MATHEMATICS HIGH SCHOOL

Prove the identity
cos(A+B+C)=cosAcosBcosC-cosAsinBsinC-sinAcosBcosC-sinAsinBcosC

Answers

Answer 1
Answer: Hello !

cos (a+b) = cos a cos b - sin a sin b
sin (a+b) = sin a cos b + sin b cos a

cos (a+b+c) = cos (a+(b+c))
cos (a+b+c) = cos a cos (b+c) - sin a sin (b+c)
cos (a+b+c) = cos a (cos b cos c - sin b sin c) - sin a (sin b cos c + sin c cos b)
cos (a+b+c)=cos a cos b cos c - cos a sin b sin c - sin a sin b cos c - sin a cos b sin c

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If f(x)=2(x)^2 + 5 square root (x-2), complete the following statement The domain for f(x) is all real numbers _____ than or equal to 2.

Answers

Answer:

Greater.

Step-by-step explanation:

The in the function , the square root term has to give a real number if is to be real. This can only happen if because if then will give a complex number and therefore will not be real.

Thus, the domain for f(x) is all real numbers greater than or equal to 2.

Answer:

The domain for f(x) is all real numbers greater than or equal to 2.

Step-by-step explanation:

Given function:

f(x)=2x^2+5 √(x-2)

The domain of a function is the set of all possibleinput values (x-values).

As the square root of a negative numbercannot be taken:

\implies x-2\geq 0

Therefore:

\implies x-2+2\geq 0+2

\implies x\geq 2

Therefore, the domain of the given function is greater than or equal to 2.

In accute triangle abc side a=10, side b=12 and angle a is 42. Find angle b to the nearest degree

Answers

A triangle has 3 sides and 3 angles. The triangle involve is an acute triangle. This means that the rest of the angles in the triangle is acute. Acute angles are angles with measurement blow 90 degrees. To solve this problem we use the Sin Law. The ratio of the side and sine of the angle apposite to the side is constant. 10/sin(42) = 12/sin(x). Solve for x. 
The answer is 53.41 degrees. 

Suppose that an object whose is 10th weighs 50 N find the weight of an object whose is 6 kg

Answers

Weight is another term for the force from mass multiplied by acceleration due to gravity, the equation being expressed as f = ma, being force, mass, and acceleration respectively.

We already have 2 parts of the equation,50 = 10a 

Acceleration due to gravity on the planet is 5 m/s^2

Plug it into the equation f = ma

f=6kg x 5m/s^2

Weight or force from gravity is 60N.

Solve the following equation:A) y = 1/2
B) y = 2/7
C) y = -2/5
D) y = 3/4
Correct answer: A

Answers

Answer: A

Step-by-step explanation: You said the correct answer is a and if you are not lying then I am right

What is the value of the expression below when y = 8 and z = 9?
5y – 2z

Answers

Answer:

\boxed {\tt 22}

Step-by-step explanation:

We are given the expression:

5y-2z

We want to find the value of the expression when y=8 and z=9. Therefore, we must substitute 8 in for y and 9 in for z.

5(8)-2(9)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Multiply 5 and 8.

40-2(9)

Multiply 2 and 9.

40-18

Subtract 18 from 40.

22

The value of the expression 5y-2z at y=8 and z=9 is 22.

Translate the following and explain where these examples could be found in real world.
a) “6 less than a number”
b) “2 times the quotient of a number and two”
c) “4 times the difference of a number and 8”

Answers

a) x-6; you have x amount of money and pay 6 dollars for a hat.
b) 2(x2);
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