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BlackZzzverrR [31]
3 years ago
10

What is the measure of an exterior angle of a regular octagon? a. 360. b. 135. c. 60. d. 45

Mathematics
2 answers:
grin007 [14]3 years ago
6 0

45^o is the correct answer just took the test

Darya [45]3 years ago
5 0
An octagon has 12 sides;
The measure of an exterior angle is:
\frac{360}{12} = 30^{0}
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Given that tan θ ≈ −0.087, where 3 2 π < θ < 2 , π find the values of sin θ and cos θ.
elena-s [515]

Answer:

  • sin θ ≈ -0.08667
  • cos θ ≈ 0.99624

Step-by-step explanation:

Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)

Likewise, straightforward use of the calculator to find the other function values gives ...

  sin(-0.08678 radians) ≈ -0.08667

  cos(-0.08678 radians) ≈ 0.99624

_____

<em>Note on inverse tangent</em>

Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.

We have shown radians in the above answer because the restriction on the angle is written in terms of radians.

_____

<em>Alternate solution</em>

The relationship between tan and sin and cos in the 4th quadrant is ...

  \cos{\theta}=\dfrac{1}{\sqrt{1+\tan^2{\theta}}}\\\\\sin{\theta}=\dfrac{\tan{\theta}}{\sqrt{1+\tan^2{\theta}}}

That is, the cosine is positive, and the sign of the sine matches that of the tangent.

This more complicated computation gives the same result as above.

4 0
3 years ago
find all integers x satisfying each of the following congruences mod n. if no such x exists, explain why not
zalisa [80]

Answer:

please find the solution:

Step-by-step explanation:

please find the correct question:

Given value:  

\to 4x \equiv  2(mod\ n) \ \ \ \ \ \ \ \ \ \ \ \ _{where} \ \  n=6\\\\\to  4x \equiv  2 (mod 6)

\to 4x-2 should be divisible by 6  we are also given that 0 \leq x < n  and start with x = 0  

\to 4x-2 =-2 which is not divisible by 6  

x= 1  

\to 4x-2 = 2 not divisilble by 6  

x= 2

\to 4x-2 = 6 which is divisible by 6  

x=3  

\to 4x-2 = 10 not divisible by 6

x=4  

\to 4x-2  = 14 not divisible by 6  

x=5

\to 4x-2  = 18 which is divisible by 6  

so such x are x = 2 and x = 5

4 0
3 years ago
The volume, V, of a right pyramid with the base area B and height h is calculated by the formula:
Lubov Fominskaja [6]

Answer:

B=V/13*h

Step-by-step explanation:

V=13*B*h

V/13*h=B

6 0
3 years ago
Another name for Plan n
EleoNora [17]

Answer:DN

Step-by-step explanation:

3 0
3 years ago
A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice th
icang [17]

Answer:

The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

D = \sqrt{l^2+w^2}                              ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

l = 2 \times w = 2w

Now, substitute these in  [1] we have;

\sqrt{(2w)^2+w^2} = w+5

Squaring both the sides we get;

4w^2+w^2 = (w+2)^2

5w^2 = w^2 + 4 + 4w

or

5w^2 -w^2 = 4w + 4 or

4w^2= 4w + 4

Simplify:

w^2-w-1 =0                         ......[2]

The quadratic equation is in the form  of ax^2+bx+c = 0

the solution is given by:  x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

w= \frac{-(-1) \pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}

w =\frac{1 \pm\sqrt{1+4}}{2} = \frac{1 \pm\sqrt{5}}{2}

Simplify:

w \approx 1.62 and w \approx -0.62

Then, the diagonal D = w+2

For w \approx 1.62

D = 1.62 +2 \approx 3.62

For w \approx -0.62

D =-0.62 +2 \approx 1.38

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4





5 0
3 years ago
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