Answer:
Train A = 214
Train B = 86
Step-by-step explanation:
a + b = 300
a - b = 128
a + b = 300
a = 128 + b
(128 + b) + b = 300
128 + b + b = 300
128 + 2b = 300
2b = 300 - 128
2b = 172
b = 172 ÷ 2
b = 86
a = 128 + b
a = 128 + (86)
a = 214
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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
Parallel have same slope
Perpendicular have opposite reciprocal slopes. Ex. 2/3 is slope of one line so the perpendicular line would have slope of -3/2.
Find slopes of these lines.
-4x-5y=-4
-4x+4 =5y
Divide by 5
Y= -4x/5 +4/5
Second line: 10x-8y=-1
10x+1=8y
Divide by 8
10x/8 +1/8 =y
Y= 5x/4 +1/8
So if you look at slope of line 1= -4/5 and line 2 it’s 5/4 so these both are perpendicular.
