Eliminate the parameter:
x = 2cost-1 y = 3sint+ 4

Answers

Answer 1

Answer:

Hi,

Step-by-step explanation:

[tex]\left\{\begin {array} {ccc}x&=&2*cos(t)-1\\y&=&3*sin(t)+4\\\end{array}\right.\\\\\\\left\{\begin {array} {ccc}\dfrac{x+1}{2}&=&cos(t\\\dfrac{y-4}{3}&=&sin(t)\\\end{array}\right.\\\\Squaring\\\\\boxed{(\dfrac{x+1}{2})^2+(\dfrac{y-4}{3})^2&=1}\\[/tex]

The curve is an ellipse having (-1,4) as center and half-axis (2 and 6)

Related Questions

Slope of (-9,-2) and (-9,-6)

Answers

Answer:

Slope is undefined.

Step-by-step explanation:

A coffee table is on sale for 20% off the original price of $115. If there is 7.5% sales tax, what is the final price of the coffee table?

Answers

Answer:

The final price for the coffee table is $98.9.

Step-by-step explanation:

1. First, is to convert the percentage to decimal form

We can do this by changing 7.5% to decimal number by dividing 7.5 by 100, we get:

\frac{7.5}{100}

100

7.5

= 0.0750.075

2. Then multiply 0.075 to the original price of $115

0.075(115) = 8.625

Then, add 8.625 to the original price of $115, we get:

115 + 8.625 = $123.625

3. After this, we subtract the 20% discount to $123.625

We can do this by converting 20% to decimal form, we get:

\frac{20}{100}

100

= 0.20.2

Then, multiply $123.625 by 0.2, we get:

123.625(0.2) = $24.725

4. Then subtract 24.725 from $123.625, we get:

123.625 -123.625−24.725 = $98.9

Final price of the table coffee which is on sale by 20% with a sales tax of 7.5% is $98.9.

WILL MARK BRAINLIST!!
I NEED THE ANSWER STEP BY STEP.
find the smallest number by which 1323 must be divided so as to get a perfect square number. Also, find the square root of the square number so obtained.

Answers

Answer:

It is 49. You will know it is right down here:

Step-by-step explanation:

1323 when factorised = 3 *3*3*7*7

Therefore it is to be divided by 7*7 = 49

Rate down here and give thanks to me!!! Hope it helps everyone!!!

The troupe’s account balance first reached $500 on Day 4. The last day the account balance was $500 was
Day 8.
(a) Determine C(5), C(6), and C(7). Explain how you determined these amounts.
(b) Estimate C(1), C(2), and C(3). Explain how you determined these amounts.
(c) The stage manager said that the amount of money taken out of the account each day between Day 8
and Day 11 was the same amount of money put into the account each day between Day 0 and Day 4.
Recall that Day 11 is when the balance first reached $0. Without doing any calculations, how could
you show the stage manager was incorrect?

Answers

Answer:

The answer is c, hope this helps

Step-by-step explanation:

find the altitude of a kite where 120 feet of string makes a 64 degree angle to the ground

Answers

Answer:

107.86 to 2 d.p.

Step-by-step explanation:

makes a triangle. 120 feet is the hypotenuse.

we want to find the opposite so we will use sine.

sin(x) = opp/hyp which means opp = sin(x)hyp.

opp = sin(64)120

opp = 107.86 to 2d.p.

Which is true about the functional relationship shown in the graph?

Answers

Answer A. Y is cost and x is weight the shopping cost is a function of the weight of the package

A number cube is rolled 15 times how many times would you expect a number less than 3 to be rolled

Answers

Answer:

Step-by-step explanation:

how many number you rolled 3 times how many times its rolled 15 x 3 +45

Therefore,the answer would be 45

Factorise completely 12 x³y - 18 xy²

Answers

Answer:

6xy(2x²-3y)

Step-by-step explanation:

factorized completely

One ball is selected at random from a bag containing 12 balls of which x are white
a) what is the probability of selecting a white ball?
when a further 6 were white balls were added the probability of selecting a white ball is doubled
b) Find x

Answers

Answer:

a) 12/18

b) 6

Step-by-step explanation:

If adding 6 white balls doubles the probability then the original amount of balls is 6 and with the new amount of 18, the likelihood of picking a white ball becomes 12/18.

