Find [tex] \frac{dy}{dx} [/tex] if [tex]x = a( \theta - \sin \theta)[/tex], [tex]y = a(1 + \cos \theta)[/tex] Or Prove that [tex] \frac{dy}{dx} = - \cot (\frac{ \theta}{2} )[/tex]

Answers

Answer 1

Hope this answer helps you

$Find [tex] \frac{dy}{dx} [/tex] If [tex]x = A( \theta - \sin \theta)[/tex], [tex]y = A(1 + \cos \theta)[/tex]$

Related Questions

Which of the following transforms y=x squared to the graph of y=(x+5) squared

Answers

The transformation which transforms y = x² to the graph of y = (x + 5)² as required in the task content is; a translation of 5 units leftwards.

Which transformation renders y = x² to the graph of y = (x + 5)²?

It follows from the task content that the transformation responsible for the mapping y = x² to the graph of y = (x + 5)² is to be determined.

Since the pre-image graph given in the task content is; y = x².

Recall that a translation of a graph f(x) by k units leftward is represented as; f (x + k).

On this note, the given transformation of y = x² to the graph of y = (x + 5)² as required in the task content can be attributed to;

A horizontal shift of 5 units leftward.

Put simply, the required transformation is; a translation of the graph of y = x² 5 units leftwards.

Answers

Answer:

Step-by-step explanation:

Given: Number of roses = 8, Number of daisies =12 and number of marigolds 48.

Since we have given,

Number of roses = 8 , Number of daisies = 12 and number of marigolds = 48.

The factors of 8 = 2 * 2 * 2

The factors of 12 = 2 * 2 * 3

The factors of 48 = 2 * 2 * 2 * 2 * 3

Therefore, greatest common factor of 8, 12 and 48 is 4.

Therefore, the total number of arrangements = 4

Answer: 4

Sample Response: The points on the number line do represent additive inverses. 3 and −3 are a zero pair, and when added they equal zero. The two numbers are the same distance from zero but in opposite directions. The following are reasons why 3 and −3 are additive inverses. Check all of the conditions you included in your response.

Answers

When two numbers added together result in 0, this is known as additive inverse. Using this notion, points on a number line are used to depict additive inverse.

Explain the term additive inverse?To get a result equal to 0, add the original number and the additive inverse by simply switching the sign of the integer. On the basis of negation of a original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

The dotted points with the numbers 3 and -3 are the places on the number line.

To determine whether the points show an additive inverse:

Points 1 and 2 add up to 0.

3 + (-3) = (3 - 3) = 0

When two numbers added together result in 0, this is known as additive inverse.

Using this notion, points on a number line are used to depict additive inverse.

Thus, the points therefore display additive inverse.

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Its in the attachment

Answers

Domain: (−∞,∞),{x|x∈R} and Range: (−∞,∞),{y|y∈R} for f(x)=0.5x

What is a function?

A relation is a function if it has only One y-value for each x-value.

Given,

Helene is selling cupcakes for $0.50 each.

The function f(x)=0.5x gives the total amount of money Helene makes after selling x cup cakes.

We need to find the domain and range of the function

solve the equation f(x)=0.5x to determine the values of the independent variable x and obtain the domain.

To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).

Domain: (−∞,∞),{x|x∈R}

Range: (−∞,∞),{y|y∈R}

Hence, Domain: (−∞,∞),{x|x∈R} and Range: (−∞,∞),{y|y∈R} for f(x)=0.5x

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Which pair of sides is perpendicular

Answers

Answer:

Step-by-step explanation:

d is the answer

Mary takes out a loan for $6,000 at a simple interest rate of 12% to be paid back in 36 monthly installments. What is the amount of her monthly payments?

Answers

The monthly payment would be an amount of $226.67.

What exactly is a monthly payment?

A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.

Mary takes out a loan for $6,000 at a simple interest rate of 12% to be paid back in 36 monthly installments.

The total payback = P× r/100 × T + P

Here P = $6,000 , r = 12, and T = 3 years

The total payback = 6,000 × 12/100 × 3 + 6,000

The total payback = 6,000 × 0.12 × 3 + 6,000

The total payback = $8,160

The total payback of the borrowings will be $8,160 over a three-year period. The monthly payment for this will be,

The monthly payment = Total payback / No. of payment

The monthly payment = 8,160/36

The monthly payment = $226.67

Therefore, the monthly payment would be an amount of $226.67.

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You are organizing party invitations. The stamps come in packs of 20. The invitations
come in packs of 15. What is the least number of stamps and invitations you can buy so
you have an even number of stamps and invitations?

Answers

Answer:

255

Step-by-step explanation:

You need the least common multiple (LCD) of 15 and 17.

The prime factorizations of 15 and 17 are

3 × 5

Since there are no common factors, the LCM is their product.

15 × 17 = 255

Answer: 255

Solve
13=d÷6 plsssssssssssssssssssssssssssssssssssssss

Answers

Well 6x13 would equal 78 which means 78 divided by 6 would be 13

5^55x55^22x55^-95=
Anyone?

