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
Evaluate -8x+5-2x-4+5x
Answer:
The value of the expression is - 9.
Evaluating the expression before simplifying is preferred because you only have to substitute once instead of substituting three times.
Step-by-step explanation:
x = 2
- 8x + 5 - 2x - 4 + 5x
= - 8x - 2x + 5x + 5 - 4
= - 10x + 5x + 1
= - 5x + 1
= - 5 ( 2 ) + 1
= - 10 + 1
= - 9
help plshddjjdhdjjdjdjdh
Help help please please
Answer:
165km
Step-by-step explanation:
if 1cm on the map = 15km,
then since 11cm is 11x 1, we multiply the kilometers by 11, getting 165km.
The volume of the cube shown below is 1000 cm". What is the length side, x of the cube in centimeters?
resnanse)
Answer: x = 10
Step-by-step explanation:
The formula to find the volume of a cube is as following:
V = x³
Since we already know the volume, let's substitute it in the formula.
1000 = x³
To find x, we should do the cube root on each side.
∛1000 = ∛x³
x = 10
Find the equation of the linear function represented by the table y 6 9 12 15 x 1 2 3 4
Answer: y = 3x + 3
Step-by-step explanation:
We know the linear function as following:
y = mx + b
m is the slope of the equation. b represents the y-intercept.
To find m, we divide the rate of change of y by the rate of change of x. We know that the rate of change y is +3 because we add three each time in order to find the next value. The rate of change of x is +1 because we add one each time to find the next value. So m would be:
m = 3/1
m = 3
Our linear equation is now as following:
y = 3x + b
In order to find b, we should first substitute a coordinate in the equation above.
y = 3x + b
6 = 3(1) + b
Then, we multiply 3 with 1
6 = 3 + b
Finally, we substract 3 on both sides. Now we've got our b value.
b = 3
Now our equation should look like this.
y = 3x + 3
To verify if the equation, we should substitute another coordinate, and verify if each side of the equation is equal.
y = 3x + 3
15 = 3(4) + 3
15 = 12 + 3
15 = 15
So we now know that the equation is indeed correct.
Answer:
y = 3x + 3Step-by-step explanation:
As per given table we have ordered pairs:
(1, 6), (2, 9), (3, 12), (4, 15)Find the slope and y- intercept to work out the equation.
y = mx + bThe slope:
m = (9 - 6)/(2 - 1) = 3/1 = 3The y -intercept:
6 = 3*1 + b6 = 3 + bb = 3The equation is:
y = 3x + 3The graph is attached
Ha car drove 200 miles at a speed of 107.0534 miles per hour how long would it take?
Answer:
1.86822
Step-by-step explanation:
take the 200 miles and devide the traveling speed
To save for retirement at age 27 you start depositing $275 at the end of each month in an IRA that pays 5.75% compounded monthly.
How much will you have in the IRA if you plan to retire at 65?
I need also to find the interest.
Answer:
81972
Step-by-step explanation:
Help this help
19. As part of a cookie recipe, you mix cup of chocolate chips for every 1 cups of
sugar. How much chocolate chips do you need if you use a whole cup of sugar?
Answer: 1 cup
Step-by-step explanation: they have a 1:1 ratio
Answer:
1
Step-by-step explanation:
If you have 1 cup of chocolate chips for every 1 cup of sugar, that is a 1:1 ratio
A whole cup of sugar is equal to 1 cup of sugar
Therefore, you will have 1 cup of choloate chips for the whole cup of sugar
Student football game tickets cost $20 Adult tickets cost $30. Write a function that shows
the total cost for s student tickets and a adult tickets.
Answer:
Here are the answers for the whole QC for CA students.
1. C
2. A
3. no
4. c
5. A
Step-by-step explanation:
Show that: [tex]\sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]
Brainliest! Brainliest..ans.