Quadrilateral ABCD has the following coordinates: A(-6,3) B(-4,5) C(-1,6) and D(-3,2) and
maps onto A"B"C"D". It will undergo transformations that will consist of a reflection over
the y-axis followed by a translation. Point D" is shown plotted in the plane after the
transformation.

A) Write the translation rule that maps point D' to point D".

B) Write the coordinates of point A"

Answers

The translation rule that maps point D' to D" is (x + 3, y) and the coordinate of point A" is (9,3)

How to determine the translation rule?

The coordinates are given as:

A(-6,3) B(-4,5) C(-1,6) and D(-3,2)

When reflected across the y-axis, the transformation rule is:

(x,y) -> (-x,y)

So, we have:

A' = (6,3)

D' = (3,2)

Point D" on the grid is (6,2).

This means that the translation rule that maps both point is (x + 3, y)

The coordinates of point A

In (a), we have:

A' = (6,3)

Using the translation rule (x + 3, y), we have:

A" = (6 + 3,3)

A" = (9,3)

Hence, the coordinate of point A" is (9,3)

Answers

Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.

What does the Central Limit Theorem state?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.

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Help!! Also the questions says “Which of the following shows JUST a variable?”

Answers

The answer is (g)

Variables are letters that represent unknown numbers
It can be any letter if the alphabet (a,b,c,d…..)
The others are what we call an (expression )which is basically when we put variables with other numbers

the diagram shows a sector of a circle radius 10cm
calculate the perimeter of the sector
give answer to 1 decimal place

Answers

Answer:

[tex]\text{Perimeter of sector = 43.6 (Rounded to the nearest tenth.)}[/tex]

Step-by-step explanation:

[tex]\text{Perimeter of the sector = Radius + arc length + radius}[/tex]

[tex]\text{Radius = 10 cm}[/tex]

[tex]\text{Perimeter of the sector = 10 + arc length + 10 }[/tex]

[tex]\text{Perimeter of the sector = 20 + arc length }[/tex]

[tex]\text{arc length = (sector angle/ 360 ) * perimeter of the circle}[/tex]

[tex]\text{Perimeter of a circle }=2\pi r[/tex]

[tex]\text{sector angle} = 135[/tex]

[tex]\text{arc length} = (135/ 360 ) * 2\pi (10)[/tex]

[tex]= (3/8) 20\pi[/tex]

[tex]= 15\pi /2[/tex]

[tex]\text{Using }\pi =3.14[/tex]

[tex]= 15 * 3.14 /2[/tex]

[tex]= 23.55[/tex]

[tex]\text{Perimeter of the sector = 20 + 23.55}[/tex]

[tex]= 43.55[/tex]

[tex]= 43.6 cm[/tex]

[tex]\text{perimeter of the sector = 43.6 cm }[/tex]

A parallelogram has a base of 16 centimeters and a height of 12 centimeters. What is the area of the parallelogram?

I think it's 192, am I correct?

Answers

Answer:

Correct (192)

Step-by-step explanation:

The formula for a parallelogram's area is just base times height. 16x12 is equal to 192, so you are correct.

A parallelogram can be:

The square, which has all its sides of equal length, and all its angles are right angles. The rhombus, which has all sides of equal length, and only two pairs of congruent angles. The rectangle, which has only its opposite sides of equal length, and all its angles are right angles.

Therefore we calculate the rectangle of a square, which is a parallelogram.

