what is the rectangular form of the parametric equations x = 4 cos t and y = 5 sint, where

What Is The Rectangular Form Of The Parametric Equations X = 4 Cos T And Y = 5 Sint, Where

Answers

Answer 1

Let's use some identities to help us solve

 

    [tex]x = 4 cos(t)\\\frac{x}{4} =cos(t)\\\\y = 5sin(t)\\\frac{y}{5} =sin(t)[/tex]

We know -->  [tex]sin^2(t)+cos^2(t) = 1[/tex]

So:

   [tex]\frac{y^2}{5^2} +\frac{x^2}{4^2}=1\\ \frac{x^2}{16} +\frac{y^2}{25} =1[/tex]

Thus the choice is the second choice

Answer 2

An equation is formed of two equal expressions. The correct option is B.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given two of the equations which can be rewritten as shown below,

x = 4 cos(t)

x/4 = cos(t)

Squaring both sides of the equation,

x²/16 = cos²(t)

y = 5 sin(t)

y/5 = sin(t)

Squaring both sides of the equation,

y²/25 = sin(t)

y²/25 = sin²(t)

Adding the two of the given equations we will get,

(x²/16) + (y²/25) = cos²(t) + sin²(t)

(x²/16) + (y²/25) = 1, this is because cos²(x) + sin²(x) = 1

The rectangular form of the parametric equations x=4cos(t)and y=5sin(t) is (x²/16) + (y²/25) = 1.

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Related Questions

If f(x) = x-3/x and g(x) = 5x-4, what is the domain of (f•g)(x)?

Answers

Answer: x cannot equal 4/5 (3rd choice)

Step-by-step explanation:

f(g(x)) = f(5x-4)

plug 5x-4 into all values of x in the f(x) equation

f(5x-4)= ((5x-4) - 3))/ (5x-4)

f(5x-4) = (5x-7)/(5x-4)

set denom = 0 and solve for x to find domain

5x-4 = 0

5x = 4

x = (4/5)

x cannot equal (4/5)

Can the following set be the domain of an odd function?
(-3,-2)U(2,3)

Answers

Yes, the given set can be the domain of an odd function if:

f(-3) = -f(3)

f(-2) = -f(2).

What is the domain of a function?

For a function y = f(x), we define the domain of the function as the set of possible values of x that we can input into the function.

And an odd function is a function such that:

f(-x) = -f(x).

In this case, we want to see if the set:

(-3,-2)U(2,3) = (-3, -2, 2, 3)

can be the domain.

It would only be the domain of an odd function if:

f(-3) = -f(3)

f(-2) = -f(2).

If you want to learn more about odd functions, you can read:

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Please help me ASAP.

Answers

The 3 inside angles of a triangle need to equal 180.


X = 180 - 70 - 20 = 90


x = 90 degrees

If ABCDE is translated 7 units to the right and 2 units up, what will happen to the polygon?

Answers

Answer:

D.

Step-by-step explanation:

It will move but stay the same size. You are translating the shape to a different spot, not adding onto its size.

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I hope this helps!

-No one

15. What effect does reducing sample size have on s?
standard deviation and margin of error?

Answers

Step-by-step explanation:

I don't know I don't know this answer really I don't know this and so sorry sorry sorry sorry

what is the area,in the square units,of the rectangle? ​

Answers

Step-by-step explanation:

[tex]area = l \times b[/tex]

[tex]area = \frac{3}{7} \times \frac{2}{9} [/tex]

[tex]area = \frac{6}{64} [/tex]

[tex]area = 0.09375units ^{2} [/tex]

What does s equal? (Write your answer like this: s = __)

Answers

Answer:

S= -15/5

the slashes are supposed to be fractions.

Step-by-step explanation:

The box-and-whisker plot below
represents some data set. What is the value of the first quartile?

Answers

Answer: 77 is right.

Step-by-step explanation:

In the given box-and-whisker plot, the value of first quartile is 85.

What is a box and whisker plot?

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.

From the given box and whisker plot,

Minimum=77

Maximum=92

First Quartile=85

Median=87

Third Quartile=89

Therefore, in the given box-and-whisker plot, the value of first quartile is 85.