Here we need to Prove that ,
[tex]\bf\implies \sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]
Lets start with LHS , which is ,
[tex]\bf\implies LHS = \sqrt[ab]{ \dfrac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \dfrac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \dfrac{ {x}^{c} }{ {x}^{a} } } [/tex]
We know that ,
[tex]\bf\implies \sqrt[n]{k^m }= k^{\frac{m}{n}}[/tex]
• So that ,
[tex]\bf\implies \sqrt[ab]{x^{a-b}} . \sqrt[bc]{x^{b-c}} .\sqrt[ac]{x^{c-a}} \\\\\bf\implies x^{\frac{a-b}{ab}} . x ^{\frac{b-c}{bc}} .x^{\frac{c-a}{ca}} \\\\\bf\implies x^{\frac{ ac - bc + ab - ac + bc - ba }{abc } }\\\\\bf\implies x^{\frac{0}{abc}} \\\\\bf\implies x^0 \\\\\bf\implies 1 = RHS [/tex]
Hence ,
[tex]\implies \boxed{\bf \red{ LHS = RHS }} [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider LHS:
[tex]\sf= \sqrt[\sf ab]{\dfrac{\sf x^{a}}{\sf x^{b}}}\cdot \sqrt[\sf bc]{\dfrac{\sf x^{b}}{\sf x^{c}}}\cdot \sqrt[\sf ac]{\dfrac{\sf x^{c}}{\sf x^{a}}}[/tex]
As we know that:
[tex]\sf\red\leadsto\dfrac{x^{a}}{x^{b}}=x^{a-b}[/tex]
We get:
[tex]\sf= \sqrt[\sf ab]{\sf x^{a-b}}\cdot \sqrt[\sf bc]{\sf x^{b-c}}\cdot \sqrt[\sf ac]{\sf x^{c-a}}[/tex]
We can also write it as:
[tex]\sf= x^{\dfrac{a-b}{ab}}\cdot x^{\dfrac{b-c}{bc}}\cdot x^{\dfrac{c-a}{ac}}[/tex]
We know that:
[tex]\sf \red\leadsto x^{a}\cdot x^{b}=x^{a+b}[/tex]
We get:
[tex]\sf= x^{\bigg(\dfrac{a-b}{ab}+\dfrac{b-c}{bc}+\dfrac{c-a}{ac}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{c(a-b)+a(b-c)+b(c-a)}{abc}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{ac-bc+ab-ac+bc-ab}{abc}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{0}{abc}\bigg)}[/tex]
[tex]\sf= x^{0}[/tex]
[tex]\sf=1[/tex]
[tex]\textsf{= RHS}\\[/tex]
4% of 50
Percent of a quantity
M
Answer:
4% of 50 is 2
Step-by-step explanation:
Find cos 30 in terms of cos 0
Answer:
cos(30) = (sqrt(3)/2) * cos(0)
Step-by-step explanation:
cos(0) = 1
cos(30) = sqrt(3)/2
Thus, we can write that:
cos(30) = (sqrt(3)/2) * cos(0)
HELP HURRY SUBTRACTION
Answer:
408, 250, and 4055 hope this helps
Mikael has a loan of $40 000.
He pays 1.6% simple interest for six months
How much interest does he pay altogether?
Step-by-step explanation:
Based on the given conditions,
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}[/tex]
[tex]Reduce the fraction: 2 \times320
[tex]Reduce the fraction: 2 \times320Calculate the product orquotient: 640[tex]
Answer 640
Answer:
[tex]\sf\longmapsto \: 640[/tex]
Step-by-step explanation:
Based on given cases:
[tex] \sf \: Formulate: 1.6\% \times 40000 \times 12 \div 12[/tex]
Reduce the fraction:
[tex] \sf \longmapsto \: \dfrac{2 \times 40000}{125}[/tex]
[tex] \sf \longmapsto \: 320 \times 2[/tex]
Calculate the product/quotient:
[tex] \sf\longmapsto \: 640[/tex]
In 1995, the cost of tuition at a large Midwestern university was $146 per credit hour. In 2001, tuition had risen to $200 per credit hour.
Determine a linear equation to represent the cost, C, of tuition as a function of x, the number of years since 1990. (Assuming the cost increases by the same amount each year.)
Linear Equation:
In the year 2008, tuition will be ($ )per credit hour.
In the year( ) , tuition will be $317 per credit hour
Answer:
72 is the correct answer
Answer:
I believe 72 is the correct answer
Step-by-step explanation:
PLEASEE I NEEEDDD HELPPPPPP
Answer:
make a chart and it will be easy for you
Evaluate the expression 6^2-(8–4^2+7
please mark this answer as brainlist
The value of given expression is 27.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 6²-(8-4)²+7.