To start solving, we obtain the following data:

Area = 16cmHeight = 12cmArea = ? ===> (It is the result that we are going to obtain)

The formula to calculate the area is:

[tex]\bf{a=b*h }[/tex]

To calculate the area, multiply the base by the height (which is represented in "h")

We clear formula, calculate the area:

[tex]\bf{A=(16 \ cm)(12 \ cm) \ \ \ ==== > \ Multiply }[/tex]

[tex]\bf{A=192 \ cm^{2} }[/tex]

Answer: The area of the parallelogram is 192 cm2. So if you're right, it was a rectangle.

represent the sum of 3/4 and -5/8 is ???

Answers

3/4 + -5/8

---Find a common denominator

6/8 + -5/8

---Simplify

1/8

Hope this helps!

Answer:

3/4 + -5/8 = 1/8

Step-by-step explanation:

When adding fractions, you always need to find a common denominator. 4 and 8 share a common denominator of 8.

You multiply 3/4 by 2/2 and get 6/8.

When adding negative numbers, it is the same as subtracting.

6/8 + (-5/8) =

6/8 - 5/8 = 1/8

So 1/8 is the answer.

I hope this helps!

Find the length of PC , the distance between San Cristobal and Panama. Show your work. Remember to scale the distance up by a factor of 10.

Answers

Answer:

Step-by-step explanation:

If a baseball player hits 10 home runs in the first 45 game, at the same rate how many home runs can he expect to hit during the 162 game season

Answers

Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the player hits 10 home runs in 45 games, hence the proportion is:

p = 10/45.

Then, in 162 games, the amount is:

HR = 10/45 x 162 = 36.

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Kelly made fruit punch to serve at a party for her chess team. She mixed 1
2/5
liters of cranberry juice and 1
3/5
liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each glass?

Answers

Answer:

1/3 liters. or 33.33333 ml

Step-by-step explanation:

1 2/5 + 1 3/5 = 3

3 liters of juice is there.

3 liters of juice/9 glasses.

1/3 liters of juice is in every glass

what is 1/10 as a decimal does it equal 0.1

Answers

1/10 is equal to 0.1 and 10%

1/10 = 10% = 0.1

Example:
What is 10% of 100?
100 X 0.1 = 10

When θ = 0, cos θ = 1. What is the next radian value that will result in cos θ = 1?

Answers

The only place where cos = 1 is at the coordinate point (1,0) on the unit circle (when theta=0). So, if you revolve around the unit circle once more from theta=0, you get that theta =2pi since the circumference of the unit circle in radians is 2pi.

The volume of air in a balloon is represented by the function v(r)=4/3 pi ^3, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function r(t) = 1².
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements.

Answers

It is true for multiple reasons

What is the value of f(x) when x=3?

Answers

Still only f the 3 adds a exponent

A rectangle is 21 meters long and 11 meters wide. what is the perimeter of this rectangle?

Answers

Step-by-step explanation:

the perimeter is simply the distance you would have to walk when going around the whole object once.

so, you would go a length, a width, another length and another width, until you are finally arriving back at the starting point.

so, the perimeter of a rectangle is

2×length + 2×width = 2×21 × 2×11 = 42 + 22 = 64 m

Simplify 7x²-x²
how to simplify this maths question

Answers

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to simplify the expression [tex]\large\pmb{7x^2-x^2}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Combine like terms! :)

That's exactly what we need to do - combine like terms.

So, we subtract:

[tex]\star~\large\pmb{7x^2-x^2}[/tex]

Which gives us:

[tex]\star~\large\pmb{6x^2}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Please help me thank you :3

Answers

Quadrilaterals are angles that has 4 sides and angles. The measure of the angle m<SPQ is 110 degrees

Angles in a quadrilateral

Quadrilaterals are angles that has 4 sides and angles. The given quadrilateral is a rhombus with equal opposite sides.

