find a if given c and θ

Step-by-step explanation:

cos 20° cos 40° cos 60° cos 80°

Simplify cos 60° to ½.

½ cos 20° cos 40° cos 80°

We can use double angle formula, sin(2θ) = 2 sin θ cos θ.  Multiply and divide by 2 sin 20°.

½ (2 sin 20° cos 20° cos 40° cos 80°) / (2 sin 20°)

½ (sin 40° cos 40° cos 80°) / (2 sin 20°)

Multiply and divide by 2 and use double angle formula again.

½ (2 sin 40° cos 40° cos 80°) / (4 sin 20°)

½ (sin 80° cos 80°) / (4 sin 20°)

Multiply and divide by 2 and use double angle formula again.

½ (2 sin 80° cos 80°) / (8 sin 20°)

½ (sin 160°) / (8 sin 20°)

Use phase shift identity sin θ = sin(180−θ).

½ (sin 20°) / (8 sin 20°)

1/16

In this case we have the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = 1 / 16, and are asked to prove that this equation is true. Let's start by using the property 'cos(s)cos(t) = cos(s + t) + cos(s - t) / 2.' Taking the bit 'cos(20°)(cos(40°)' we know that s should = 20°, and t should = 40°.

[tex]\mathrm{Using\:the\:following\:identity}:\quad \cos \left(s\right)\cos \left(t\right)=\frac{\cos \left(s+t\right)+\cos \left(s-t\right)}{2},[/tex]

[tex]\cos \left(20^{\circ \:}\right)\cos \left(40^{\circ \:}\right)=\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\\[/tex]

[tex]\mathrm{Substituting\:the\:value\:back}:\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]

This expression is indeed not simplified, but remember that we can use the identities 'cos(- 20°) = cos(20°)' and 'cos(60°) = 1 / 2.' Let's substitute one step and a time.

[tex]\cos \left(-20^{\circ \:}\right)=\cos \left(20^{\circ \:}\right): \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]

[tex]\cos \left(60^{\circ \:}\right)=\frac{1}{2}:\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]

[tex]\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\cos \left(80^{\circ \:}\right)\left(1+2\cos \left(20^{\circ \:}\right)\right)}{8}[/tex]

Now that we have this 'simplified expression,' if we take the numerator as a whole in decimal form, it will = 0.5. Respectively 0.5 / 8 = 1 / 2 / 8 = 1 / 16. Hence our equation is true.

[tex]\cos \left(80^{\circ \:\:}\right)\left(1+2\cos \left(20^{\circ \:\:}\right)\right) = 0.5,\\0.5 / 8 = (1 / 2) / 8 = 1 / 16[/tex]

Answer:

$1,020

Step-by-step explanation:

There is a $200 difference in the every monthly pay.

Because of this we know that the first month was an amount minus $200.

If we subtract 1220 and 200, you get the pay of 1020 for 0 hours.

Answer:

5.6

Step-by-step explanation:

(2+3+5+7+11)/5

=5.6

x = - 5

2x + 2 = - 8

2x = - 8 - 2

2x = - 10

x = - 10 : 2

x = - 5

Answer:

x=-5

Step-by-step explanation:

1.) 2x+2=-8   start to isolate the variable by subtracting 2 to -8

2.) 2x=-10 divide both sides by 2

3.) x=-5

Hope this helped

The answers are in order 3/50,1/20, greater than.

Answer:

1.b 2.a 3.b

Step-by-step explanation:

Answer:

[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]

Step-by-step explanation:

Given the rational expression: [tex] \frac{2x + 3}{x^2 - 5x + 4} [/tex], to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

[tex] x^2 - 5x + 4 [/tex]

[tex] x^2 - 4x - x + 4 [/tex]

[tex] (x^2 - 4x) - (x + 4) [/tex]

[tex] x(x - 4) - 1(x - 4) [/tex]

[tex] (x- 1)(x - 4) [/tex]

Thus, we now have: [tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex]

Step 2: Apply the concept of Partial Fraction

Let,

[tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex] = [tex] \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]

Multiply both sides by (x - 1)(x - 4)

[tex] \frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) [/tex] = [tex] (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4) [/tex]

[tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]

Step 3:

Substituting x = 4 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]

[tex] 2(4) + 3 = A(4 - 4) + B(4 - 1) [/tex]

[tex] 8 + 3 = A(0) + B(3) [/tex]

[tex] 11 = 3B [/tex]

[tex] \frac{11}{3} = B [/tex]

[tex] B = \frac{11}{3} [/tex]

Substituting x = 1 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]

[tex] 2(1) + 3 = A(1 - 4) + B(1 - 1) [/tex]

[tex] 2 + 3 = A(-3) + B(0) [/tex]

[tex] 5 = -3A [/tex]

[tex] \frac{5}{-3} = \frac{-3A}{-3} [/tex]

[tex] A = -\frac{5}{3} [/tex]

Step 4: Plug in the values of A and B into the original equation in step 2

[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]

[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]

Answer:

Step-by-step explanation:

Given the rational expression: , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

Thus, we now have:

Step 2: Apply the concept of Partial Fraction

Let,

=

Multiply both sides by (x - 1)(x - 4)

=

Step 3:

Substituting x = 4 in

Substituting x = 1 in

Step 4: Plug in the values of A and B into the original equation in step 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The function  has a domain x ≥ 5.

