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3 years ago

Help please!! 30 Pts!!

Mathematics

2 answers:

WITCHER [35]3 years ago

3 0

The answer to the first is you can convert the radians to length using a formula

Black_prince [1.1K]3 years ago

3 0

Answer:

Step-by-step explanation:

The definition of one radian is "a unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius." So, on the unit circle, because the radius is one, one radian's arc length is also one. Basically, on the unit circle, the radian measure of an angle is equal to the arc length is makes.

Trig Functions are just the coordinates on the unit circle plotted on to a graph. Think about it this way, if you pin a point on the unit circle and spin the circle, the point will go up and down and up and down forever (if there is no friction). This is the same thing with trig functions. They repeat them selves over and over again. In an actual triangle, we can't get angles more than 180 degrees, but because the trig functions go on forever, we can virtually plug in any angle degrees we want and produce an answer. The unit circle help us understand that some angles are just other angles written in another way, like 90 degrees and 450 degrees are actually the same thing.

You might be interested in

If m= (-3) and passes through (1,-5), the equation of the line is y= ?

irinina [24]

Y = -3x + c

Using (1,-5):
-5 = -3(1) + c
c = -5 + 3(1) = -2

Therefore:
y = -3x - 2

6 0

3 years ago

A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind. Find the speed of the wind

Lunna [17]

Given:

A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind.

Pilot's speed in still air is 315 miles per hour.

To find:

The speed of the wind.

Solution:

Let the speed of wind be x miles per hour.

Speed with wind = 315+x miles per hour

Speed against wind = 315-x miles per hour

We know that,

$Time=\dfrac{Distance}{Speed}$

According to the question,

$\dfrac{450}{315+x}=\dfrac{360}{315-x}$

Divide both sides by 90.

$\dfrac{5}{315+x}=\dfrac{4}{315-x}$

By cross multiplication, we get

$5(315-x)=4(315+x)$

$5(315)-5x=4(315)+4x$

$5(315)-4(315)=4x+5x$

$(5-4)315=9x$

Divide both sides by 9.

$\dfrac{(1)315}{9}=x$

$35=x$

Therefore, the speed of wind is 35 miles per hour.

4 0

3 years ago

I need the answers and explanation to a b c and d

snow_lady [41]

Answer:

a) 4x -3y ≥ -24

b) 2x +3y ≥ -12

c) 4x -3y ≤ 12

d) 2x +3y ≤ 24

Step-by-step explanation:

All of the given points are on the axes, so it is useful to know the intercept form of the equation for a line is ...

x/a +y/b = 1 . . . . . . where a is the x-intercept and b is the y-intercept.

The boundary line for the first side is ...

x/-6 +y/8 = 1

4x -3y = -24 . . . . . . multiply by -24 to put in standard form

The graph shows the quadrilateral is to the right of this line, so its inequality is ...

4x -3y ≥ -24

The boundary line for side 2 has equation ...

x/-6 +y/-4 = 1

2x +3y = -12 . . . . . multiply by -12

The quadrilateral is to the right of this line, as well, so its inequality is ...

2x +3y ≥ -12

We can see from the graph that the x-intercept of the boundary line for side 3 is x=3. The equation for that boundary line is ...

x/3 +y/-4 = 1

4x -3y = 12

The quadrilateral is to the left of this line, so its inequality is ...

4x -3y ≤ 12

Apparently, side 4 is intended to use points already given. We assume it passes through (6, 4) and (0, 8). This boundary is parallel to side 2, so will have the same equation, but with a different constant.

2x +3y = 2(0) +3(8) = 24

The quadrilateral is to the left of this line, so its inequality is ...

2x +3y ≤ 24

The second attachment shows a graph of the four inequalities with their shading.

_____

<em>Additional comment</em>

All of the inequalities are written in standard form, so the x-coefficient is positive for all of them. The direction of the inequality symbol can be chosen to select values of x that are greater than or less than those on the boundary line. If the shading is to be to the right, then larger x-values are required, and the inequality will have the form ax + by ≥ c (a > 0). If shading is to the left, then smaller x-values are required, and the inequality symbol points in the other direction.

The figure is a parallelogram, not a rectangle.