Learn more about the box plot here:

https://brainly.com/question/1523909.

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1. What is the center of dilation used to dilate quadrilateral WXYZ to quadrilateral W'X'Y'Z'?

A. (-1,3)

B. (0,0)

C. (-3,4)

D. (-1,0)

Answers

Answer: I believe the answer is C. (-3,4)

Step-by-step explanation:

Determine the value of the angle.



Angle BDC=

Answers

90°-53°=37°

The whole angle is right angled

The answer is 37 degrees.

what is 8(4 - x) = 7x + 2

Answers

-32 is the answer to your question I’m pretty sure

Answer: x = 2

Step-by-step explanation:

8(4 - x)  = 7x + 2= 8(-x + 4) = 7x + 2= -8x + 32 = 7x + 2= -8x + 32 - 32 = 7x + 2 - 32= -8x = 7x + 2 - 32 = -8x = 7x = 30= -8x - 7x = 7x + 30 - 7x= -15x = 7x - 30 - 7x= -15x = 30 -15x/-15 = -30/-15 = x = -30/-15= x = 2

And thats how you get the answer!

1) Advertisement XYZ Company charges $35 for the first four lines and $5.25 per extra
line to run the ad for one week. Jacqueline plans to sell her house and places a 15-line
ad.
a. What will Jacqueline's ad cost to run for one week?
b. What will Jacqueline's ad cost to run for four weeks?

Answers

Answer:

a)  $92.75

b)  $371

Step-by-step explanation:

Let x = number of lines in the ad

Let x = total charge per week to run the ad

Given:

Charge per week for first 4 lines = $35Charge per week for each additional line = $5.25

Create equations based on the given information:

y = 35   for x < 4

y = 35 + 5.25(x - 4)  for x ≥ 4

Part (a)

Given:

Jacqueline's ad = 15 lines

⇒ y = 35 + 5.25(15 - 4)

      = 35 + 5.25(11)

      = 35 + 57.75

      = 92.75

So the ad will cost $92.75 to run for 1 week.

Part (b)

Cost to run the ad for 4 weeks = 4 × cost of 1 week

                                                    = 4 × 92.75

                                                   = $371

Use the calculator to find the product of 4.17 and 2.3 × 106. Which statements are true about finding the product? Check all that apply.

4.17 is equivalent to 4.17 × 100.

4.17 is equivalent to 4.17 × 101.

The product has a positive exponent.

The coefficient is 6.

The E in the product is the indicator that the solution is in scientific notation.

The exponent of the product is the product of the original exponents.
PLSSS HELP

Answers

Answer:

I'm assuming that "106" is really 10^6

Step-by-step explanation:

4.17 is equivalent to 4.17 × 100.  NO  4.17 x 100 = 417

[If this is really 4.17 is equivalent to 4.17 × 10^0.  Then YES.  10^0 = 1]

4.17 is equivalent to 4.17 × 101.   NO  4.17 x 101 = 421.17

Again, if this is 10^1, then no.  10^1 = 10

The product has a positive exponent.   YES  

The coefficient is 6.

Coefficient?  NO.  Exponent?  Then YES

The E in the product is the indicator that the solution is in scientific notation.  YES  4.17E6 is 4.17 x 10^6

The exponent of the product is the product of the original exponents.

NO.  In multiplication, the exponents are added (as long as they have the same base)

A)4.17 is equivalent to 4.17 × 100.B)The product has a positive exponent.C)The E in the product is the indicator that the solution is in scientific notation.

EDGE 2022

pls answer (10 points given)

Answers

Answer:

C

Step-by-step explanation:

Its not greater than or equal to and its less than 6.

Answer:

A. x < 3

Step-by-step explanation:

2x < 6

Simplify:

2x < 6 <== divide both sides by 2

/2   /2

x < 3

Rules:

Open circle: < (going left) or > (going right)

Closed circle: ≤ (going left) or ≥ (going right)

For our answer: x < 3

It would be an open circle going left. The only number line that illustrates this is line A.

Hope this helps!

