All categories

2 years ago

Which equation in rectangular form describes the parametric equations x=5-3cost and y=4+2sint?

Mathematics

1 answer:

Sidana [21]2 years ago

8 0

Answer:

D. (-x+5)^2/9+(y-4)^2/4=1 (I assume there was a mistype)

Step-by-step explanation:

The first step is isolating the sine and cosine functions.

x=5-3cos(t)

x + 3cos(t) = 5

3cos(t) = 5 - x

cos(t) = (5 - x)/3

y=4+2sin(t)

y - 4 = 2sin(t)

(y - 4)/2 = sin(t)

Then, square at both sides of the equal sign

cos²(t) = (5 - x)²/3² = (5 - x)²/9

sin²(t) = (y - 4)²/2² = (y - 4)²/4

Recall the trigonometric identity and replace.

cos²(t) + sin²(t) = 1

(5 - x)²/9 + (y - 4)²/4 = 1

You might be interested in

Find the slope of the line(s) passing through the given points. Then tell whether the line(s) rises, falls, is horizontal, or is

bonufazy [111]

Answer:

21) falls

22) vertical

23) rises

24) rises

25) falls

26) horizontal

27) rises

28) horizontal

29) falls

Step-by-step explanation:

We shall use the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ to calculate the slopes of the line passing through each pair of point.

21: (3,1), (2,6)

The slope is $m=\frac{6-1}{2-3}$

$\implies m=\frac{5}{-1}=-5$ .

A negative slope means this line falls

22) (-2,5), (-2,4)

The slope is $m=\frac{4-5}{-2- -2}=\frac{-1}{0}$ = undefined

An undefined slope means this line is vertical

23) The given point is (0,8) (2,10)

The slope is $m=\frac{10-8}{2-0}=\frac{2}{2}=+1$

A positive slope means this line rises

24) The points are (-3,-3), (3,1)

The slope is $m=\frac{1--3}{3--3}=\frac{4}{6}=+\frac{2}{3}$

A positive slope means this line rises

25) The points are: (5,0) (6,-2)

Slope: $m=\frac{-2-0}{6-5}=\frac{-2}{1}=-2$

A negative slope means this line falls

26) The points are (-2,-8) , (5,-8).

Slope: $m=\frac{-8--8}{5--2}=\frac{0}{7}=0$

A zero slope means this line is horizontal

27) The points are: (-1,2) , (5,3)

Slope: $m=\frac{3-2}{5--1}=+\frac{1}{6}$

A positive slope means this line rises

28) The points are: $(\frac{1}{2},4)$ , (-1,4)

Slope: $m=\frac{4-4}{-1-\frac{1}{2}}=\frac{0}{\frac{1}{2}}=0$

A zero slope means the line is horizontal

29) The points are: $(4,\frac{1}{2}), (5,\frac{1}{4})$

Slope: $m=\frac{\frac{1}{4}-\frac{1}{2}}{5-4}=-\frac{1}{4}$

A negative slope means this line falls.

6 0

3 years ago

I NEED HELP PLEASE, THANKS! :) Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)^4.

Amiraneli [1.4K]

Answer: a) zeros: x = {0, 4, -2}

b) as x → ∞, y → ∞

as x → -∞, y → ∞

Step-by-step explanation:

I think you mean (a) find the zeros and (b) describe the end behavior

(a) Find the zeros by setting each factor equal to zero and solving for x:

x (x - 4) (x + 2)⁴ = 0

x = 0 Multiplicity of 1 --> odd multiplicity so it crosses the x-axis

x = 4 Multiplicity of 1 --> odd multiplicity so it crosses the x-axis

x = -2 Multiplicity of 4 --> even multiplicity so it touches the x-axis

Degree = 6

(b) End behavior is determined by the following two criteria:

Sign of Leading Coefficient (Right side): Positive is ↑, Negative is ↓
Degree (Left side): Even is same direction as right side, Odd is opposite direction of right side

Sign of the leading coefficient is Positive so right side goes UP

as x → ∞, y → ∞

Degree of 6 is Even so Left side is the same direction as right (UP)

as x → -∞, y → ∞

7 0

3 years ago

Shaded areas please help guys ❤❤❤

pentagon [3]

Answer:

77cm

Step-by-step explanation:

Area of a rectangle=L×B

7×11=77cm

3 0

3 years ago

Read 2 more answers

Rewrite using a negative exponent. 5/x^2

SashulF [63]

Answer:

5x^-2 is rewritten as a negative exponent

4 0

3 years ago

2. Trey measured the mass of some pebbles What is the combined mass of the pebbles that are 4 1/2 grams or more?

Romashka-Z-Leto [24]

Answer:

Step-by-step explanation:

3 0

3 years ago