1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alborosie
3 years ago
7

If cos (A+B) = cosAcos B – sinAsin B , find the value of cos 75

Mathematics
1 answer:
kirill [66]3 years ago
4 0

Answer:

Step-by-step explanation:

Cos 75 = Cos ( 30 + 45)  {Use Cos (A + B) identity}

            = Cos 30*cos 45 - Sin 30 Sin 45

            = \frac{\sqrt{3}}{2}*\frac{1}{\sqrt{2}}-\frac{1}{2}*\frac{1}{\sqrt{2}}\\\\= \frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}\\\\=\frac{\sqrt{3}-1}{2\sqrt{2}}\\\\=\frac{(\sqrt{3}-1)*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\=\frac{\sqrt{3}*\sqrt{2}-\sqrt{2}}{2*2}\\\\=\frac{\sqrt{6}-\sqrt{2}}{4}

You might be interested in
Solve each system of equations <br> 2x- 5y = 7<br> 3x - y = -9
Darina [25.2K]

Answer:

x = -4; y = -3

Step-by-step explanation:

2x - 5y = 7

3x - y = -9

Rewrite top equation. Multiply both sides of bottom equation by -5. Add equations. This eliminates y, and we solve for x.

         2x - 5y = 7

(+)   -15x + 5y = 45

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

      -13x         = 52

Divide both sides by -13.

x = -4

Substitute -4 for x in the first original equation and solve for y.

2x - 5y = 7

2(-4) - 5y = 7

-8 - 5y = 7

-5y = 15

y = -3

Answer: x = -4; y = -3

-5 =

8 0
3 years ago
What is $10.56x3?<br> Help me plz
kodGreya [7K]
31.68 is your answer
3 0
3 years ago
Read 2 more answers
Equations of Lines help!
Vedmedyk [2.9K]
The answer is D. Note that the y-intercept is -3, not 3. So, when x is at 0, y should be -3. Choice D is the only graph with a y-intercept of -3.
7 0
3 years ago
1. a baker had 10 sacks containing the following amounts of flour: 4 1/2 kg , 31/4 kg ,2 1/2 kg ,2 1/2 kg , 4 kg ,3 1/4 kg ,4 1/
OleMash [197]
Baker's Flour in kg Y x x A x x X x x x x x x I ----------------------------------------------------------- S 2 1/2 3 1/4 4 4 1/4 4 1/2 5 X axis It would be 3.5 in each bag after the baker redistributes the flour. This is because the total flour would be 35 kg. 35 divided by 10 is 3.5 kg of flour in each bag.
3 0
3 years ago
(a) Derive an equation of the line passing through the points A(0, 545) and B(4, 726). (Let t be the independent variable and y
a_sh-v [17]

Answer:

The equation of the line is y=45.25t+545

Step-by-step explanation:

The general for of a line is:

y=mt+n       (1)

where:

m is the slope of the line and m is the intercept with the axis of the dependent variable, y in this case.

In order to obtain the value of the slope (m) we can use the corresponding slope formula:

m=\frac{y_{2}-y_1 }{t_2-t_1}         (2)

where t_1, t_2, y_1 and y_2 are the corresponding coordinates of the given points. In this case:

t_1=0\\t_2=4\\y_1=545\\y_2=726\\

Substituting these values in equation (2) we obtain:

m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25

Hence, the line equation is now:

y=45.25t+n     (3)

Now to obtain the value of n you can follow two options:

  1. You can substitute one of your points, A or B, in equation (3). In this way, you will obtain an equation where the variable is n

Note that for this question, it is easier to select point A because of having the independent variable equals to zero t=0. Hence, substituting point A in equation (3):

45.25*0+n=545\\n=545

Therefore, the line equation is: y=45.25t+545

The second option to find n is to think of the meaning of the <em>intercept</em>. The <em>intercept </em>of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that n is equal to 545.

See the attachment for a plot of the line.

7 0
3 years ago
Other questions:
  • Nolan calculates his profit selling cakes by using the function p(c) = 7.5c -35, where c represents the number of cakes sold Whi
    5·1 answer
  • Solve the equation if there is no solution, write no solution | m | / 2 - 1 = -3
    9·2 answers
  • Find the range of the sample data 0.62, 1.05, 0.58, 1.17, 1.04, 1.37, 1.32, 0.67, 1.25 1.38, 0.86
    7·2 answers
  • Please help me answer questions 2, 3 and 4!!
    5·2 answers
  • How many solutions does the system have?
    14·2 answers
  • Prove sin^2 π/6 + cos^2 π/3 - tan^2 π/4 = -1/2​
    6·1 answer
  • 1. Enrico sold a 10-pound box of assorted chocolates. Some of the chocolates in the box sold
    5·1 answer
  • What is the equation of the line that passes through the point (5, 4) and has a slope of 4/5
    9·1 answer
  • Does anyone know this answer??
    7·1 answer
  • The line segment determined by A(4,7) and B(2, 9) along &lt;0, –2&gt;
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!