I’m confused I need this answered please

Answers

Answer:

30°

Step-by-step explanation:

145-115=30°

it is the answer

Answer:

30

Step-by-step explanation:

Since Angle FGH=FGJ+JGH, we can set the equation 145=115+x

[tex]145=115+x\\145-115=x\\30=x[/tex]

PLS HELP
Ignore everything above and below the simplify question

Answers

I think it’s 1/6 or 0.16, those two are basically the same thing

PLEASE HELP (questions in photo) I’ll mark brainliest

Answers

Answer:

a) 405, -315 b) 540, -180 c)195, -525

Step-by-step explanation:

a) 45+360= 405, 45-360=-315

b) 180+360=540, 180-360=-180

c) -165+360=195, -165-360=-525

hope this helped

All digits in a dropdown number are different and one of its digits is the average of all its digits. It has at least two digits. For example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number. a Find the smallest dropdown number.

Answers

The dropdown numbers is an illustration of combination

The smallest dropdown number is 1025

How to determine the smallest dropdown number?

From the question, we have the following parameters:

The dropdown number is 4-digitThe digits are different.

We start counting from 1023, 1024, 1025, 1026...........

The sum of digits in 1023 is 6, and the average is 1.5The sum of digits in 1024 is 7, and the average is 1.75The sum of digits in 1025 is 8, and the average is 2

The number 1025 satisfies the given conditions

Hence, the smallest dropdown number is 1025

Read more about combination at:

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You roll a number cube ten times and it lands on a 5 two times. What is the theoretical probability that it lands on a 5 on your next roll?​

Answers

Answer:

2/10 = 1/5

Step-by-step explanation:

It landed five 2 times and you rolled it 10 times

What is the sum of 2/5 and 1/8

Answers

21/40 is the answer because you need to multiply the denominators to get the same lowest value. in this instance, that is 40 because 5•8 = 40 and 8•5 = 40

(1+i)^2(x+yi)=4+5i
Solve for x and y

Answers

Answer:

x = 5/2

y = -2

Step-by-step explanation:

(1+i)² (x+yi) = 4+5i

(1+2i+)(x+yi) = 4+5i

(1+2i-1)(x+yi) = 4+5i

2i(x+yi) = 4+5i

2i²y + 2xi = 4+5i

-2y + 2xi = 4 + 5i

By comparing both sides,

-2y = 4

y = -2,

2x = 5

x = 5/2

Nevaeh spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 7475 feet.
Nevaeh initially measures an angle of elevation of 16° to the plane at point A. At
some later time, she measures an angle of elevation of 43° to the plane at point B.
Find the distance the plane traveled from point A to point B. Round your answer to
the nearest tenth of a foot if necessary.
INTL
0

Answers

Using the slope concept, it is found that the distance the plane traveled from point A to point B was of 18052.4 ft.

What is a slope?

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

At point A, the vertical change is of 7475 ft, with an angle of 16º, hence the equation below can be solved to find the position:

[tex]\tan{16^\circ} = \frac{7475}{x_A}[/tex]

[tex]x_A = \frac{7475}{\tan{16^\circ}}[/tex]

[tex]x_A = 26068.4[/tex]

At point B, the angle is of 43º, hence:

[tex]\tan{43^\circ} = \frac{7475}{x_B}[/tex]

[tex]x_B = \frac{7475}{\tan{43^\circ}}[/tex]

[tex]x_B = 8016[/tex]

Hence, the distance in feet is given by:

[tex]d = x_A - x_B = 26068.4 - 8016 = 18052.4[/tex]

More can be learned about the slope concept at https://brainly.com/question/18090623

Hi please help me out I’m really struggling with geometry rn and I can’t afford to buy the tutor thing

Answers

Alright let's solve this problem step by step:

Question 1: Find the perimeterDefinition of Perimeter: basically all the side lengths added up

   The figure is made up triangles

      ⇒ however, we do not know the slanted line that goes from the tip to

           the edge of the base.

           ⇒ we can use the Pythagorean Theorem to help us

                 [tex]2^2 + (5.7)^2 = slanted-line^2\\slanted-line = 6.04[/tex]

   Perimeter = 6.04 + 6.04 + 6.04 + 6.04 + 6.04 + 4 + 4 + 4 + 4 + 4

                      = 50.2 inches

Question 2: Find the slant heightDefinition of Slant height: is the distance measured along a lateral face from the base to the tip along the "center" of the face.

