eliminate the parameter,t, in the parametric equation, x=6cos t, and y =3 sin t

Answers

Answer 1

To eliminate the parameter t in the parametric equations x = 6 cos t and y = 3 sin t, we can use the trigonometric identity

cos⁡²t + sin⁡²t = 1cos²t + sin²t = 1.

Starting with x=6 cos t, we can rewrite it as cos t=x6 and from y=3 sin t, we can rewrite it as sin t = (y/3).

Now, we square both equations:

(cos t)² = (x/6)²

(sin t)² = (y/3)²

As soon as we multiply both sides by 36, we arrive at:

x² + 4y² = 36

Therefore, the equation x² + 4y² = 36 is the Cartesian equation that eliminates the parameter t from the given parametric equations.

To eliminate the parameter t in the parametric equations x=6 cos t and y=3 sin t, we use trigonometric identities.

From x=6 cost, we get cos t = x//6, and from y = 3 sin t, we get sin t = (y/3).

Squaring both equations and using the identity cos2t+sin2t=1 we obtain (x/6)² + (y/3)² = 1. Simplifying, we get (x²/36) + (y²/9) = 1 which, after multiplying by 36, becomes x² + 4y² = 36. Thus x² + 4y² = 36 is the Cartesian equation eliminating the parameter t.

Complete Question:

Eliminate the parameter, t, in the parametric equation, x=6 cos t, and y =3 sin t.

Related Questions

This graph shows how much Marie earns babysitting compared with the number of hours she works select the correct statement about the graph

Answers

The answer is D

The graph reflects that she is getting paid 10 dollars an hour

If you plot the points, you will see she makes 5 dollars every half hour

Answer:

Option D is the answer.

Step-by-step explanation:

This graph represents a linear function representing earnings of Marie at y axis and hours of working at x axis. To get the change in Marie's earnings for every 5 hours we will find the slope of the given line.

Slope of the line will define the rate of change in earning of Marie with respect to the time.

End points of the line at time t = 0 and t = 5 hours are (0, 0) and (5, 50).

Therefore slope = [tex]\frac{y-y'}{x-x'}=\frac{50-0}{5-0}=\frac{50}{5}=10[/tex]

So for each hour she works her earnings go up by $10.

Option D is the correct option.

Oil-rich countries in the middle east cover about 4% of earth’s total land area but possess about 48% of the world’s known oil reserves. what is the main reason for the high concentration of reserves in this part of the world?

Answers

I'd say this high concentration is due to geological processes
Geological processes are things such as erosion, tectonic plate shifts, e.t.c.

You have a 45-gallon jug and a 124-gallon jug. neither of the jugs has any markings (although you do know their capacities). describe a way to measure exactly one gallon of water.

Answers

Pour 4 times of 124-gallon into a big jug.
Amount of water = 124 x 4 = 496 gallons

Then use the 45-gallon jug to scoop out the water 11 times.
Amount of water scooped out = 11 x 45 = 455 gallons

Water remaining = 496 - 450 = 1 gallon.

4*124 = 496
11*45 = 495

Fill the 124-gallon jug 4 times, emptying it each time into the 45-gallon jug. After the 45-gallon jug has been filled 11 times, there will be 1 gallon remaining in the 124-gallon jug.

_____
Mathematically, this works fine. In practice, you're looking for a 1-gallon difference after handling 495 gallons of water. That's about 0.2% of the total amount of water transferred. Any error along the way will substantially affect the outcome.

A technique used to rewrite a quadratic function in standard form to vertex form is

Answers

The vertex form of a quadratic function is given by
[tex]f(x)=a(x-h)^{2}+k, [/tex]
where (h,k) is the vertex of parabola. In some literatures, the standard form of the quadratic equation is written as
[tex]f(x)=a x^{2} +bx+c[/tex]
Therefore, in order to avoid the confusion, the first equation is taken as a vertex form. When the standard form is converted into the vertex form, the process is called completing the square.

Answer:

completing the square.

Step-by-step explanation:

trust me

Bruce bought a map that cost $7.35 he used a $10 bill to pay for his map what is the change

Answers

$2.65

You can get this by subtracting the 7.35 from the 10.

10 - 7.35 = 2.65

if an object is propelled upward from a height of s feet at an initial velocity of v feet per second h=-16t^2+96t+8 after how many seconds is the height 116 feet?

Answers

654 is the answer for this question

What percent of the scores were between 71 and 96

Answers

Any more info? Please?

Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The figures are not drawn to scale

A. yes; 1:1:2
B. yes; 1:1:4
C. yes; 1:2:4
D. no

Answers

we have that
smaller figure
ha=8.7
ra=1.6

larger figure
hb=10.44
rb=1.92

ha/hb=8.7/10.44----> 0.83
ra/rb=1.6/1.92-------> 0.83

ratio smaller figure to the larger figure
1.6/1.92-------> divided by 1.6 both members
[1.6/1.6]/[1.92/1.6]-------> 1/1.2

the ratio ha/hb is equal to the ratio ra/rb
so
the smaller figure and the larger figure are similar
and the ratio smaller figure to the larger figure is equal to----> 1/1.2

the answer is
the option
yes 1/1.2

hey can you please help me posted picture of question

Answers

The solutions to the given quadratic equation can be determined using quadratic formula.

[tex]x= \frac{-b+- \sqrt{ b^{2} -4ac} }{2a} [/tex]

b =coefficient of x term = -1
a = coefficient of squared term = 4
c = constant term = 9

Using the values in the above formula we get:

[tex]x= \frac{1+- \sqrt{1-4(4)(9)} }{2(4)} \\ \\ x= \frac{1+- \sqrt{-143} }{8} \\ \\ x= \frac{1+-i \sqrt{143} }{8} [/tex]

So, option D gives the correct answers

You have been averaging 55 sales per day. Per our new policy, everyone needs to increase his or her sales per day by 10% in the next month. Rounding up, by next month you will need to be up to __________ sales.

Answers

The next month sales should be 1,815.

Given that,

You have been averaging 55 sales per day. increase his or her sales per day by 10% in the next month

Based on the above information, the calculation is as follows:

[tex]= 55 \times 1.10 \times 30 days[/tex]

= 1,815

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Final answer:

To meet the new policy of a 10% increase in sales, you would multiply your current average sales by the increase percentage and round up to the nearest whole number. Starting from 55 sales, a 10% increase results in an additional 5.5 sales, which when rounded up equals 6. Therefore, you need to achieve 61 sales per day.

Explanation:

If you have been averaging 55 sales per day and need to increase your sales by 10%, you will first need to calculate the increase. To calculate a 10% increase, you multiply your current average sales (55) by the percentage increase (10%), expressed as a decimal (0.10). The increase in sales can be found by the formula:

Increase = Current Sales × Percentage Increase

For your sales:

Increase = 55 × 0.10 = 5.5 sales

Since you need to round up, the increase will be 6 sales when considering whole units, as you cannot sell half a unit.

Therefore, the new target sales per day will be:

New Sales Target = Current Sales + Increase

New Sales Target = 55 + 6 = 61 sales

By next month, you will need to be up to 61 sales per day after rounding up.

Find the derivative of f(x) = (1 + 5x2)(x − x2) in two ways. use the product rule. f '(x) = perform the multiplication first. f '(x) = do your answers agree? yes no

Answers

Answer:

The answers agree.

[tex]f^{\prime}(x) = - 20x^{3} + 15x^{2} - 2x + 1[/tex]

Step-by-step explanation:

The product rule is:

[tex]f(x) = g(x)h(x)[/tex]

[tex]f^{\prime}(x) = g^{\prime}(x)h(x) + g(x)h^{\prime}(x)[/tex]

In this problem, we have that:

[tex]f(x) = (1 + 5x^{2})(x - x^{2})[/tex]

[tex]g(x) = 1 + 5x^{2}[/tex]

[tex]g^{\prime}(x) = 10x[/tex]

[tex]h(x) = x - x^{2}[/tex]

[tex]h^{\prime}(x) = 1 - 2x[/tex].

[tex]f^{\prime}(x) = g^{\prime}(x)h(x) + g(x)h^{\prime}(x)[/tex]

[tex]f^{\prime}(x) = (10x)*(x - x^{2}) + (1 + 5x^{2})(1-2x)[/tex]

[tex]f^{\prime}(x) = 10x^{2} - 10x^{3} + 1 - 2x + 5x^{2} - 10x^{3}[/tex]

[tex]f^{\prime}(x) = - 20x^{3} + 15x^{2} - 2x + 1[/tex]

Multiplication first:

[tex]f(x) = (1 + 5x^{2})(x - x^{2})[/tex]

[tex]f(x) = x - x^{2} + 5x^{3} - 5x^{4}[/tex]

[tex]f(x) = -5x^{4} + 5x^{3} - x^{2} + x[/tex]

[tex]f^{\prime}(x) = -20x^{3} + 15x^{2} - 2x + 1[/tex]

Comparing the results, we can see that the derivatives obtained using the two methods are indeed the same. The answer is yes.