This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.

Hence, (x - 5) ≥ 0

⇒ x ≥ 5

Now, for all x values that are greater than equal to 5 the value of  will be negative.

So,  

⇒  

⇒ y ≤ 3

Therefore, the range of the function is y ≤ 3. (Answer)

Note: Thanks rani

Answer:

Let N be the unknown number

The we have 6 x reciprocal of N/7  which is 6 x 7/N which is 42/N

HOPE THIS HELPS YOU

Multiply six and the reciprocal of the quotient of a number and seven can be written as 42/M.

Where M is the number.

Given,

Multiply six and the reciprocal of the quotient of a number and seven.

We need to find this expression.

It means to divide.

The quotient of a and b:

=  a ÷ b.

= a / b

Find the expression.

Let the number be M.

Now,

The quotient of a number and 7 can be written as:

= M ÷ 7

= M / 7

Reciprocal of the quotient of a number and seven.

= 1 / (M/7)

= 7 / M

Now,

Multiply six and the reciprocal of the quotient of a number and seven.

It can be written as:

= 6 x 7 / M

= 42 / M

Thus multiply six and the reciprocal of the quotient of a number and seven can be written as 42/M.

Learn more about the quotient of a number and its reciprocal here:

https://brainly.com/question/673545

#SPJ2

Answer:

7, 14, 14,21, and 28

Step-by-step explanation:

Only 1, 7 is pair of numbers that has 7 as its least common multiple.

Given that,
Pairs ( 1, 7 ), ( 3, 4 ), ( 7, 21), ( 14, 28).
A pair or pairs to be determined that have 7 as its least common multiple.

In mathematics, it deals with numbers of operations according to the statements.

In arithmetic, LCM is defined as the lowest common multiple of two integers X and Y, usually represented as by LCM X, Y, and is the smallest favorable integer that is dividable by both X and Y.

Since the Least common multiple of pair of numbers has 7, this is only possible for 1 * 7, because the LCM of 1 and7 is 7. So from given option 1, 7 is the required pair.

Thus, only 1, 7 is pair of numbers that has 7 as its least common multiple.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

5

Step-by-step explanation:

A factor is a number or an expression that is multiplying something.

5 is multiplying -3n + 8.

Answer: 5 is a factor.

Answer:

f(x)= -2x + 1

Step-by-step explanation:

The function we will find is to be written in slope-intercept form, which is y=mx+b.

One way to find the answer would be by graphing the function, wich you can do on an online calculator or a sheet of paper.

Another way to get to our answer without even having to graph is by finding the y-intercept, or the b, of the function given in the table.

We can do this by looking at the 0 value of the table. The table tells us that the y-intercept is 1.

So, we have to look at our options and see which one has +1 for the y-intercept.

The option f(x)=-2x+1 is the answer

How to check your work: input the given x values into the chosen function, in this case f(x)= -2x + 1

So for example, you could check that this answer is the function by doing

Make sure to do this to all values.

Hope this helps!

Answer:

a = 1/4

Step-by-step explanation:

Divide each side by 36:

36a = 9

a = 1/4

Answer:

a=1/4=0.25

Step-by-step explanation:

to get the value of a divide 36 by 9.

[tex]36a=9\\ \frac{36a}{36}=\frac{9}{36}\\ a=\frac{9}{36}\\ (simplify) \\ a=\frac{1}{4}=0.25[/tex]

Answer:

s. 0/10

6. 5/0

7. 1/10

8. 4/10

9. 5/10

Answer: cos(0) = 1

hope this helped

Answer:

X= 139

Step-by-step explanation:

the square on the E means its a right side so that would be 90 degrees.  All triangles add up to 180.  F would be 41 degrees.  that mean X is  139 i think.

Answer:

36.083

Step-by-step explanation:

SOHCAHTOA

Cosine is adjacent over hypotenuse, so the

cos(49) = the adjacent side (x) || over the hypotenuse (55)

cos(49) = x/55

55cos(49) = x

x = 36.083

Answer: You would owe $1,263 and 75c! Have a fantastic day!

Answer:

[tex]54^\circ[/tex]

Step-by-step explanation:

Given :

[tex]m\angle A=(2x+10)^{\circ}[/tex]

[tex]m\angle B=(3x+15)^{\circ}[/tex]

And angles [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.

To find:

The measure of [tex]\angle B[/tex].

Solution:

First of all, let us learn about complementary angles.

Complementary angles are the angles whose sum is equal to [tex]90^\circ[/tex].

And we are given that angles [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.