         *look at image attached to better understand this definition

           ⇒ Slant height = 5.7inches

Question 3: Find the Lateral AreaDefinition of Lateral Area: area of the non-base faces only

   Lateral Area = 5 * (Area of Triangle Faces)    

                         = [tex]5 *(\frac{1}{2} *5.7 * 4) = 5*2*5.7 = 5 * 11.4[/tex]

                         = 57 in^2

Hope that helps!

What is the sun of this question somebody tell me

Answers

Answer:

2/10 +28/10020+28/10048/10012/25

Answer:

first of all you have to take the L.C.M of both which will be 100

Step-by-step explanation:

[tex]2 \div 10 + 28 \div 100 \\ = \frac{20 + 28 }{100} \\ = \ \frac{12}{25} [/tex]

a sector has radius 14 in central angle 120 find the area of the sector​

Answers

Answer:

205.25072

Step-by-step explanation:

1. A(sector)=x/360πr^2

2. A(sector)=120/360π(14^2)

3. A(sector)=1/3π(196)

4. A(sector)=205.25072

5. Round as necessary

will someone please help me?

Answers

Answer:

x=-1

Step-by-step explanation:

1.(-9-11)(-4)/-7^2+(11*2^2)

2. =-20/-4/-7^2+11(2^2)

3. =5/7^2+11(2^2)

4. =5/-49+11(2^2)

5. =5/-49+(11)(4)

6. = 5/-49+44

7.=5/-5

8. x=-1

Please help ASAP

Find all the values of k so that the quadratic expression factors into two binomials. Explain the process used to find the values.

3x^2 + kx - 8

Answers

Answer:

Any value of k

Step-by-step explanation:

The quadratic expression can be factored into two binomials if it has two real roots.

Two real roots possible with non-negative discriminant:

D ≥ 0

As D = b² - 4ac, we get the following inequality

k² - 4(3)(-8) ≥ 0k² + 96 ≥ 0k² ≥ - 96

This is true for any value of k

k ∈ (- ∞, + ∞)

Answer:

(-∞, ∞)  or  [tex]k \in \mathbb{R}[/tex]

Step-by-step explanation:

Binomial:  two terms connected by a plus or minus sign.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

If a quadratic expression factors into two binomials, it will have two real roots.  Therefore, the discriminant will be greater than zero.

Given quadratic expression:

  [tex]3x^2+kx-8[/tex]

[tex]\implies a=3, \quad b=k, \quad c=-8[/tex]

Substitute the values of a, b and c into the discriminant, set it to > 0:

[tex]\implies k^2-4(3)(-8) > 0[/tex]

[tex]\implies k^2+96 > 0[/tex]

As k² ≥ 0 for all real numbers,

[tex]\implies k^2+96 \geq 96[/tex]

Therefore, the values of k are (-∞, ∞)  or  [tex]k \in \mathbb{R}[/tex]

Which of the x values are solutions to both of the following inequalities

100< X and x<150

Answers

100<x =x>100-(1)x<150-(2)

From both equations

100<x<150

Hence the solution set in interval notation

x[tex]\in[/tex](100,150)

I NEED THIS IN 10 MINUTES

Answers

Answer:

I believe the answer is C, the area of a circle, because pi is irrational, and anything multiplied by it will always result in an irrational number.

Step-by-step explanation:

I hope this helps and please mark me as brainliest!

Tony cut a piece of string 90 cm long into three in the ratio of 2:5:3.What is the length of the medium piece?

a. 18cm b. 24cm c. 27cm d. 45cm

Answers

Answer:

D

Step-by-step explanation:

We know the ratio of the cut string is 2 : 5 : 3. If we add 2, 5, and 3 together, we get 10. We can do 90 ÷ 10 = 9. Each number in the ratio should be multiplied by 9 to find the actual length after it is cut.

Left piece : 2 x 9 = 18 cm

Middle piece : 5 x 9 = 45 cm

Right piece : 3 x 9 = 27 cm

D is the correct answer.

I hope this helps and please mark me as brainliest!

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