What's the function about?

The derivative of f(x) = (1 + 5x2)(x − x2) can be found using the product rule and by performing the multiplication first.

Using the product rule:

The product rule states that the derivative of f(x)g(x) is f′(x)g(x)+f(x)g′(x).

In this case, f(x) = 1 + 5x2 and g(x) = x − x2. So the derivative of f(x)g(x) is:

f′(x)g(x)+f(x)g′(x)

=(10x+10x3)(x−x2)+(1+5x2)(2x−2x3)

=10x2−10x3+10x3−10x4+2x−2x3+1+10x2−10x3

=−10x4+12x2+2x

Performing the multiplication first:

We can first multiply out the expression (1 + 5x2)(x − x2) to get:

x2−5x4+x3−5x3+x−x2

=−5x4+12x2+x

Then, we can take the derivative of this expression to get the same derivative as we found using the product rule:

f′(x)=−10x4+12x2+2x

Therefore, the derivative of f(x) = (1 + 5x2)(x − x2) is -10x4+12x2+2x, regardless of whether we use the product rule or perform the multiplication first.

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A rectangular storage area is to be constructed along the side of a tall building. a security fence is required along the remaining 3 sides of the area. what is the maximum area that can be enclosed with 800 m of fencing? (a = lw)

Answers

Let l represent the length of fence parallel to the side of the building. Then the width will be that of half the remaining fence, (800 -l)/2. The total area will be
A = lw = l(800 -l)/2

This is the equation of a downward-opening parabola with zeros at l=0 and l=800. The zeros are symmetrical about the axis of symmetry of the parabola, which axis goes through the vertex. That is, the vertex is located at
l = (0 +800)/2 = 400

The maximum aea that can be enclosed is 400 m long by 200 m wide, so is
(400 m)×(200 m) = 80,000 m²

Final answer:

To find the maximum area enclosed with 800 m of fencing, the dimensions of the rectangular storage area need to be determined. The perimeter equation is derived to eliminate a variable, allowing the area to be expressed in terms of the remaining variable. Using this approach, the dimensions that maximize the area can be found.

Explanation:

To find the maximum area that can be enclosed with 800 m of fencing, we need to determine the dimensions that will result in the largest possible area. Let's assume the length of the rectangular storage area is L and the width is W.

Since there are 3 sides already covered by the security fence, the perimeter of the rectangular storage area will be: 2L + W = 800 m.

To find the maximum area, we need to eliminate one variable from the equation above. We can do this by expressing W in terms of L and substituting it back into the area formula A = LW.

By applying this approach, we can find the dimensions of the rectangular storage area that will enclose the maximum area with 800 m of fencing.

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A standard dartboard has a diameter of 18 in. What is its area to the nearest square inch?

Answers

The meaning of the area is the measurement of a surface in this case a circle, which can be find by using the formula [tex]A= \pi r^{2} [/tex], where r is equal to the radius of the circle.

In this exercise is given that the diameter of a standard cardboard is 18 inches or a radius of 9 inches and it is asked to find its area. Therefore, to find the area of the circle you should substitute the value of the radius into the previous mention formula.

[tex]A= \pi r^{2}[/tex]
[tex]A= \pi (9 in)^{2} [/tex]
[tex]A= \pi (81 in^{2})[/tex]
[tex]A=254.47 in^{2} [/tex]

The area of the standard dartboard is 254.47 square inches or 254 square inches.

Joe and jill set sail from the same point, with joe sailing in the direction s4 degrees e and jill sailing in the direction s9 degrees w. after 4 hr, jill was 2 miles due west of joe. how far had jill sailed?

Answers

The angle between Joe and Jill's initial directions is 4° +9° = 13°. The angle Joe measures after 4 hours between Jill's position and their starting point is 90° -4° = 86°. The law of sines can be used to find Jill's travel distance.

Jill's distance = (distance to Joe)*(sin(86°)/sin(13°))
Jill's distance = (2 mi)*0.99756/0.22495
Jill's distance = 8.869 mi

Jill had sailed 8.9 miles in 4 hours.

write an expression that represents the difference between t and 8

Answers

An expression could be x= t-8

Hello there, and thank you for posting your question here on brainly.