Therefore [tex]\angle A[/tex] + [tex]\angle B[/tex] = [tex]90^\circ[/tex]

[tex]\Rightarrow 2x+10+3x+15=90\\\Rightarrow 5x+25=90\\\Rightarrow 5x=65\\\Rightarrow x =13[/tex]

Putting the value in [tex]\angle B[/tex].

[tex]m\angle B=(3\times 13+15)^{\circ} = 54^\circ[/tex]

Therefore, the answer is [tex]\bold{\angle B = 54^\circ}[/tex]

Answer:

x=6

Step-by-step explanation:

first we'll use distributive property: we will distribute and multiply 3 by x and - 2

2x + 3x -6 = 24

then we'll add like terms which are 2x and 3x , 24 and 6 the sign of 6 will change from negative to positive:

2x + 3x =24 + 6

5x = 30

after that we will divide both sides by 5 in order to get x

5x/5 = 30/ 5

x = 6

Answer:A

Step-by-step explanation:

Sqrt(4000)= 20

Step-by-step explanation:

BD bisects ∠ABC.  Therefore:

m∠DBC = ½ m∠ABC

y + 5 = ½ (5/2 y)

y + 5 = 5/4 y

4y + 20 = 5y

y = 20

Therefore, m∠ABC = 50°, and m∠ABD = 25°.

Answer:

2. 14

4. -6

Step-by-step explanation:

#2

(x²-4y)/2, given x=4, y=-3

 [(4)²-4(-3)]/2

=[16+12]/2

=28/2

=14

------------------------

#4

19-x², given x=-5

 19-(-5)²

=19-25

=-6

Answer:

68

Step-by-step explanation:

We can see that the nth term would be the sum of the previous two terms. Continuing this would result in 68.

Answer:

2.5 mile inch 158400

Step-by-step explanation:

It's on google

158400

You can just ask google

Answer:

[tex]3\frac{1}{4}[/tex]

Step-by-step explanation:

Given the two  -3 1/4 and -6 1/2 numbers  on the line, the distance between he numbers can be gotten by simply taking the differences between both values as shown;

[tex]= -3\frac{1}{4} -(-6\frac{1}{2} )\\ \\= -\frac{13}{4} + \frac{13}{2}\\ \\= \frac{-13+26}{4}\\ \\= \frac{13}{4} \\\\= 3\frac{1}{4}[/tex]

Hence the distance between two numbers on the number line is [tex]3\frac{1}{4}[/tex]

Four more than twice a number is –10 is the same as 2n + 4 = 10

Steps to solve:

2n + 4 = 10

~Subtract 4 to both sides

2n = 6

~Divide 2 to both sides

n = 3

Best of Luck!

Answer:

i). x³ + 9x² + yz - 15

ii). -21m³np - 8p⁵q + mnp + 4mn + 100

Step-by-step explanation:

Question (38)

i). Two expressions are -5x² - 4yz + 15 and x³+ 4x²- 3yz

  By subtracting expression (1) from expression (2) we can the expression by addition which we can get expression (1).

 (x³+ 4x²- 3yz) - (-5x² - 4yz + 15) = x³ + 4x² - 3yz + 5x² + 4yz - 15

                                                    = x³ + 9x² + yz - 15

ii). -15m³np + 2p⁵q - 6m³pn + mnp + 4mn - 10qp⁵+ 100

  = (-15m³np - 6m³np) + (2p⁵q - 10qp⁵) + mnp + 4mn + 100

  = -21m³np - 8p⁵q + mnp + 4mn + 100

Answer:

[tex]x=\pm i\text{ or }x=\pm2i[/tex]

Step-by-step explanation:

So we have the equation:

[tex]x^4+5x^2+4=0[/tex]

Let's let u be equal to x². So:

[tex]u^2+5u+4=0[/tex]

Factor:

[tex](u+1)(u+4)=0[/tex]

Zero Product Property:

[tex]u+1=0\text{ or } u+4=0[/tex]

Subtract:

[tex]u=-1\text{ or }u=-4[/tex]

Replace:

[tex]x^2=-1\text{ or }x^2=-4[/tex]

Take square root:

[tex]x=\pm\sqrt{-1}\text{ or }x=\pm\sqrt{-4[/tex]

Simplify:

[tex]x=\pm i\text{ or }x=\pm2i[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 15 °}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{x + 30 ° + 100 ° + 3x - 10 ° = 180 °}[/tex]

( Sum of angle in straight line )

Collect like terms

⇒[tex] \sf{4x + 30 ° + 100 ° - 10 ° = 180 °}[/tex]

Calculate the sum or difference

⇒[tex] \sf{4x + 120 ° = 180 °} [/tex]

Move 120 to right hand side hand change it's sign

⇒[tex] \sf{4x = 180 ° - 120 °}[/tex]

Subtract 120 from 180

⇒[tex] \sf{4x = 60 ° }[/tex]

Divide both sides of the equation by 4

⇒[tex] \sf{ \frac{4x}{4} = \frac{60}{4} }[/tex]

Calculate

⇒[tex] \sf{x = 15  °}[/tex]

Hope I helped!

Best regards!!