Order these numbers from least to greatest.

You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

3 years ago

Jamal watched his older brother Robert lift weights. The bar alone had a mass of 20 kg. on the bar he had two 11.4 weights, two

Leto [7]

What you have to do is add them all!
20 bar
11.4 2 11.4 weights
11.4
4.5 2 4.5 weights
4.5
450.0 4 450 weights
450.0
450.0
+450.0
---------
1.8
10
200
+1,600
--------------
1,811.8 is the answer

6 0

3 years ago

Manas receives a commission of Rs.5,000 on sales of Rs.65,000.How much commission will he get on sales of Rs.20,000.

tangare [24]

$\\
\text{Let Manas receives a commission of Rs. 5000 on sales of Rs. 65000}\\
\\
\text{We need to find how much commision he will get on the sale of Rs.20000}\\
\\
\text{To find the commision, we use the unitary method.}\\
\\
\text{On sales of Rs. 65000, Manas receives a commision of}=5000\\
\\
\text{so on sales of Rs. 1, Manas will receiv a commision of}=\frac{5000}{65000}\\
\\
\text{Hence on sales of Rs. 20000, Manas will receiv a commision of}\\
\\=\frac{5000}{65000}\times 20000\\
\\
=1538.46$

Hence, on the sales of Rs. 20000, Manas will receive a commission of: Rs. 1538.46

6 0

3 years ago

The angles in a triangle are represented by 5x, 8x, and 2x+9. What is the value of x?

Ahat [919]

Answer:

x = 11.4

Step-by-step explanation:

The sum of the angles of any triangle must add up to 180°. Since we have the expressions for each angle: 5x, 8x, and (2x +9), we can solve for the variable of 'x' by adding the expressions together and setting them equal to 180:

5x + 8x + (2x +9) = 180

Combine like terms: 15x + 9 = 180

Use inverse operations: 15x + 9 - 9 = 180 - 9

15x = 171 or x = 11.4

Check: 5(11.4) + 8(11.4) + 2(11.4) + 9 = 57 + 91.2 + 22.8 + 9 = 180

8 0

3 years ago

Convert 7TV/ 6 radians into degrees

zhenek [66]

Answer:

YEkk

Step-by-step explanation:

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5 0

3 years ago