Short answer: t - 8

Why?

When we are finding the difference between two numbers, we are subtracting. So, the difference between t and 8 would be t - 8.

Hope this helped you! ♥

How would you solve:

|*| 2x + 7 = 3 |*|
????

Answers

2x + 7 = 3
2x = 3 - 7
2x = -5
x = -5/2

hey user

the answer to this is going to be
we do this math

2x + 7 = 3
and then
2x = 3 - 7
then
2x = -5
and we get

x = -5/2

hope l helped

have a good day

The elevation is 12,000 feet. the altimeter reading in an airplane is 17.00 in hg. this pressure is equal to

Answers

The elevation is 12,000 feet. the altimeter reading in an airplane is 17.00 in hg. this pressure is equal to:
There are 29.92inHg in 1 atm
thus
17 inHg×(1 atm/29.92inHg)
=17/29.92
=0.5682 atm

Answer: 0.5682 atm

Iris is building a model of the Washington Monument. Her model measures 15 in. tall and is 1.5 in. wide at the base. The actual width measurement at the base of the Washington Monument is about 55 ft. About how tall is the Washington Monument?

Answers

Using how tall it is over how wide
=>tall/wide
The model 15in/1.5in
The actual x/55ft

Convert everything into the same units so 55ft to inches
There are 12in in 1ft
55ft * 12in/1ft
The ft cross out leaving in
55*12in= 660 in

So
15in/1.5in = x/660in
Now solve for x my multiplying both side by 660in
660in *15in/1.5in=x
x= 6600in tall

Answer: 550

Step-by-step explanation:Solve the proportion: 15 in./1.5 in. = h/55 ft. The value of h is 550 ft. The Washington Monument is about 550 ft tall.

Find the area of the figure

Answers

You can solve each figure individually; the parallelogram, and the trapezoid.

The parallelogram, you can just do base * height. The base is 11 yards, and the height is 4 yards. 11 * 4 = 44 square yards.

Now for the trapezoid. If you split it up into a rectangle and a triangle, it becomes much more easier to solve. The rectangle and triangles can be made by splitting the figure down the center. This makes a rectangle with a length of 7 yards and a height of 8, and a triangle with a base of 7 yards and a height of 8 as well.

Solve for the area of both shapes.

The rectangle: Multiply length * height: 7 * 8 = 56 square yards

The triangle: Multiply base * height, and then divide by 2: 7 * 8 = 56
56 / 2 = 28 square yards

Now add the areas together.

28 + 56 + 44 = 128 square yards

Hope this helped!

These are the steps:
1. Find area of the trapezium.
2. Find area of the parallelogram.
3. Add the 2 areas together.

Step 1: Find the area of the trapezium:

Formula : area = 1/2 (a + b) h

Area = 1/2(7 + 14) (8) = 84 yd²

Step 2: Find the area of the parallelogram:

Formula : area = base x height

Area = 11 x 4 = 44 yd²

Step 3: Find the total area:

Total Area = 84 + 44 = 128 yd²

Answer: 128 yd²

Suppose that 44% of all Americans approve of the job the President is doing. The most recent Gallup poll consisted of a random sample of 1,400 American adults.

a. What is the mean of the sampling distribution?

b. What is the standard deviation of the sampling distribution (don't forget to justify the use of the formula)?

c. Describe the normal approximation for this sampling distribution (don't forget to justify this) You can simply write as N (mean, standard deviation)

d. What is the probability that the Gallup poll will come up with a proportion within three percentage points of the true 44%

Answers

a) Mean = n × p, n is 1400 and p is 0.44, using what you know 0.44 (p)× 1400 (n) = 616

b) SD = √ (n×p×q) n 1400 p is 0.44 and q = 1-p=1-0.44=0.56

find the volume of the cylinder in terms of pi h=11 r=3.4

Answers

Volume of a cylinder= pi*r2*h
=3.142 * (3.4*3.4) * 11
=3.142 * 11.56 * 11
=36.32152 * 11
=399.53672

V=399.54
Hope this helps

3.4 *3.4 = 11.56
11.56 * 11 = 127.16

The answer is 127.6(Pi)m^3

Hope this helps

hey can you please help me posted picture of question

Answers

The solutions to the given quadratic equation can be determined using quadratic formula.

