Simplify 2m(8m) ....

Evaluate.<br>4-6(3-5)1-3<br>

CaHeK987 [17]

Answer:

13

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

What type of conic section is represented by the parametric equations below? X=3cos(t)-1 y=3sin(t)+4

Andrei [34K]

Answer:

Circle

Step-by-step explanation:

Examples of conic sections are the circle, the ellipse, the parabola and the hyperbola. Parametric equations are used to express the x and y variables in terms of a less complicated manner using a third variable (t or θ).

The parametric equation for a circle with an equation $(x-h)^2+(y-k)^2=r^2$ is given by:

$x=rcos(t)+h, y=rsin(t)+k$

where r is the radius of the circle and (h, k) is the center of the circle.

A conic section with a parametric equations X=3cos(t)-1, y=3sin(t)+4 is a circle with center at (-1, 4) and radius of 3. The equation of the circle is:

(x + 1)² + (y - 4)² = 3²

3 0

2 years ago

Use the data to find the lower quartile value.

grandymaker [24]

Answer:$9.75

Step-by-step explanation:

6 0

3 years ago

Find the equation of the straight line that has slope m = -6 and passes through point (2, -7)

MAXImum [283]

Answer:

y

=

3

2

x

+

1

Explanation:

To find the slope

(

m

)

of the straight line that passes through two points

(

x

1

,

y

1

)

and

(

x

2

,

y

2

)

apply:

(

y

1

−

y

2

)

=

m

(

x

1

−

x

2

)

In this example our two points are

(

0

,

1

)

and

(

2

,

4

)

Hence:

(

1

−

4

)

=

m

(

0

−

2

)

−

3

=

−

2

m

→

m

=

3

2

The equation of a straight line in slope

(

m

)

and intercept

(

c

)

form is:

y

=

m

x

+

c

In this example:

y

=

3

2

x

+

c

Since the point

(

0

,

1

)

is on this line

→

1

=

0

+

c

Hence,

c

=

1

∴

y

=

3

2

x

+

1

is our required straight line.

Step-by-step explanation:

3 0

3 years ago

A camera is mounted at a point 4000 feet away from a geyser. If the water is rising vertically at 900 ft/s when it is 3000 feet

Leno4ka [110]

Answer:

$\dot \theta = 0.144\,\frac{rad}{s}$ , $\dot \theta = 8.251\,\frac{deg}{s}$ (Option B)

Step-by-step explanation:

The trigonometric diagram is included herein as attachment. The expression is presented below:

$\tan \theta = \frac{y}{x}$

Where:

$x$ - Horizontal distance between the geyser and the camera.

$y$ - Vertical distance between the geyser and the camera.

The rate of change in terms of time is:

$\dot \theta \cdot \sec^{2}\theta = \frac{\dot y\cdot x-y\cdot \dot x}{x^{2}}$

$\dot \theta \cdot \left(\frac{1}{\cos^{2}\theta} \right) = \frac{\dot y \cdot x - y\cdot \dot x}{x^{2}}$

$\dot \theta = \left(\frac{\dot y \cdot x - y \cdot \dot x}{x^{2}} \right)\cdot \cos^{2}\theta$

$\dot \theta = \left(\frac{\dot y \cdot x - y\cdot \dot x}{x^{2}} \right)\cdot \left(\frac{x^{2}}{x^{2}+y^{2}} \right)$

$\dot \theta = \frac{\dot y \cdot x - y\cdot \dot x}{x^{2}+y^{2}}$

Finally,

$\dot \theta = \frac{\left(900\,\frac{ft}{s} \right)\cdot (4000\,ft)-(3000\,ft)\cdot \left(0\,\frac{ft}{s} \right)}{(4000\,ft)^{2}+(3000\,ft)^{2}}$

$\dot \theta = 0.144\,\frac{rad}{s}$

$\dot \theta = 8.251\,\frac{deg}{s}$

3 0

2 years ago