circle in order to connect any 2 points on circle.

If a satellite launch has a 97% chance of success, what is the probability of three consecutive successful
launches? ...?

Answers

91%

0.97 ^ 3 = 0.91

= 91%

Answer:  The required probability of three consecutive successful launches is 91.27%.

Step-by-step explanation:  Given that a satellite launch has a 97% chance of success.

We are to find the probability of three consecutive successful launches.

Let P(A) denotes the probability of the event of the success of the satellite launch.

Then, according to the given information, we have

[tex]P(A)=97\%=\dfrac{97}{100}=0.97.[/tex]

Therefore, the probability of three consecutive successful launches will be

[tex]p\\\\=P(A)\times P(A)\times P(A)\\\\=0.97\times0.97\times0.97\\\\=0.912673\\\\=0.912673\times100\%\\\\=91.2673\%\\\\=91.27\%.[/tex]

Thus, the required probability of three consecutive successful launches is 91.27%.

The mean number of hours that Raphael worked over the past four weeks is 37.75. If he works 40 hours this week, what will the mean number of hours be that he will have worked over the five-week period?
What is the five-week mean?

Answers

Multiply 37.75 x 4 to get the total number of hours Raphael worked the past 4 weeks. (The mean is just the total number divided by the number of parts).

37.75 x 4 = 151

Then, add 40 to that total to get the new total.

151 + 40 = 191

Now, divide that number by 5 (as in 5 weeks, the new number of parts).

191/5 = 38.2 hours
The mean for the first four weeks:
Total hours in 4 weeks / 4 = average of four weeks.
Total hours in 4 weeks = 37.75 x 4
= 151
Total hours in 5 weeks = 151 + 40
= 191
5-week mean = 191 / 5
= 38.2

is 87 a prime or composite

Answers

The answer is a prime number

Answer:

Prime

Step-by-step explanation:

77 is composite

It has other factors besides 1 and itself

68 -composite

52-composite (it is even)

31 -prime

59-prime

In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B′. What is the scale factor of the dilation?

1

2

0.5

-0.5

Answers

Answer:

The diameter of B is from -2 to 2, which = 4 units.

The diameter of B' is from -1 to 1, which equals 2 units.

2/4 = 1/2 = 0.5 scale factor.

The answer is C. 0.5

Step-by-step explanation:

Other Questions
If 3000ft/3 of air crossing an evaporator coil and is cooled from 75F to 55F, what would be the volume of air,in ft/3, exiting the evaporator coil? Math 7. Grade 7Evaluate: 6(px) - 2x , if p = 6 and x = 3.SHOW ALL OF YOUR WORK! sentence using the two words plain and stain Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.Find the distance CC' The volume v of a rectangular prism is determined using the formula where l is the length w is the width and h is the height of the prism l. Carltren solves for w and writes the equivalent equation w=V/lh. Using this formula what is the width of a rectangular prism that has a volume of 138.24 cubic inches a height of 9.6 inches and a length of 3.2 inches Check my answer, please? Los hijos son __________. responsable responsables (my answer) cmica cmico Over the weekend, Statton and Tyler drove to Montana to go hunting. Now they're preparing to go hunting. Tyler needs gas for his jeep, which gets 22 miles gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank, he buys more gas for $1.25 per gallon. If Tyler spends $22 on gas, what is the total distance the boys could travel? Which is not a responsibility of a county government Read the passage underlined (2). There may be a mistake in punctuation, capitalization, or spelling. If you find a mistake, choose the answer that corrects the mistake. If there is no mistake, choose Correct as is. A)Correct as is. B)while the President is on board the term is commonly used C)while, the President is on board, the term is commonly used D)while the President, is on board, the term is commonly used The constitution was completed in 1776. true false user: by the end of the convention, 39 delegates signed the constitution. true false In 2 or 3 sentences, explain if rent control is a price floor or price ceiling. Then name one advantage and one disadvantage of rent control. What is the decimal representation of 2/10 ? a.20b. 2.0c. .2d. 2.10 As compared to piaget, vygotsky placed _____ emphasis on the _____ bases of cognitive development. In the state of Texas, how many hours of instruction must a certified food service manager program provide?4101440 about how many gallons of water are used to refill the bathub everyday for 31 days? explain. A turtle walks at a rate of 1/5 mile in 45 minutes. If the turtle continues at the same rate, how much of a mile will the turtle walk in 1 hour? Which of these was a political goal for farmers? a. fair prices for shipping b. lower prices for gold c. fair wages for day laborers d. lower prices for cotton H E L P P L E A S ESolve and check. 16 = 1/4p All of the careers in the health and wellness field are positions dedicated to helping people. True or False? All of the careers in the health and wellness field are positions dedicated to helping people. The answer is True. which of the following describes a similarity between China's Tang and Song dynasties in the post-classical eraA) Both relied on maritime trade instead of land-based routesB)Both isolated china from its neighbors to protect its cultureC) Both grew wealthy through trade along the Silk RoadD) Both fiercely persecuted religious and ethnic minorities Steam Workshop Downloader