[tex]x= \frac{-b+- \sqrt{ b^{2} -4ac} }{2a} [/tex]

b =coefficient of x term = -2
a = coefficient of squared term = 1
c = constant term = 10

Using the values in the above formula we get:

[tex]x= \frac{2+- \sqrt{4-4(1)(10)} }{2(1)} \\ \\ x= \frac{2+- \sqrt{-36} }{2} \\ \\ x= \frac{2+-6i}{2} \\ \\ x=1+3i, x=1-3i [/tex]

So the correct answer to this question is option A

Ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. After recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. What does 0.45 represent in the equation? A) the lowest ticket price B) the number of miles traveled C) the expected change in the price of multiple tickets Eliminate D) the expected change in price of the ticket for each mile traveled

Answers

D) the expected change in price of the ticket for each mile traveled
Because it is a coloration between the two

Noa was paid a 25 percent commission for selling a used car.

Percents

Total

100%

If she was paid $1,631.24, what was the selling price of the car?

Answers

25 percent of x is equal to $1631.24
.25*4 is equal to 100 percent
Substitute
1631.24*4=x
x=6524.96

Answer:

$6,524.96 Is Your Answer :3

sq root of x +11 =15

Answers

Hello!

You can solve for x by subtracting 11 from 15 to get 4. Once you've got 4, you can power 4 by 2 (4²) to get 16 as your answer

x=16

So the value of x is 16

I hope this helps!

Remark
I take it you want to find x.

Square both sides.
(sqrt(x + 11))^2 = (15)^2
x + 11 = 225 Subtract 11 from both sides.
x = 225 - 11
x = 214

Edit
This answer is edited to reflect which interpretation is correct. If you give out Brainlys (and you should) give it to Brick123. We all need them.

Sqrt(x) + 11 = 15 Subtract 11 from both sides.
sqrt(x) = 15 - 11
sqrt(x) = 4 Square both sides.
(sqrt(x)^2 = 4^2
x = 16

Evaluate 10m + n2/4 when m = 5 and n = 4

Answers

Answer:

[tex]54[/tex]

Step-by-step explanation:

we have

[tex]10m+\frac{n^{2}}{4}[/tex]

For [tex]m=5.n=4[/tex]

substitute the values of m and the value of n in the equation

[tex]10(5)+\frac{4^{2}}{4}[/tex]

[tex]50+4[/tex]

[tex]54[/tex]

Answer:54

Step-by-step explanation:

A table is going to be painted. How much less surface area of the table will be painted if the underside remains unpainted. The length is 22 in, the width is 20 in, and the height is 1 in

Answers

The answer is the surface area will be 440 square inches less.

dr. Trekcir has $875 to invest. he invests some of it in account#1 paying 8% annual interest and the rest of it in account#2 paying 4% annual interest. After 1 year total interest is $49.00. find hou much is invested in each account

Answers

Here's what the equation would look like (I'm using the variable n for the investments):
0.08n + 0.04(875-n) = 49
Multiply both sides by 100:
8n + 3500 - 4n = 4900
Simplify:
4n+3500=4900
Isolate n:
4n = 1400
n = 350
8% invested: 350
4% invested: 525

The height of an object from a distance

Answers

y = height
x = distance from tower

tan(19.9) = y/x

tan(21.8) = y/(x-50) ( x is 50 feet closer so subtract 50 from x)

find the tan of the angles:
tan19.9 = 0.362
tan21.8 = 0.400

replace those values in the equations:
0.362 = y /x
0.400 = y / (x-50)

rewrite to solve for height:
0.362x = y
0.400(x-50) = y distribute the 0.400 and rewrite as 0.400x-20 =y

now solve:

0.362x = 0.400x-20

add 20 to each side:
0.362x +20 = 0.400x

subtract 0.362x from each side:

20 = 0.038x

divide both sides by 0.038
x = 20 / 0.038 = 526.3 feet

now that x is known replace x in the original equation and solve for y:

tan19.9 = y /x

0.362 = y / 526.3
y = 0.362 x 526.3
y = 190.5

the height of the tower is 190.5 feet

a proton moves in an electric field such that its acceleration a is a=-20(1+2t)^-2, where t is the time in seconds. Find the velocity as a function of time if v sub zero =30 when t=0

Answers

a = dv/dt, therefore, to get an expression for v(t), we would integrate the expression for a:
a = -20/(1+2t)^2
v = (1/2)*20/(1+2t) + k = 10/(1+2t) + k
At t = 0:
v0 = 10/1 + k = 30
Therefore, k = 20, and the expression for v(t) is
v(t) = 10/(1+2t) + 20

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