The rectangular equation for the curve is [tex]y = \frac{x^{2}}{2} -1[/tex].
In this question, we have a set of parametric equation which must be reduced into a single rectangular equation both by algebraic and trigonometric means, that is to say:
[tex]x = f(\theta), y = g(\theta) \to y = h(x)[/tex]
If we know that [tex]x = 2\cdot \cos \theta[/tex] and [tex]y = \cos 2\theta[/tex], then the rectangular equation is:
[tex]y = \cos 2\theta[/tex]
[tex]y = \cos^{2}\theta - \sin^{2}\theta[/tex]
[tex]y = 2\cdot \cos^{2}\theta -1[/tex]
[tex]\cos \theta = \frac{x}{2}[/tex]
[tex]y = 2\cdot \left(\frac{x}{2} \right)^{2}-1[/tex]
[tex]y = \frac{x^{2}}{2} -1[/tex]
The rectangular equation for the curve is [tex]y = \frac{x^{2}}{2} -1[/tex].
We kindly invite to check this question on parametric equations: https://brainly.com/question/23070611
hi pls help me!!! thank you
Step-by-step explanation:
Circumference (C):
[tex]C = 2\pi r = 2\pi(5\:\text{ft}) = 31.4\:\text{ft}[/tex]
Area (A):
[tex]A = \pi r^2 = \pi(5\:\text{ft})^2 = 78.5\:\text{ft}^2[/tex]
How would I be able to simplify 12/3? Please explain step by step
Answer:
4/1
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator. GCD of 12 and 3 is 3.
12 ÷ 33 ÷ 3.
Reduced fraction: 41. Therefore, 12/3 simplified to lowest terms is 4/1.
Answer:
i think you divide 12/3 and you get the answer of 4
Step-by-step explanation:
carry out of the indicate operations and simplify 1/4b(x-4)
Answer:
When putang ina mo one said i hated yepero mahal kita yiee kilig to the bones ang potcha haha
Select all of the terms that are "like." 1/2 xy x 2 2xy -xy xy 2 2x 2y
Answer:
not sure about it this one is tuff
I need help, how do i solve the equations and get the degree for the circle
Answer:
D 130º
Step-by-step explanation:
3x-70=x+10
so 2x-70=10
x=40
What is the answer to this equation
Answer:
-34/45
Step-by-step explanation:
first step you wanna do is Multiply the numbers -1/5- 1 (-2/3)- (5/6)= -1/5 and -5/9 then subtract those two fractions and you get -34/45 since both of the fractions were negative the answer results as a negative aswell
a number is ____ by another number if the quotient is a counting number and the remainder is 0.
A number is divisible by another number if the quotient is a counting number and the remainder is 0.
x+2y-z=5
-X-y+2z=-13
2x+y-2z=14
Answer:
[tex]x+2y-z=5 ...(1)\\ -x-y+2z=-13...(2) \\ 2x+y-2z=14...(3) \\ \\ add \: (2) + (3) \\\boxed{x= 1} \\ 2 \times (1) + (2) \\ x + 3y = - 3 \\ 1 + 3y = - 3 \\ 3y = - 4 \\ \boxed{y = - \frac{4}{3} }\\ solve \: for \: z \\ x + 2y - z = 5 \\ 1-\frac{4}{3}(2)-z=5\\3-8-3z=15\\3z=-20\\\boxed{z = - \frac{20}{3} }[/tex]
Peter Piper picked 3 pecks of pickled peppers in 2.5
hours. How many pecks of pickled peppers does
Peter pick in 15 hours?
The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes. a. What is the probability density function for the time it takes to complete the task? b. What is the probability that it will take a worker less than 4 minutes to complete the task? c. What is the probability that it will take a worker between 6 and 10 minutes to complete the task?
Sowy about all my questions b-b-but please help with another one?
Answer:
A
Step-by-step explanation:
count both sides divide by missing pieices
there are 270 sixth grade students and 45 chaperones going on a field trip. how many students will be with each chaperone if the groups are divided equally.
Answer:
6
Step-by-step explanation:
270 divided by 45
=6
Completely Factor the following equations.
a) 3x^3 + 15x^2 + 18x
What is the value of 7x (3 + x/4) when x = −8?
Answer:
Third option
Step-by-step explanation:
[tex]7x (3 + \frac{x}{4}) = -56 * (3 + -\frac{8}{4}) = -56 * (3 - 2) = -56 * 1 = -56[/tex]
(7x)(2xy) how do I rewrite that as a sum
-7 over 1 3rd written as a fraction is
Answer: 22/3 I think
sorry if it’s wrong
Answer:
7 1/3
i hope this helps you can do it
The number of marbles each sister gets when m marbles are shared equally among four sisters x = m/4
Answer:
m/4
Step-by-step explanation:
Given f(x)=3x(to the scnd power)−5x−2. What is the value of f(−2/3)? 1 8/3 3 10/3
Given:
[tex]f(x)=3x^2-5x-2[/tex]; find f(-2/3)
Answer:
[tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
Step-by-step explanation:
1. Insert [tex]-\frac{2}{3} \\[/tex] as X; [tex]f(-\frac{2}{3}) = 3 (-\frac{2}{3} )^2 - 5 (-\frac{2}{3}) - 2[/tex]
2. Solve equation; [tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
wii mark brainlest answer with explanation
A? It makes the most sense i gues... So sorry if wrong!
please help with this algebra ii question
Answer:
Second Choice
Step-by-step explanation:
The vertex form can be expressed as:
[tex] \displaystyle \large{f(x) = a {(x - h)}^{2} + k}[/tex]
We know that the vertex is (h,k) which we are given (-3,-1). Substitute h = -3 and k = -1 in:
[tex] \displaystyle \large{f(x) = a {(x - ( - 3))}^{2} - 1} \\ \displaystyle \large{f(x) = a {(x + 3)}^{2} - 1}[/tex]
Now we know that the parabola passes through (-2,1). Substitute x = -2 and f(x) = 1 then solve for a.
[tex] \displaystyle \large{1= a {( - 2 + 3)}^{2} - 1} \\ \displaystyle \large{1= a {(1)}^{2} - 1} \\ \displaystyle \large{1= a - 1} \\ \displaystyle \large{1 + 1= a } \\ \displaystyle \large{2 = a}[/tex]
Therefore a = 2.
Hence:-
[tex] \displaystyle \large{f(x) = 2{(x + 3)}^{2} - 1}[/tex]
NEED HELP ASAP RIGHT ANSWER ONLY 69 POINTS
In two or more complete sentences, determine the appropriate model for the given data and explain how you made your decision.
(2,−1), (3,0.5), (6,1.5),
Answer:
A Least Square Regression Line is the best thing to use for this because there is inconsistencies and no direct equation to be able to fill all of these points. They may be outliers and therefore we should use a calculator for a Regression Line to be calculated to find the residual.
Step-by-step explanation:
Can you please Help me?
Answer:
D. 5i
Step-by-step explanation:
edge 2021
Data was recorded for the temperature, in degrees Celsius, of a cup of coffee over a 30-minute period. Given the regression equation, , what is the predicted temperature after 3 minutes?
33.45 oC
62.24 oC
65.17 oC
66.69 oC
Answer:
62.24
Step-by-step explanation:
The predicted temperature after 3 minutes will be 62.24 °C. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
A cup of coffee's temperature was measured over a 30-minute period in degrees Celsius.
Let T be the temperature and t be the time. Then the regression equation is given as,
ln T = 4.20 - 0.023 t
Then predicted temperature after 3 minutes is given as,
ln T = 4.20 - 0.023 x 3
ln T = 4.20 - 0.069
ln T = 4.131
T = 62.24 °C
The predicted temperature after 3 minutes will be 62.24 °C. Then the correct option is B.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ5
The mean of a soccer team goals is 6 goals after 4 games. If the team scored 5 goals in the first game, 6 goals in the second game and 6 goals in the third game, how many goals did they score at the 4th game?
=====================================================
Work Shown:
We have this set of data
[tex]\begin{tabular}{|l|l|}\textbf{game} & \textbf{goals}\\ 1 & 5 \\ 2 & 6 \\ 3 & 6\\ 4 & x \end{tabular}[/tex]
where x is some positive whole number. Add up everything in the second column:
5+6+6+x = x+17
This represents the total number of goals made over the four games.
Divide this over the number of games played (4) and set that equal to the mean of 6. Solve for x.
(x+17)/4 = 6
x+17 = 4*6
x+17 = 24
x = 24-17
x = 7
7 goals were scored in the fourth game.
Find g(x) for each x value in the table
Answer:
-2 = -2/7
-1= -1/7
0=0
1= 1/7
2= 2/7
Step-by-step explanation:
it gives you a function of 1/7 so you multiply it by x and u get the g(x) also know as Y
round to the nearest ten 7096.88
I know how to do it just then one’s a bit confusing
Answer:
208 ft^3
Step-by-step explanation:
Let the plane through the 4 ft X 4ft square at the top of the figure break the figure into 2 boxes, one has dimensions (8-7) by 3 by 4 = 1ft X 3ft X 4ft, and the other has dimensions 7 by 7 by 4 = 7ft X 7ft X 4ft.
They have volumes of (1)(3)(4) = 12 ft^3, and (7)(7)(4) = 196 ft^3, respectively, so the total volume = 12 + 196 = 208 ft^3, the answer.
Graph the line with slope 1 passing through the point (-3, 1).
Answer:
[tex]y = x + 4[/tex]
Step-by-step explanation:
[tex]1 = 1(- 3 )+ b \\ 1 = - 3 + b \\ b = 4 \: \: \: \: y - intercept[/tex]
20000 divided by 2 x 56 x 7898 - 100
First to Answer gets brainliest!!!
NO LINKS PLEASE!!!!
Answer:
0.0226122585576093
A sales person at a car dealership earns a monthly salary of $2400 and $250 for each vehicle sold
3. The car dealership sets a goal for each salesperson to sell at least 12 cars per month. The salesperson
achieves this goal every month for the entire year. What is the minimum amount of money the
salesperson earns for the entire year? Show your work.
I
Answer:
8 vehicles
Step-by-step explanation:
Given: Monthly salary of salesperson is $2400
Incentive of salesperson is $250 per vehicle sold.
First, lets compute income to earned apart from salary.
∴ Deduct salary from the target amount
$2000 need to be earned only through incentive, which is $250 per vehicle sold.
Now, solving to get number vehicles to be sold to earn $2000 as incentive.
Number of vehicle=
8 vehicles need to be sold by salesperson to get total earning as $4400.