MATHEMATICS HIGH SCHOOL

Determine the general solution of:

sin 3x - sin x = cos2x

Answers

Answer 1
Answer: sin³ x-sin x=cos ² x

we know that:
sin²x + cos²x=1  ⇒cos²x=1-sin²x
Therefore:

sin³x-sin x=1-sin²x
sin³x+sin²x-sin x-1=0

sin³x=z

z³+z²-z-1=0

we divide by Ruffini method:
              1     1     -1     -1
        1           1      2      1                z=1
-------------------------------------
              1     2      1      0
       -1         -1      -1                       z=-1
--------------------------------------
              1     1       0                       z=-1

Therefore; the solutions are z=-1 and z=1

The solutions are:
if z=-1, then
sin x=-1   ⇒x= arcsin -1=π+2kπ    (180º+360ºK)   K∈Z


if z=1, then
sin x=1   ⇒ x=arcsin 1=π/2 + 2kπ   (90º+360ºK)   k∈Z

π/2 + 2kπ    U   π+2Kπ=π/2+kπ     k∈Z    ≈(90º+180ºK)

Answer: π/2 + Kπ    or     90º+180ºK          K∈Z
Z=...-3,-2,-1,0,1,2,3,4....

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The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function?A.(x – 11)2 + 58 B.(x + 22)2 – 121 C.(x + 7)2 – 47 D.(x – 15)2 + 94

Consider the equation 6x+3y=9. Which equation, when graphed with the given equation, will form a system with infinitelymany solutions?
y+ 2x - 3
Oy+ 2x - 9
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Oy--2x9

Answers

Answer:

y=-2x+3

Step-by-step explanation:

6x+3y=9\n \n3y=-6x+9\ny=-2x+3

step 1: subtract 6x on both sides

step 2: divide all numbers by 3 to get y by itself.

3 plus the product of 2 and h in algebraic expression

Answers

Answer:

3 + 2 · h = 3 + 2h
How is this high school math? What does product mean? It means multiplication is involved. the product of 2 and h is written as what? 2*h, or 2h. Now, we need to do 3 + that. Your answer is 2h+3.

Over twenty years, it was found that the number of doctors of medicine, MD (in thousands), in the United States can be approximated by MD=(28,390+693t)/(85-t) where t=0 represents 1980. The number of doctors of osteopathy, DO (in thousands), can be approximated by DO=(776-12t)/(65-2t) .Write an expression for the total number I of doctors of medicine (MD) and doctors of osteopathy (DO). Simplify the result.

How many MDs did the United States have in 2010? How many MDs did the United States have in 2010?

Answers

The expression for the total number of doctors is (-1374t^2+43192.22t+67805.35)/((65-2t)(85-t) )

We have to write an expression for the number of MD and DO

a. MD + DO

(28390+693t)/(85-t) +(776-12t)/(65-2t)

This can be simplified as

((28390+693t)(65-2t)+(776-12t)(85-t) )/((85-t)(65-2t) )

= (-1374t^2+43192.22t+67805.35)/((65-2t)(85-t) )

b. If t = 0 in 1980, in 2010, t = 30

The number of MD would be

(28390+693*30)/(85-30) \n= 379

The number of DO would be

(776-12*30)/(65-2*30)\n\n= 83

Read more on mathematical expressions here: brainly.com/question/723406

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Answer:

16. the expression below.

17. about 470,933 MD's and about 18,743 DO's

7.8+ (x-18)=31
Please Help Asap
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Answers

Answer:

x=41.2

Step-by-step explanation:

hope this helps

Answer:

x=41.2

Step-by-step explanation:

First, subtract 7.8 from both sides of the equation, resulting in x-18=23.2

Then, add 18 to both sides of the equation, creating x=41.2

Hope this helps.

1 . a person who weighs 100 pounds on earth weighs 16.6 ib on the moon. part a. how much would a 185 pound astronaut weigh on the moon? use an equation to explain how u know part
b. how much would a man the weighs 50 pounds on the moon weigh on earth?

Answers

M = E/6

a) 185/6 lb = 30.8333... lb
b) 300 lb

The distance between -32 and
13

Answers

Answer:   To find the distance between -32 and 13, we need to calculate the absolute difference between the two numbers.

The absolute difference is the positive value of the subtraction of one number from another. In this case, we subtract -32 from 13.

13 - (-32) = 13 + 32 = 45.

Therefore, the distance between -32 and 13 is 45 units.
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