Given the following angles

m<SPR = 2x + 15

m<QPR = 3x - 5

From the figure

m<SPR = m<QPR

Substitute

2x+ 15 = 3x - 5

2x - 3x = -5 - 15

x = 20

Determine the measure of <SPQ
m<SPQ = 3x - 5 +2x +15

m<SPQ = 5x + 10
m<SPQ =5(20) + 10
m<SPQ = 110 degrees

Hence the measure of the angle m<SPQ is 110 degrees

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The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was bought at a wholesale price of \$113.00$113.00dollar sign, 113, point, 00, and Jessica's Furniture Store marks up all furniture by 45%, percent.

Answers

Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

How much should the manager charge for the couch that just arrived?

Given that;

Purchase price = $113.00 marks up = 45%Selling price = ?

First, we determine the mark price.

Since the Furniture Store marks up all furniture by 45%.

Mark up price = mark up × purchase price

Mark up price = 45% × $113.00

Mark up price = 0.45 × $113.00

Mark up price = $50.85

Now, the selling price will be;

Selling price = Purchase price + mark up price

Selling price = $113.00 + $50.85

Selling price = $163.85

Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

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The slope of a line is 7/8 The y-intercept of the same line is 4
Complete the slope-intercept form equation

Answers

Answer:

y = -7/8x + 4

Step-by-step explanation:

Slope-intercept form :

y = mx + b

m = slopeb = y-intercept

Hence, the equation formed is :

y = -7/8x + 4

how can i find area of abd triangle. .............

Answers

Answer:

6 square units

Step-by-step explanation:

The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.

angles

Any right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.

Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.

segments

The fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.

The tangent ratio is ...

Tan = Opposite/Adjacent

Applying that to angle β, we have

tan(β) = OD/AD [eqn 1]

tan(β) = BC/AC [eqn 2]

These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.

area

Equation [eqn 1] tells us ...

AD = OD/tan(β)

Equation [eqn 2] tells us ...

BC = AC·tan(β)

The area of ΔADB is ...

Area = 1/2bh

Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))

Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel

The length of AC is given as 6, and we know OD = 2, so the area is ...

Area = 1/2(2)(6) = 6

The area of triangle ADB is 6 square units.

What is the phenotypic ratio of the offspring? 1:1:1:1:2:2:2:2:4 1:3:3:9 1:4 4:12

Answers

The phenotypic ratio of the offspring as shown in the given Punnett square is: 1:3:3:9.

What is Phenotypic Ratio?

Phenotypic ratio is quantitative relation of the number of offspring of a cross that manifest a certain combination of traits or characteristic.

From the Punnett square given, there are:

9 round and yellow individuals3 round and green individuals3 wrinkled and yellow individuals1 wrinkled and green individuals

Therefore, the phenotypic ratio would be: 1:3:3:9.

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Answer:

B it the answer 1:3:3:9

Step-by-step explanation:

Which point is one fourth of the way between point A and point B on the line segment AB shown on the coordinate plane below?

Answers

The coordinate of the point between point A and point B on the line segment AB is [tex](\frac 92, -\frac{19}4)[/tex]

How to determine the point?

The points are given as:

A = (4,-5)

B = (6,-4)

m : n = 1 : 3

The coordinate of the point is then calculated using:

[tex]P = \frac{1}{m + n}(mx_2 + nx_1,my_2 + ny_1)[/tex]

So, we have:

[tex]P = \frac{1}{1 + 3}(1 * 6 + 3 * 4, 1 * -4 + 3 * -5)[/tex]

Evaluate the sum of product

[tex]P = \frac{1}{4}(18, -19)[/tex]

Evaluate the product

[tex]P = (\frac 92, -\frac{19}4)[/tex]

Hence, the coordinate of the point is [tex](\frac 92, -\frac{19}4)[/tex]

Eliminate the parameter: x = 2cost-1 y = 3sint+ 4

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Eliminate the parameter:
x = 2cost-1 y = 3sint+ 4