Find the volume of each figure. Round your answers to the nearest tenth, if necessary

Find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of a regular dodecagon.

IgorLugansk [536]

See the picture to better understand the problem

we know that
A regular dodecagon has 12 sides
Central angle of a regular polygon is an angle whose vertex is the center of the polygon with two consecutive radii
thus
the measure of a central angle is
m∠AOC=360/n
where n is the number of sides
so
m∠AOC=360/12-----> 30°

therefore

the answer Part a) is
the measure of the angle formed by two consecutive radii is 30 degrees

Part b)
we know that
OAC is an isosceles triangle
so
OA=OC
m∠OAC=m∠OCA

the sum of the internal angles of a triangle is 180 degrees
so
180=2*m∠OAC+m∠AOC-----> m∠OAC=[180-30]/2----> 75°

the answer part b) is
the measure of the angle formed by a radius and a side is 75°

8 0

3 years ago

Solve the following problem. 3/8×3/4=

mel-nik [20]

Answer: 9/32

Step-by-step explanation: Multiply Straight across.

Brainliest please

3 0

3 years ago

Can i get help on this asap!!!!!!! PLZ

FrozenT [24]

Answer:

unpaid utility bill that has been given to collection agency

-the person's credit rating

-the person's social security number

-an inquiry from a bank that requested the person's credit report

Step-by-step explanation:

Credit report is termed as a record which shows the credit history of a borrower from different sources. For example credit card companies, banks, government, and collection agencies.If a person submits application for a credit it is then taken to credit bureau for clarification in order to determine whether you are worth to be given a credit and whether you can repay the debt.

3 0

3 years ago

Read 2 more answers

Find the length of AB

aniked [119]

FIRST QUESTION
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula = $\sqrt{ (x_{2}- x_{1})^{2} + ( y_{2} - y_{1} )^{2} }$

Now, plug the values into the formula, So,
distance = $\sqrt{ (6- 2)^{2} + ( 2 - (-4))^{2} }$

= $\sqrt{ (6- 2)^{2} + ( 2 +4))^{2} }$

= $\sqrt{ (4)^{2} + ( 6))^{2} }$

= $\sqrt{ 16+36}$

= $\sqrt{52}$

= $2 \sqrt{13}$

So, the length of AB is $2 \sqrt{13}$ .

THIRD QUESTION
Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.

Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint = $(\frac{ x_{1}+ x_{2} }{2} , \frac{ y_{1}+ y_{2} }{2} )$

$(1, 1)=(\frac{ 3+ a }{2} , \frac{ -2+b }{2} )$

Now, equaling the ordered pair, we have,

$1=\frac{ 3+ a }{2}$ .............equation (1)

$1=\frac{ -2+b }{2}$ ................equation (2)

Now, taking equation (1)
$1=\frac{ 3+ a }{2}$

$1*2=3+a$

$2-3=a$

$a=-1$

Now, taking equation (2)
$1=\frac{ -2+b }{2}$

$1*2=-2+b$

$2+2=b$

$b=4$

So, the co ordinates of C are (a, b) which is (-1 , 4)


SECOND QUESTION:
Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1

Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4

So, x=1 and y=4

6 0

3 years ago

Find the equation of the sphere passing through P(negative 4 comma 7 comma 6 )and Q(8 comma negative 3 comma 5 )with its center

Juli2301 [7.4K]

Answer: The equation of the sphere is:

(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2

Step-by-step explanation:

The centre of the sphere is the midpoint of the diameter, which is

1/2

[(-4,7,6) + (8,-3,5)] =(2,2,5/2)

The length of the diameter is

=sqrt |(8,-3,5) - (-4,7,6)|^2

=sqrt (12^2 + (-10)^2 + (-1)^2)

=sqrt (144+100+1)

=sqrt(245)

so the radius of

the sphere is:

1/2(sqrt(245)) = sqrt(245)/2.

The equation of the sphere is:

(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2

4 0

4 years ago

Find the volume of each figure. Round your answers to the nearest tenth, if necessary​

Find the volume of each figure. Round your answers to the nearest tenth, if necessary