Find two positive numbers such that the sum of the first and twice the second is 100

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

2 years ago

Can someone help me please

IgorLugansk [536]

Answer:

B

Step-by-step explanation:

The slope is 4.

Let's find the slope between your two points.

(1,−2); (3,6)

(x1,y1) = (1,−2)

(x2,y2) = (3,6)

Use the slope formula:

m = y2−y1 / x2−x1

= 6− −2 / 3−1

= 8 / 2

= 4

Answer:

m = 4

7 0

2 years ago

Read 2 more answers

Assume that advanced students average 93% on an achievement test and regular students averaged 75%. If 100 advanced students and

Lemur [1.5K]

Average (mean) = (sum of all the data) / (# of data)

sum of all the data = (average)(# of data)

Thus for 100 students with an average of 93,
sum of all data = (93)(100) = 9300

and for 300 students with an average of 75,
sum of all data = (75)(300) = 22500

Therefore you would expect the overall average to be
(9300 + 22500) / (100 + 300) = 79.5 %

Now if there are x # of advanced students and y # of regular students, then

x + y = 90 (total # of students) and 93x + 75y = 87(x + y) (overall average)

The second equation can be simplified to x - 2y = 0

Subtracting the two equations yields

x = 60 and y = 90

Therefore you would need 60 advanced and 30 regular students.

7 0

3 years ago

Help!! does anyone know what it’s called when there is two or more functions on the same graph?

Lubov Fominskaja [6]

Answer:

System

Step-by-step explanation:

4 0

3 years ago

Sydney is 5 feet and 1 inch tall. What would her height be in centimeters? (1 foot = 12 inches, 1 inch = 2.54 centimeters) 24.01

Alik [6]

Answer:

154.94 cm so pick the third answer.

Step-by-step explanation:

5*12+1=61 total inches.

61*2.54=154.94 cm

8 0

3 years ago

Read 2 more answers