Here, 6²-(8-4)²+7
= 6²-(4)²+7
= 36-16+7
= 20+7
= 27
Therefore, the value of given expression is 27.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ2
A salesperson earns an income of $600 per week aus an dditional 5% commission on her total sales for that weck a. Write an equation that models the Salespersons total weekly income. b. What would be the salespersons income if her total sales were $10.000 that week? c. How much would a salesperson have to sell to have a $2000 weekly
3x^2-24x+48 pls help me
Answer:
This polynomial is either a function like f(x), or it's just =0 and it's solved by a quadratic equation.
Step-by-step explanation:
Let's say it's equal to 0, we can easily divide the whole expression with 3, as obviously 3,24,48 have the same divisor(3), then we are left with:
x²-8x+16=0, then we apply the quadratic equation, and we got only 1 solution and that's x=4
If it is a function f(x), than it will have roots(root of a quadratic function is the x-coordinate where y=0, basically when the parabola intersects the x-axis(y=0), as we'll get that the only root is x=4
Scientists often write very large or very small numbers using exponents. How might a scientist write the number shown using exponents?
make it look like a seventh grader wrote it please
HW
Example 7: While chasing the Joker, the Batmobile was traveling at 120 miles per hour. The
Joker's get-away car was traveling at 176 feet per second. Who was traveling faster, Batman or the
Joker? Explain your answer.
Answer:
this is a trick question 176 fps is equal to 120 mph
so 120=120
Does anyone have the answer key for this assignment?
Answer:
try searching it up
Step-by-step explanation:
What’s the greatest common factor of (280, 168)
Answer:
Greatest common factor of 280 and 168 is 56
-NULL
Brainliest will be appreciated thank you!
Hi ppl of brainly. I need some help with my math assignment. explain if u can (if u can't, that's okay ) if you dont know it. please dont answer it. if u have any questions about the question, please drop in a comment!
Answer:
17.156
Step-by-step explanation:
A rational number has has a terminating decimal expansion or a decimal expansion of non-terminating repeating digits. Here, the decimal expansion is terminating, so it is a rational number.
Answer:
C. 17.156
Step-by-step explanation:
A rational number is any number that can be expressed as a fraction. So for example, since [tex]\sqrt{2}[/tex] cant be expressed as a fraction, it isn't rational. A number like 1.25 on the other hand IS rational as it can be expressed as [tex]\frac{5}{4}[/tex] or [tex]\frac{125}{100}[/tex].
Option C can be expressed as [tex]\frac{17156}{1000}[/tex], so it must be rational.
- Note that if a number has a finite amount of digits after the decimal (ie it doesn't go on forever like option B), it can be represented as a fraction and thus is rational.
(Score for Question 2: of 5 points)
2. Consider the function f(x)= xº + 2x² – 3 .
(a) Graph the function.
(b) What are the x- and y-intercepts of the graph?
Answer:
Answer:
(-1,0) (0,-2) (1,0)
Step-by-step explanation:
the function crosses the axis in this 3 points
ive been stuck for so long. pls help
Answer:
B
Step-by-step explanation:
Might be C, but I hope it helps
1.0286 as a fraction
Answer:
1 143 /5000
Step-by-step explanation:
What are the slope and y-intercept of the linear function?
2
-3 -2 -1.
2
оа
Oь
slope:-2: y-intercept: 2
1
slope: 2 :y-intercept: 1
Ос
1
slope: 2 :y-intercept: 2
slope: 2; y-intercept: 1
Od
lim┬(x→1)〖(1-√x)/(x^2-1)〗
Answer:
- 1/4
Step-by-step explanation:
[tex]\frac{1-\sqrt{x} }{x^{2}-1 } = \frac{(1-\sqrt{x})*(1+\sqrt{x} ) }{(x+1)(x-1)(1+\sqrt{x} )} \\= \frac{1-x}{-(1-x)(x+1)(1+\sqrt{x} )} \\= - \frac{1}{(x+1)(1+\sqrt{x} )} \\ \lim_{->1} - \frac{1}{(x+1)(1+\sqrt{x} )} \\ = -\frac{1}{(1+1)(1+\sqrt{1}) } = - 1/4[/tex]
Thirty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired, whereas the other 30% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly four will end up being replaced under warranty
Answer:
40%
Step-by-step explanation: