Answer: The 2 litter bottle holds more
Step-by-step explanation:
Answer:
The solutions of the equation are 0 , π
Step-by-step explanation:
* Lets revise some trigonometric identities
- sin² Ф + cos² Ф = 1
- tan² Ф + 1 = sec² Ф
* Lets solve the equation
∵ tan² x sec² x + 2 sec² x - tan² x = 2
- Replace sec² x by tan² x + 1 in the equation
∴ tan² x (tan² x + 1) + 2(tan² x + 1) - tan² x = 2
∴ tan^4 x + tan² x + 2 tan² x + 2 - tan² x = 2 ⇒ add the like terms
∴ tan^4 x + 2 tan² x + 2 = 2 ⇒ subtract 2 from both sides
∴ tan^4 x + 2 tan² x = 0
- Factorize the binomial by taking tan² x as a common factor
∴ tan² x (tan² x + 2) = 0
∴ tan² x = 0
<em>OR</em>
∴ tan² x + 2 = 0
∵ 0 ≤ x < 2π
∵ tan² x = 0 ⇒ take √ for both sides
∴ tan x = 0
∵ tan 0 = 0 , tan π = 0
∴ x = 0
∴ x = π
<em>OR</em>
∵ tan² x + 2 = 0 ⇒ subtract 2 from both sides
∴ tan² x = -2 ⇒ no square root for negative value
∴ tan² x = -2 is refused
∴ The solutions of the equation are 0 , π
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Answer:
Step-by-step explanation:
3(a+3)-6=21
<=>3a+9-6=21
<=>3a+3=21
<=>3a=18
<=>a=6
Answer:
x = 7 and y = −2
(7, -2)
Step-by-step explanation:
x = 1 - 3y
3x + 3y = 15
Substitute −3y + 1 for x in 3x + 3y = 15:
3(1 - 3y) + 3y = 15
3 - 9y + 3y = 15
3 - 6y = 15
-3 -3
-6y = 12
/-6 /-6
y = -2
Now we solve for x. Substitute −2 for y in x = −3y + 1:
x = 1 - 3y
x = 1 + (-3)(-2)
x = 1 + 6
x = 7
Now we check our solution.
x = 1 - 3y
7 = 1 + (-3)(-2)
7 = 7 ✅
3x + 3y = 15
3(7) + 3(-2) = 15
21 - 6 = 15
15 = 15 ✅
