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lorasvet [3.4K]
2 years ago
8

Here's the question, please help!

Mathematics
2 answers:
asambeis [7]2 years ago
8 0
  • x=2sint
  • y=3sint

#1

  • x²/2+y²/3
  • (2sint)²/2+(3sint)²/3
  • 4sin²t/2+9sim²t/3
  • 2sin²t+3sim²t
  • 5sin²t

False

#2

  • x²+y²
  • 4sin²t+9sin²t
  • 13sin²t

False

#3

  • 3x²+2y²
  • 3(4sin²t)+2(9sin²t)
  • 12sin²+18sin²t
  • 30sin²t

False

None of the above

nata0808 [166]2 years ago
6 0

Answer:

None of these

Step-by-step explanation:

To convert the parametric curve into Cartesian form,
rewrite the equation for x to make \sin t the subject:

x=2\sin t

\implies \sin t=\dfrac{x}{2}

Substitute this into the given equation for y:

\begin{aligned}y & =3 \sin t\\\implies y & = 3 \left(\dfrac{x}{2}\right)\\y& = \dfrac{3}{2}x\end{aligned}

Therefore, the Cartesian form of the parametric curve is:

y=\dfrac{3}{2}x

<u>Further Information</u>

<u />

\dfrac{x^2}{2}+\dfrac{y^2}{3}=1 \quad \textsf{is the equation of a vertical ellipse}

\textsf{with center (0, 0), co-vertex }\sf \sqrt{2}, \textsf{ and vertex }\sqrt{3}

x^2+y^2=6 \quad \textsf{is the equation of a circle}

\textsf{with center (0, 0) and radius }\sf \sqrt{6}

3x^2+2y^2=1 \quad \textsf{is the equation of a vertical ellipse}

\textsf{with center (0, 0), co-vertex }\sf \dfrac{\sqrt{3}}{3}, \textsf{ and vertex }\dfrac{\sqrt{2}}{2}

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Someone pls pls pls help me
WINSTONCH [101]

Answer:

  A, C, D, E

Step-by-step explanation:

According to the rational root theorem, any rational roots will be of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

The constant is 8, and its divisors are 1, 2, 4, 8.

The leading coefficient is 6, and its divisors are 1, 2, 3, 6.

So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:

  • A, 2/3
  • C, -8
  • D, 4
  • E, -1/6
8 0
3 years ago
A) What is the domain and range of the graph? (Use the equations editor or explain)
riadik2000 [5.3K]

The domain: -5 < x ≤ 1 and the range: -3 ≤ y ≤ 1 is a function. b)

No, the vertical line crosses the graph in more than one place, therefore, the relation shown is a function.

<h3>What is the domain and range of the function?</h3>

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The domain of a relation is the set of values of the independent variable for a defined function.

The domain is the horizontal extent of the graph.

The range of a relation is the set of values of the dependent variable for a defined function.

The range is the vertical extent of the graph.

The vertical line can intersect the graph in at most one place.

a)

This graph extends from x > -5 to x = 1.

The domain

 -5 < x ≤ 1   ------   (-5, 1] in interval notation

This graph extends from y = -3 to y = 1.

The left side of the graph does not include the point (-5, 1), but the right side includes the point (1, 1).

y = 1 is one of the output values of the relation.

The range

 -3 ≤ y ≤ 1 . . . . . . . . [-3, 1] in interval notation

b)

No, the vertical line crosses the graph in more than one place, therefore, the relation shown is a function.

Learn more about the domain and range of the function:

brainly.com/question/2264373

#SPJ1

8 0
2 years ago
Please help! This is due soon!!!
daser333 [38]

Answer:

The slope of the line is

\frac{1}{3}

3 0
3 years ago
What is the compound interest if $480 is invested for 12 years at 6% compounded continuously?
Anna [14]

Answer:

<em>$506.13</em>

Step-by-step explanation:

A = Pe^{rt}

A = $480 \times e^{0.06 \times 12}

A = $986.13

The account will be worth $986.13.

The interest earned is $986.13 - $480 = $506.13.

6 0
3 years ago
Write the inequality that represents the solution set for −6z17&lt;−23
Rashid [163]
Still need help??!? if so I have and idea probably -∞yuf4
8 0
3 years ago
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