1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aleksandrvk [35]
3 years ago
15

What is the rectangular equivalence to the parametric equations?

Mathematics
1 answer:
zaharov [31]3 years ago
4 0

Notice that

(<em>x</em> - 1)²/4 + (<em>y</em> + 2)²/9 = (2 sin(<em>θ</em>))²/4 + (3 cos(<em>θ</em>))²/9

… = sin²(<em>θ</em>) + cos²(<em>θ</em>)

… = 1

Solve for <em>y</em> in terms of <em>x</em> :

(<em>x</em> - 1)²/4 + (<em>y</em> + 2)²/9 = 1

(<em>y</em> + 2)²/9 = 1 - (<em>x</em> - 1)²/4

(<em>y</em> + 2)² = 9 - 9/4 (<em>x</em> - 1)²

<em>y</em> + 2 = ± √(9 - 9/4 (<em>x</em> - 1)²)

<em>y</em> + 2 = ± 3/2 √(4 - (<em>x</em> - 1)²)

<em>y</em> = -2 ± 3/2 √(4 - (<em>x</em> - 1)²)

In order for the square root to be defined, one needs

4 - (<em>x</em> - 1)² ≥ 0

(<em>x</em> - 1)² ≤ 4

-2 ≤ <em>x</em> - 1 ≤ 2

-1 ≤ <em>x</em> ≤ 3

so <em>x</em> must belong to the interval [-1, 3].

You might be interested in
You start 80 miles east of pittsburgh and drive east at a constant speed of 65 miles per hour. (assume that the road is straight
Masja [62]
We get 65 miles away from Pittsburgh each hour, but we also started 80 miles away. Thus, our formula for dd is dd = 65tt + 80
7 0
3 years ago
Convert 14 1/8 to a decimal. <br> A. 14.1<br> B. 14.12<br> C. 14.125<br> D. 14.13
stepladder [879]
C. 14.125

------------------------------
7 0
3 years ago
Read 2 more answers
The degree measure of angle a is 135°. which expression below is equivalent to the radian measure of angle a?
Kazeer [188]

It is given that \angle a=135^{\circ}.

Now, know that in 180 degrees there are \pi radians. This can be written as:

180^{\circ}=\pi radians

\therefore 1^{\circ}=\frac{\pi}{180} radians (dividing both sides by 180)

Thus, to find the measure of the given angle of 135^{\circ} in radians, we will have to multiply the above equation by 135. Thus, we get:

135^{\circ}=\frac{\pi}{180}\times 135 radians

135^{\circ}\approx2.356 radians

Thus, equivalent to the radian measure of angle a is 2.356


7 0
4 years ago
Read 2 more answers
The amount of chlorine in a swimming pool varies directly with the volume of water. the pool has 2.5 milligrams of chlorine per
Mandarinka [93]
1 gallon = 3.785 liters
Water in pool = 8000 x 3.785
Water in pool = 30,280 liters

Chlorine dosage = 2.5 mg / liter
Chlorine = 2.5 x 30,280
Chlorine = 75,700 mg
To the nearest thousand milligram:
Chlorine = 76,000 mg
8 0
3 years ago
Please answer all please​
Firdavs [7]

Answer:

Step-by-step explanation:

The first parabola has vertex (-1, 0) and y-intercept (0, 1).

We plug these values into the given vertex form equation of a parabola:

y - k = a(x - h)^2 becomes

y - 0 = a(x + 1)^2

Next, we subst. the coordinates of the y-intercept (0, 1) into the above, obtaining:

1 = a(0 + 1)^2, and from this we know that a = 1.  Thus, the equation of the first parabola is

y = (x + 1)^2

Second parabola:  We follow essentially the same approach.  Identify the vertex and the two horizontal intercepts.  They are:

vertex:  (1, 4)

x-intercepts:  (-1, 0) and (3, 0)

Subbing these values into y - k = a(x - h)^2, we obtain:

                                            0 - 4 = a(3 - 1)^2, or

                                                -4 = a(2)².  This yields a = -1.

Then the desired equation of the parabola is

y - 4 = -(x - 1)^2

7 0
3 years ago
Other questions:
  • Hans's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Hans
    7·1 answer
  • If you answer this question you don’t just get brainliest. You also get a cookie
    13·2 answers
  • HURRY PLEASE !!!!
    13·2 answers
  • ex weighed 80 pounds a year ago. Now he weighs 92 pounds. What is the percent increase in his weight?
    14·1 answer
  • What shape dosent belong and why
    11·2 answers
  • What is 15/8 in mixed number form
    7·2 answers
  • Solve for x. 12x+252=324
    11·2 answers
  • Hi I really need help on this question please
    12·1 answer
  • Write 0.2 as and fraction
    13·2 answers
  • Are the ratios 6:3 and 2:1 equivalent?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!