Answers

Answer:

2.4938705426067307E - 8

Step-by-step explanation:

Juan runs out of gas in a city. He walks 12 yards west and then 5 yards south looking for a gas station. How far is he from his starting point?

Answers

Answer:17

Step-by-step explanation:when we add the 12+5 together and will be the answer

Find the values of X and Y. State which theorem(s) you used.

Answers

Using alternating and corresponding angle theorem, the value of x and y are (8, 146), (86, 94) and (21, 29.5) respectively

Alternate and Corresponding Angle Theorem

Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent. Corresponding and Alternate angles are the most fundamental angles formed when two parallel lines are intersected by a transversal line.

3x = 5x - 64

Reason: Alternate angles are equal

5x + 3x = 64

8x = 64

x = 8

y + 5x - 6 = 180

Reason: Angles on a straight line are equal to 180

y + 5(8) - 6 = 180

y + 40 - 6 = 180

y + 34 = 180

y = 146

6) x = 86

Reason: Alternating angles are equal to one another

y + 86 = 180

Reason = 94

7) 2y = 59

Reason: Vertical angles are equal

y = 59 / 2

y = 29.5

2y = 3x - 4

Reason: Alternate angles are equal

2(29.5) = 3x - 4

59 = 3x - 4

3x = 59 + 4

3x = 63

x = 21

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SAS
HL
State how the triangles can be proven
congruent, if possible.
AAS
ASA

Answers

Answer:

SAS or HL

Step-by-step explanation:

SAS, you have two sides and two angles congruent on each triangle

HL, you have two hypotenuses and two right angles congruent

Francesca is way behind on email. Over winter break, she resolves to deal with 5 emails per
day.
Write an equation that shows the relationship between the number of days Francesca has
been on winter break, x, and the total number of emails she has dealt with, y.
y =
Submit

Answers

The equation for the total number of emails Francesca has dealt with is; y = 5x.

Explain the term linear equation?A linear equation is just an algebraic expression of the form y=mx+b, where m represents the slope while b is the y-intercept, while only a constant and the first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equations of two variables."

For the stated question-

Five emails are handled by Francesca each day.Assume that Francesca has been away on winter break for 'x' days.Let y represent the overall amount of emails she has handled.

Then, the linear equation forms is-

y = 5x

Thus, the equation for the total number of emails Francesca has dealt with is; y = 5x.

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When subtracting two numbers, you add the (_______) of the number being subtracted

Answers

Answer:

When subtracting two numbers you add the (additive inverse) of the number being subtracted.

Step-by-step explanation:

That's one of the rules of subtracting integers.

what is -57.17 as a mixed number

Answers

The value of 57.17 as a mixed number is - 57 17/100.

In simple terms, what is a mixed number?

A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction value remains constant. We can say that the simplified mixed number and the actual mixed number are fractions that are equivalent.

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the proper fraction that results in the mixed number.

In this case, -57.17 will be:

= -57 + (17/100)

= -57 17/100.

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HELP ME. I HATE MATH DUDE.

Answers

Refer to the photo taken.

Can someone help me solve these problems?

Answers

Answer:

2. A is false

B is false

C is false

D is true

*1/2
*4 to 4
*2:1
*8/4

Answers

Answer:

1/2

Step-by-step explanation:

shaded sections = 4

total sections = 8

4/8

(4:4)/(8:4)

1/2

Answer:

The answer is 4:4.

Step-by-step explanation:

What is 12% sugar syrup using 5 grams of sugar

Answers

I think you divide 12 and 5 which would be 2.5%

In circle M with m ∠ L M N = 106 and LM=4 units, find the length of arc LN. Round to the nearest hundredth.

Answers

The length of arc LN of the circle is 7.40 units rounded to the nearest hundredth.

How to calculate for the length of arc of a circle

To calculate for the length of an arc of a circle, we use 2πr × (θ/360), where r is the radius and θ is the angle formed from the arc.

Thus we evaluate for the length of the arc as follows;

for π = 3.14, r = 4 and θ = 106°

2 × 3.14 × 4 × (106/360)°

25.12 × 0.2944

7.3953

Therefore, the length of the arc 7.3953 and rounded up to 7.40 to the nearest hundredth.

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Which statements are always true regarding the diagram? Select three options.

m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°

Answers

The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:

C. m∠5 + m∠6 =180°.

D. m∠2 + m∠3 = m∠6.

E. m∠2 + m∠3 + m∠5 = 180°.

What is the Linear Pair Postulate?

The Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two (2) adjacent angles would be equal to 180º when two (2) parallel lines are cut through by a transversal:

m∠5 + m∠6 =180°.

What is the exterior angle property?

The exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:

m∠2 + m∠3 = m∠6.

