In a circle, what is the ratio of the circumference to its diameter?
area
radius
volume
PI

Answer:

[tex] \sin A= \frac {1} {\sqrt {82}}[/tex]

Step-by-step explanation:

[tex]\sin A= \frac {BC} {BA} \\\\

\sin A= \frac {1} {\sqrt {82}} \\\\[/tex]

The exact value of sin A in simplest radical form is  1 /√82.

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle.

Now from the given triangle we have,

Hypotenuse, AB = √82

Perpendicular, BC = 1

Base, AC = 9

Since, sine function is the  ratio of the length of the opposite side to that of the hypotenuse.

Thus, Sin A = Perpendicular / Hypotenuse

⇒ Sin A = 1 /√82

which is the required the exact value of sin A in simplest radical form.

Thus, the exact value of sin A in simplest radical form is  1 /√82

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Answer:

[tex]AB = \sqrt{a^2 + b^2-2abCos\ C}[/tex]

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

[tex]Sin\ C = \frac{h}{a}[/tex]

Make h the subject:

[tex]h = aSin\ C[/tex]

Also, in BOC (Using Pythagoras)

[tex]a^2 = h^2 + x^2[/tex]

Make [tex]x^2[/tex] the subject

[tex]x^2 = a^2 - h^2[/tex]

Substitute [tex]aSin\ C[/tex] for h

[tex]x^2 = a^2 - h^2[/tex] becomes

[tex]x^2 = a^2 - (aSin\ C)^2[/tex]

[tex]x^2 = a^2 - a^2Sin^2\ C[/tex]

Factorize

[tex]x^2 = a^2 (1 - Sin^2\ C)[/tex]

In trigonometry:

[tex]Cos^2C = 1-Sin^2C[/tex]

So, we have that:

[tex]x^2 = a^2 Cos^2\ C[/tex]

Take square roots of both sides

[tex]x= aCos\ C[/tex]

In triangle BOA, applying Pythagoras theorem, we have that:

[tex]AB^2 = h^2 + (b-x)^2[/tex]

Open bracket

[tex]AB^2 = h^2 + b^2-2bx+x^2[/tex]

Substitute [tex]x= aCos\ C[/tex] and [tex]h = aSin\ C[/tex] in [tex]AB^2 = h^2 + b^2-2bx+x^2[/tex]

[tex]AB^2 = h^2 + b^2-2bx+x^2[/tex]

[tex]AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2[/tex]

Open Bracket

[tex]AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C[/tex]

Reorder

[tex]AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C[/tex]

Factorize:

[tex]AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C[/tex]

In trigonometry:

[tex]Sin^2C + Cos^2 = 1[/tex]

So, we have that:

[tex]AB^2 = a^2 * 1 + b^2-2abCos\ C[/tex]

[tex]AB^2 = a^2 + b^2-2abCos\ C[/tex]

Take square roots of both sides

[tex]AB = \sqrt{a^2 + b^2-2abCos\ C}[/tex]

Answer:

40

Step-by-step explanation:

200 divided by 40 is  5

240 divided by 40 is 6

Complete Question

The access code for a car's security system consists of 6 digits, the first digit cannot be 8 and the last digit must be odd, how many different codes are available

Answer:

There are 450000 possible different codes

Step-by-step explanation:

Given

Code = 6 digits

First = All but 8

Last = Odd

Required

Determine the possible number of codes

Analyzing each individual digit that makes up the code.

First: can be any of 0,1,2,3,4,5,6,7,9 ----- 9 possible numbers

Second, Third, Fourth and Fifth can be any of 0,1,2,3,4,5,6,7,8,9 since there's no restriction ----- 10 possible numbers

Last can be any of: 1,3,5,7,9 ----- 5 possible numbers

So, the number of possible selections is:

[tex]Selection = 9 * 10 * 10 * 10 * 10 *5[/tex]

[tex]Selection = 450000[/tex]

Hence, there are 450000 possible different codes

Answer: 45.5 miles

Step-by-step explanation: divide182 by 4

Answer:

182/4=45.5

the bus travels 45.5 miles in 1 hour

I hope this helps!!

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Answer:

1 out of 17

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/3 of a mile in 15 minutes. 1.333 (4/3) miles an hour

Answer:

x=6

Step-by-step explanation:

Answer:

3(10x+4)=8(3x+6)

Step 1: Simplify both sides of the equation.

3(10x+4)=8(3x+6)

(3)(10x)+(3)(4)=(8)(3x)+(8)(6)(Distribute)

30x+12=24x+48

Step 2: Subtract 24x from both sides.

