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Anettt [7]
3 years ago
13

Find the measure of

Mathematics
2 answers:
UkoKoshka [18]3 years ago
5 0

Answer:

20°

Step-by-step explanation:

In circle geometry, one of the theorem States that angle at the center of a circle is twice angle at the circumference.

Let x be the angle at the centre and y be angle at the circumference. The theorem can be expressed mathematically as;

x = 2y

According to the diagram <BOC is the angle at the center represented as x which is 40°

Angle<BAC is at the circumference of the circle represented as y.

To find <BAC, note that

<BOC = 2<BAC

40° = 2<BAC

<BAC = 40°/2

<BAC = 20°

Ivenika [448]3 years ago
3 0

Answer:

The measure of angle BAC is 20°

Step-by-step explanation:

step 1

Find the measure of arc BC

we have that

m∠BOC=arc BC ------> by central angle

we have

m∠BOC=40°

therefore

arc BC=40°

step 2

Find the measure of angle BAC

we know that

The inscribed angle is half that of the arc it comprises

so

m∠BAC=(1/2)[arc BC]

we have

arc BC=40°

substitute

m∠BAC=(1/2)[40°] =20°

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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

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

=sqrt (144+100+1)

=sqrt(245)

so the radius of

the sphere is:

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The equation of the sphere is:

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

4 0
3 years ago
A motorboat takes 5 hours to travel 150 miles going upstream. The return trip takes 3 hours going downstream. What is the rate o
lys-0071 [83]

Answer:

The rate of the boat in still water is 40 miles per hour

The rate of the current is 10 miles per hour

Step-by-step explanation:

we know that        

The speed or rate is equal to divide the distance by the time

Let

x ----> the rate of the current (miles per hour)          

y ----> the rate of the boat in still water (miles per hour)        

we have that          

<em>going upstream              </em>

y-x=\frac{150}{5}        

y-x=30 ----> equation A            

<em>going downstream                                  </em>

y+x=\frac{150}{3}                            

y+x=50 ----> equation B                            

Solve the system of equations by elimination                            

Adds equation A and equation B                                      

y-x=30\\y+x=50\\------\\y+y=30+50\\2y=80\\y=40                    

<em>Find the value of x                                </em>

y+x=50                

40+x=50            

x=10          

therefore          

The rate of the boat in still water is 40 miles per hour      

The rate of the current is 10 miles per hour      

8 0
3 years ago
Help me please no one is answering i need help on math :(
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3         3

6         9

9        15

12        21

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For the time add 3 each time

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