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3 years ago

An angle measures 4.3 radians. To the nearest degree, what is the measure of the angle? degrees

Mathematics

2 answers:

ElenaW [278]3 years ago

7 0

Answer:

Step-by-step explanation:

$\frac{deg}{rad}=\frac{360}{2\pi}=\frac{180}{\pi}\\ \\ deg=\frac{180rad}{\pi}\\ \\ deg=\frac{180(4.3)}{\pi}\\ \\ deg=\frac{774}{\pi}^o\\ \\ deg\approx 246^o$

Thepotemich [5.8K]3 years ago

4 0

Answer:

246

Step-by-step explanation:

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4 years ago

What is the most precise classification of the quadrilateral formed by connecting in order the midpoints of the figure below? Sh

AlekseyPX

Answer:

Rhombus

Step-by-step explanation:

The given trapezoid has vertices at M(-4,0), J(-2,4), K(2,4), and L(4,0).

Use the midpoint formula: $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

To obtain the midpoint of MJ:

$A=(\frac{-4+-2}{2},\frac{0+4}{2})=(-3,2)$

Similarly, the midpoint of of JK is B=(0,4), the midpoint of KL is C=(3,2), and the midpoint of LM is D=(0,0).

Now use the slope formula;

$m=\frac{y_2-y_1}{x_2-x_1}$

To find the slope of AB = $\frac{4-2}{0--3}=\frac{2}{3}$

The slope of BC = $\frac{2-4}{3-0} =-\frac{2}{3}$

The slope of CD= $\frac{0-2}{0-3}=\frac{2}{3}$

The slope of AD= $\frac{0-2}{0--3}=-\frac{2}{3}$

We can see that the slope of the opposites sides are parallel, CD is parallel to AB and AD is parallel to BC.

The product of the slopes of the adjacent sides is not -1.

Hence the shape formed by connecting the midpoint of the isosceles trapezoid is a parallelogram.

Obviously the side lengths are equal since we connected all midpoints.

The parallelogram is a rhombus.

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3 years ago

HELP PLS Given a polynomial function f(x), describe the effects on the Y-intercept, regions where the graph is increasing and de

Mashcka [7]

1. Remarks:

f(x) to f(x)-3 is the whole graph of f(x), shifted 3 units down.

f(x) to -2f(x):

The effect of "multiplication by -" is that the whole graph is reflected with respect to the x axis, so it is turned upside down.

The effect of "multiplication by 2" is that every point is "stretched vertically by a factor of 2" . So for example the point (-1, -4) in the original function, becomes (-1, -8) in the second one. Or (2, 5) would become (2, 10).

The only points that do not change (are not streched vertically) are the roots. For example if (4,0) is an x-intercept (a root) in the original function, (4,0) is still a root in the second one because 2 times 0 is still 0.

2. Consider the polynomial function of degree n:

$f(x)= a_{n} x^{n} +a_{n-1} x^{n-1}+....+a_{2} x^{2}+a_{1} x^{1}+a_{0}$

a. Y-intercept

The y - intercept is the value of the polynomial function at x=0.
So it is f(0)= $a_{0}$ , that is, the constant term of f(x)

in f(x)-3 the y intercept is shifted 3 units down as any other point, so it becomes $a_{0}-3$

In -2f(x), the y-intercept $a_{0}$ becomes $-2a_{0}$

b. Regions of f decreasing or increasing

f(x)-3 is f(x) just shifted down 3 units, so they are both increasing and decreasing in the same intervals of x

-2f(x) is f(x) turned upside down, so -2f(x) is increasing in all intervals f(x) is decreasing and it is decreasing in all intervals f(x) is increasing.

c. End behaviors

By now it is clear that end behaviors of f(x) and f(x)-3 are same, and f(x) with -2f(x) are opposite

d. Evenness, oddness

If f(x) is even, then f(x)=f(-x)

Let g(x)=f(x)-3

g(x)=f(x)-3=f(-x)-3=g(-3), so in this case f(x)-3 is even

If f(x) is odd, then f(-x)=-f(x)

g(x)=f(x)-3=-f(-x)-3,

so -g(x)=f(-x)+3

g(-x)=f(-x)-3,

so g(-x) is not equal to -g(x). Which means f(x)-3 is not odd if f(x) is

Consider f(x)=-2f(x)

If f(x) is even, f(x)=f(-x)

g(x)=-2f(x)=-2f(-x)
g(-x)=-2f(-x)

So g(x)=g(-x), which means -2f(x) is even if f(x) is even

If f(x) is odd, f(x)=-f(-x)

let g(x)=-2f(x)=-2(-f(-x))=2f(-x)

g(-x)=-2f(-x)=-2(-f(x))=2f(x)

so g(-x) is not equal to -g(x), thus -2f(x) is not odd if f(x) is odd.

The conclusions about oddness and evenness can be also derived from the discussions about the graphs.

6 0

3 years ago