Answer:
or .
Step-by-step explanation:
How are tangents and secants related to sines and cosines?
.
.
Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, . Therefore, for the square of tangents,
.
This equation will thus become:
.
To simplify the calculations, replace all with another variable. For example, let . Keep in mind that .
.
.
Solve this equation for :
.
.
.
Given that , is the only possible solution.
,
, where (i.e., is an integer.)
Given that ,
.
or . Accordingly,
or .
Answer
1. x = (2/3)y²
2. x = 54 when y = 9
3. y = 7.35 when x = 36
Explanation
1. x ∝ y²
x = 24, y = 6
x = ky²
24 = k x 6²
24 = 36k
k = 24/36
k = 2/3
∴ x in terms of y is x = (2/3)y²
2. Using x = (2/3)y² to to find x when y = 9, we have
x = (2/3) x 9²
x = 2/3 x 81
x = 2 x 27
x = 54
∴ x = 54 when y = 9
3. Using x = (2/3)y² to to find y when x = 36, we have
36 = (2/3)y²
36 = 2y²/3
2y² = 36 x 3
y² = 108/2
y² = 54
y = √54
y = 7.35
∴ y = 7.35 when x = 36
Answer:
6a^3 + 22a^2 - 6a - 10
Step-by-step explanation:
(3a + 5)(2a^2 + 4a - 2)
distribute 3a
6a^3 + 12a^2 - 6a
distribute 5
10a^2 + 20a - 10
combine like terms/simpify
6a^3 + 22a^2 - 6a - 10
Since it's a one-variable equation, it has only one solution:
25 - 4x = 15 - 3x + 10 - x
25 - 4x + x = 15 - 3x + 10
25 - 3x = 15 - 3x + 10
- 3x = 15 - 3x + 10 - 25
- 3x = 15 - 3x - 15
- 3x + 3x = 15 - 15
0 = 15 - 15
0 = 0
Hope it helped,
BioTeacher101