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pantera1 [17]
2 years ago
10

(3cosx-4sinx) + (3sinx+4cosx) = 5

Mathematics
1 answer:
Ksenya-84 [330]2 years ago
3 0
(3 cos x-4 sin x)+(3sin x+4 cos x)=5
(3cos x+4cos x)+(-4sin x+3 sin x)=5
7 cos x-sin x=5
7cos x=5+sin x
(7 cos x)²=(5+sinx)²
49 cos²x=25+10 sinx+sin²x
49(1-sin²x)=25+10 sinx+sin²x
49-49sin²x=25+10sinx+sin²x
50 sin² x+10sinx-24=0

Sin x=[-10⁺₋√(100+4800)]/100=(-10⁺₋70)/100
We have two possible solutions:
sinx =(-10-70)/100=-0.8
x=sin⁻¹ (-0.8)=-53.13º      (360º-53.13º=306.87)

sinx=(-10+70)/100=0.6
x=sin⁻¹ 0.6=36.87º

The solutions when  0≤x≤360º are:  36.87º and 306.87º.


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BartSMP [9]

Answer:

x -y =4

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

   = (1- -4)/(5 - 0)

    = (1+4)/(5-0)

   5/5

   = 1

Then we can use slope intercept form

The slope is 1 and the y intercept is -4

y = mx+b

y = 1x-4

We want it in standard form

Ax + By = C where A is a positive integer

Subtract x from each side

-x +y = -4

Multiply by -1

x -y =4

8 0
2 years ago
There are 59 boys and 49 girls in this year's baseball league. If the league has nine teams how many players will be on each tea
liraira [26]

Answer: There are 12 players in each team.

Step-by-step explanation:

Since we have given that

Number of boys in this year's baseball league = 59

Number of girls in this year's baseball league = 49

Total number of players in altogether is given by

59+49=108

Now, there are 9 teams in the league ,

So,

\text{Number of players in each team}=\frac{108}{9}=12

Hence, there are 12 players in each team.

8 0
3 years ago
In football a field goal is worth 3 points which function rule relates the number of field goals f and the number of points p
Strike441 [17]
The answer would be B. If you want to FIND how many points a person has, you put the "p" on its own on the left of the equation, and since every field goal (f) you score is worth 3 points, just multiply "f" by 3 (3f).

For example, if someone scored 5 field goals in a game, to find how many points they totalled, just plug in the 5 for "f":

1. Get equation:

p = 3f

2. Plug in field goals for "f":

p = 3(5)

3. Solve:

p = 15
4 0
3 years ago
Jean closet is having a 15% off storewide sale. You want to buy a pair of jeans originally marked $32.99. What is the sale price
Oliga [24]

Answer:

Discount= $4.94

Final Price= $28.04

Step-by-step explanation:

Discount = original price x discount / 100

Discount= 32.99 x 15/ 100

Discount= 494.85/ 100

You save= $4.9485 ($494)


Final Price= original price - discount

Final Price= 32.99 - 4.9485

Final Price= $28.04

6 0
3 years ago
Write the denominator of the fractiona 7/20 as the product of prime factors
gtnhenbr [62]

Answer:

Step-by-step explanation:

prime factors of 20 = 2 * 2 * 5

\frac{7}{20}=\frac{7}{2*2*5}

5 0
3 years ago
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