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koban [17]
2 years ago
9

Here is a square inscribed in a circle with radius 1 meter. What is the perimeter of

Mathematics
1 answer:
Dimas [21]2 years ago
3 0

Answer:

4\sqrt{2}

Step-by-step explanation:

distance formula:\sqrt{\left(x_2-x_1\right)^{2}+\left(y_2-y_1\right)^{2}}

set square to be centered on the origin and find the distance between 2 of the connected points

\sqrt{\left(3-2\right)^{2}+\left(2-1\right)^{2}}

= \sqrt{\left(1\right)^{2}+\left(1\right)^{2}}

= \sqrt{2}

multiply by 4 as it is a square and all of its sides are equal

4\sqrt{2}

insert units

4\sqrt{2}\ \ meters

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What is tan(θ/2), when tan(θ) = 4/3 and when π < θ < 3π/2?
Tamiku [17]
Tan (Ф/2)=⁺₋√[(1-cosФ)/(1+cosФ)]
if π<Ф<3π/2;
 then,  Where is Ф/2??
π/2<Ф/2<3π/4; therefore Ф/2 is in the second quadrant; then tan (Ф/2) will have a negative value.

tan(Ф/2)=-√[(1-cosФ)/(1+cosФ)]

Now, we have to find the value of cos Ф.
tan (Ф)=4/3
1+tan²Ф=sec²Ф
1+(4/3)²=sec²Ф
sec²Ф=1+16/9
sec²Ф=(9+16)/9
sec²Ф=25/9
sec Ф=-√(25/9)        (sec²Ф will have a negative value, because Ф is in the        sec Ф=-5/3                                 third quadrant).

cos Ф=1/sec Ф
cos Ф=1/(-5/3)
cos Ф=-3/5

Therefore:

tan(Ф/2)=-√[(1-cosФ)/(1+cosФ)]
tan(Ф/2)=-√[(1+3/5)/(1-3/5)]
tan(Ф/2)=-√[(8/5)/(2/5)]
tan(Ф/2)=-√4
tan(Ф/2)=-2

Answer: tan (Ф/2)=-2; when tan (Ф)=4/3


3 0
3 years ago
In parts ​(a) through ​(e)​ below, mark the given statement as True or False. Justify each answer. All vectors are in set of rea
Oxana [17]

Answer:

(c)

"The given statement is true, by definition of length of a vector v, ||v|| = \sqrt{v\bullet v}"

Step-by-step explanation:

(a) v  \bullet v = || v ||^2

That is completely correct Remember that if  v = (x_1,x_2,x_3)\\ then

v \bullet v = x_1*x_1+x_2*x_2+x_3*x_3 = x_1^2+x_2^2+x_3^2 = ||v||^2

Therefore the correct answer would be (c).

"The given statement is true, by definition of length of a vector v, ||v|| = \sqrt{v\bullet v}"

5 0
3 years ago
Aaron rides his bike at a constant rate of 10 miles per hour. Which table represents y, the number of miles Aaron rides his bike
Tema [17]

Answer:

I believe the answer is c. but I'm not too sure.

Step-by-step explanation:

my reasoning for this is because it's the chart that is constant. y starts out with 5=0.5 & they add five more on y's side. & x increased the same amount throughout the chart.

5 0
3 years ago
Read 2 more answers
to estimate the sum of two mixed carla round one number to 3 and other number to7 . what is the perimeter of the frame
Sloan [31]

Answer:a


Step-by-step explanation:

2 5/5=2.625 round 3

8 0
3 years ago
Taylor and Nora go to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks
fgiga [73]

Answer:

The system if equation that can be used to derive this are

6x + 4y = 69 AND

12x + y = 96

The price of a drink is $7.5

Step-by-step explanation:

The question here says that Taylor and Nora went to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks and 4 bags of popcorn Nora spends a total of $96.00 on 12 drinks and bag of popcorn.And we are now told to write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations,we should determine and state the price of a drink, to the nearest cent .

Now, Let's assume that the price of a drink is "X" and that of a bag of popcorn to be Y

The first person made a purchase which led to the equation

6x + 4y = 69______ equation 1

And the second person also made a purchase that lead to the equation

12x + y = 96_____ equation 2

We make y the subject of the formula in equation 2 and apply it in 1

Y = 96 - 12x

Now apply the above in equation 1

6x + 4y = 69

6x + 4(96 - 12x)= 69

6x + 384 - 48x = 69

42x = 384 - 69

X = 315/42

X = 7.5

Substitute x= 7.5 in equation 2

12x + y = 96

12(7.5) + y = 96

90 + y = 96

Y = 6

Therefore, the price of a drink is $7.5

4 0
3 years ago
Read 2 more answers
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