30x+12−24x=24x+48−24x

6x+12=48

Step 3: Subtract 12 from both sides.

6x+12−12=48−12

6x=36

Step 4: Divide both sides by 6.

6x = 36

Answer:

x=6

Answer:

Step-by-step explanation:

Given that:

sin2xcos x + cos2xsin x = -1

Recall that;

SInAcosB + cosASinB = SIn (A+B)

SIn (2x +x) = -1

Sin (3x) = -1

[tex]x = \bigg [\dfrac{Sin ^{-1} (-1)}{3} \bigg ][/tex]

[tex]x = \dfrac{\pi}{2} + \dfrac{2 \pi \ k}{3}[/tex]

[tex]x = \dfrac{\pi}{2}, \dfrac{7 \pi}{6}, \dfrac{11 \pi}{6}[/tex]

Answer:

9u² + 4u + 9

Respond w/ any questions...

Answer:

9u^2 + 4u + 9

Step-by-step explanation:

eliminate parentheses - 4u + 9 + 9u^2

rearrange terms - 9u^2 + 4u + 9

Answer:

it's easy u stupido perra

Step-by-step explanation:

Answer:

Your first point should be at (0,-2), because of the y intercept. Then, since the slope is 3, you want to rise 3 and run 1. Go up 3, then to the right 1. That should be  your next point. Then do it again, and again, how many ever times you need to.

Answer:

There are 42 animals at the shelter

Answer: 2

Step-by-step explanation:

(x1,y1) = (-1,0)

(x2,y2) = (3,8)

m = (8–0)/(3-(-1))

m = 8/(3+1)

m = 8/4

m = 2

Answer:

The Tigers are in first place and Joe has a good taste in basketball teams.  I'm not sure if you can conclude anything else from that.

Answer:

80

Step-by-step explanation:

40% of 200=80

Answer:

80

Step-by-step explanation:

40% of 200

40/100×200

80

Answer is 80

Answer:

5/8

.625

62.5%

Step-by-step explanation:

Answer:

2826/25

Step-by-step explanation:

28.26×4=========2826/25

Answer:

I think the equation is 20$+X=Y

Step-by-step explanation:

y = x + 20

Topic: algebraic equations

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

Answer:

I have no clue how to slide this I don't quite understand the problem can you try to explain better?

Answer:

y=3x-2 or y=3x+2

Step-by-step explanation:

Answer:  y = 3x-2

Step-by-step explanation:

Answer:

Equation of line b in standard form is: [tex]\mathbf{2x+y=-11}[/tex]

Option A is correct.

Step-by-step explanation:

We need to find equation of line b that passes through the point ( (6,4) and has a slope of -2.

First we need to find y-intercept of line using formula: [tex]y=mx+b[/tex] where m is slope and b is y-intercept.

Using m=-2 , x=6 and y=4 the y-intercept will be:

[tex]y=mx+b\\4=-2(6)+b\\4=12+b\\b=4-12\\b=-11[/tex]

Now finding the equation of line having slope m=-2 and y-intercept b=-11

[tex]y=mx+b\\y=-2x-11[/tex]

Writing the equation in standard form

[tex]y=-2x-11\\2x+y=-11[/tex]

So, equation of line b in standard form is: [tex]\mathbf{2x+y=-11}[/tex]

Option A is correct.

Answer:

ilyilyilyilyily thank you

Answer:

thats so sweet thank you!!!

Step-by-step explanation:

Answer:

x = 61°

Step-by-step explanation:

Property of a triangle,

Sum of interior angles of a triangle = 180°

By applying this property in ΔABC,

m∠A + m∠B + m∠C = 180°

x° + 67° + 52° = 180°

x + 119° = 180°

x = 180 - 119

x = 61°

Therefore, measure of angle A = x = 61°  

Answer:

D. (-3,1)

Step-by-step explanation:

When putting pairs it is (X,Y) (horizontal,vertical)

The ones both meet at point D. (-3,1)

Answer:

each student gets 3 erasers

Step-by-step explanation:

You have to divide 20 total erasers by the 6 students and you get about 3.33... and this number rounded down is 3.

Have an stupendous day! I hope this answer was helpful to you.

Each student get 3 erasers.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Total number of students = 6

Number of erasers = 20

Now,

Since, Total number of students = 6

And, Number of erasers = 20

Hence, Number of eraser getting by each students = 20 ÷ 6

                                                                   = 3.33

Thus, Each student get 3 erasers.

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