In conclusion, the sum of all the angles formed by a triangle is equal to 180º:

m∠2 + m∠3 + m∠5 = 180°,

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I need to find x and y

Answers

Using the same-side interior angles theorem,

[tex]8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}[/tex]

Using vertical angles,

[tex]6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}[/tex]

Type the integer that makes the following subtraction sentence true:
- -188 = -559
Submit

Answers

Answer: -787

188 is positive, negative and negative equals positive

559 is negative

the answer needs to be negative as 559 is negative so you add 559 and 188 and get 787 and add a negative sign so it's more "negative" than 188. (hard to explain in writing)

-787--188=-559

-787+188=-559

-559=-559

Can somebody help me solve

Answers

Answer:17.5

Step-by-step explanation: trust me

perimeter of a rectangle is 36 cm . If the length of the rectangle is 12 cm . Find its area.

Answers

Answer: 72 cm

Step-by-step explanation:

So since we know its length is 12 cm, that leaves us with finding the width. You could do that by adding the two length's together to get 24, then subtract that from the perimeter to get 12. The widths being added together must equal 12 and be the same, so we can divide by 2 to get 6 cm as the width. Then multiply 6 times 12 to get 72

Answer: A=72 cm²

Step-by-step explanation:

Let the width of the rectangle be x

Hence, P=36 cm l=12 cm

P=2(l+x)

P=2l+2x

P-2l=2x

Divide both parts of the equation by 2

Thus,

[tex]\displaystyle\\x=\frac{P-2l}{2} \\\\x=\frac{36-2(12)}{2}\\\\x=\frac{36-24}{2} \\\\x=\frac{12}{2} \\\\x=6 cm\\\\[/tex]

Area A=l*x

A=12*6

A=72 cm²

Con Beads for Everyone Mrs. Harris wants her nineteen students to each have twenty-four beads to make a bracelet. Mrs. Harris finds beads in bags at the store. There are twelve beads in each bag. How many bags of beads does Mrs. Harris need to buy so she has exactly enough beads for her nineteen students? Each bag of beads costs $0.59. How much will Mrs. Harris spend on the beads? Show all your mathematical thinking.

Answers

Answer:

i.She needs 96 bags of beads

ii.She will spend $56.64 on the beads

Step-by-step explanation:

i.19×24=456

12÷456=96

96 bags

ii.96×0.59

=56.64

$56.64

If I get $147.00 every two weeks for child support? In a year how much would that equal up to?

Answers

Answer:

Step-by-step explanation:

52 weeks in a year

Divide 52 by 2 = 26 weeks

26 weeks x 147 dollars = 3822 dollars

Thus the answer is 3822 dollars yearly

Answer:$3,528

Step-by-step explanation:

since there are 4 weeks in a month that would mean you would have to multiply 147 by two and that would = to $294.00/month so then you would have to multiply that by 12 so then that would = to $3,528.00 a year.

Question 2 (1 poing
This table shows the total shipping costs for objects of
different weights.
Shipping Costs
$6.00
$3.00
$1.50
O $1.25
Weight of Object
(in pounds)
4
8
12
16
Total Shipping Cost
(in dollars)
5
11
17
23
Based on the information in the table, by how many dollars
does the total shipping cost increase if the weight of an
object increases by 1 pound?

Answers

Based on the information in the table, the dollars that the total shipping cost will increase if the weight of an object increases by 1 pound is C. $1.50

What is an equation?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It should be noted that from the information, the table shows the total shipping costs for objects of different weights.

In this case, let the dollar amount be x.

Based on the information, this will be:

4x = 6

Divide

x = 6/4

x = 1.5

In conclusion, the correct option is C.

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What is the equation of a line that is parallel to 2x + 3y = 3 and passes through the point (3, -4)?
Enter your answer as a slope intercept equation (y=mx+b) in the box.

Answers

Answer:

y = - [tex]\frac{2}{3}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

given

2x + 3y = 3 ( subtract 2x from both sides )

3y = - 2x + 3 ( divide through by 3 )

y = - [tex]\frac{2}{3}[/tex] x + 1 ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

• Parallel lines have equal slopes , then

y = - [tex]\frac{2}{3}[/tex] x + b ← is the partial equation

to find b substitute (3, - 4 ) into the partial equation

- 4 = - 2 + b ⇒ b = - 4 + 2 = - 2

y = - [tex]\frac{2}{3}[/tex] x - 2 ← equation of parallel line

Write a variable expression for a number w decreased by 7

Answers

Answer:

Let the number be x. "Seven less than a number" means that we need to subtract 7 from unknown number and result would be 34. . Then, x−7=34Add 7 on both sides of the equationx−7+7=34+7x=41.

Step-by-step explanation:

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Find [tex] \frac{dy}{dx} [/tex] if [tex]x = a( \theta - \sin \theta)[/tex], [tex]y = a(1 + \cos \theta)[/tex] Or Prove that [tex] \frac{dy}{dx} = - \cot (\frac{ \theta}{2} )[/tex]​

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Find [tex] \frac{dy}{dx} [/tex] if [tex]x = a( \theta - \sin \theta)[/tex], [tex]y = a(1 + \cos \theta)[/tex] Or Prove that [tex] \frac{dy}{dx} = - \cot (\frac{ \theta}{2} )[/tex]