James keeps his socks separately in a drawer. The drawer contains four red socks , five white

Find a cartesian equation for the curve and identify it. r = 10 tan(θ) sec(θ)

Vilka [71]

For a cartesian equation
$x=r\cos\theta \ and \ y=r\sin\theta \\ \\ \cos\theta=\frac{x}{r} \ and \ \sin\theta=\frac{y}{r} \\ \\ \tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{y}{r}\cdot\frac{r}{x}=\frac{y}{x} \\ \\ \sec\theta=\frac{1}{\cos\theta}=\frac{r}{x}$

Given r = <span>10 tan(θ) sec(θ)
$r=10\tan\theta\sec\theta=10\cdot\frac{y}{x}\cdot\frac{r}{x} \\ \\ \Rightarrow10y=x^2 \\ \\ \Rightarrow y= \frac{1}{10} x^2$

Therefore,</span>the curve is a parabola opening upward with vertex (0, 0).

3 0

3 years ago

A segment in the complex plane has a midpoint at 7 – 2i. If the segment has an endpoint at 11 – 3i, what is the other endpoint?

Gnoma [55]

Answer:

3 – i hope i helped :)))))

Step-by-step explanation:

3 0

3 years ago

You are jumping off the 12 foot diving board at the municipal pool. You bounce up at 6 feet per second and drop to the water you

NARA [144]

Answer:

When do you hit the water?

1.075 seconds after you jump.

What is your maximum height?

the maximum height is 12.5626 ft

Step-by-step explanation:

The equation:

h(t) = -16*t^2 + 6*t + 12

Is the height as a function of time.

We know that the initial height is the height when t = 0s

h(0s) = 12

and we know that the diving board is 12 foot tall.

Then the zero in h(t)

h(t) = 0

Represents the surface of the water.

When do you hit the water?

Here we just need to find the value of t such that:

h(t) = 0 = -16*t^2 + 6*t + 12

Using the Bhaskara's formula, we get:

$t = \frac{-6 \pm \sqrt{6^2 - 4*(-16)*12} }{2*(-16)} = \frac{-6 \pm 28.4}{-32}$

Then we have two solutions, and we only care for the positive solution (because the negative time happens before the jump, so that solution can be discarded)

The positive solution is:

t = (-6 - 28.4)/-32 = 1.075

So you hit the water 1.075 seconds after you jump.

What is your maximum height?

The height equation is a quadratic equation with a negative leading coefficient, then the maximum of this parabola is at the vertex.

We know that the vertex of a general quadratic:

a*x^2 + b*x + c

is at

x = -b/2a

Then in the case of our equation:

h(t) = -16*t^2 + 6*t + 12

The vertex is at:

t = -6/(2*-16) = 6/32 = 0.1875

Evaluating the height equation in that time will give us the maximum height, which is:

h(0.1875) = -16*(0.1875 )^2 + 6*(0.1875) + 12 = 12.5626

And the height is in feet, then the maximum height is 12.5626 ft

6 0

3 years ago

What is the best measure of center for the following data set?

Rom4ik [11]

Answer:

b) median: there are 7 numbers listed; 20 is the middle number among them

range: subtract lowest from highest number 25-2=23

mean: add all the numbers together =129

mode: place numbers in order (smallest to greatest), then see which number appears the most 2, 18, 18, 20, 22, 24, 25=18

Step-by-step explanation:

5 0

3 years ago

You exercise for one hour each day and you burn 8.5 calories per minute. If you graphed the number of calories you burned as the

mezya [45]

For every minute you exercise you burn 8.5 calories. It's a linear pattern, so the graph would be a line.
The more minutes you exercise, the more calories you burn, so the graph would rise from left to right.
The number of minutes and the number of calories can't be negative numbers, so the graph would be only in the first quadrant.
The larger the number of minutes, the more calories you would burn.

The answer is D.

4 0

3 years ago