Answer:
9-0+1-1×2
Step-by-step explanation:
<em>So</em><em> </em><em>the</em><em> </em><em>right</em><em> </em><em>answer</em><em> </em><em>is</em><em> </em><em>of</em><em> </em><em>option</em><em> </em><em>D</em><em>.</em>
<em>L</em><em>ook</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>picture</em>
<em>H</em><em>ope</em><em> </em><em>it</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>you</em>
Answer:
P(5) - P(3) = 4
Step-by-step explanation:
<em>Lets explain how to solve the problem</em>
Assume that P(x) is a linear function, that because the sum of P(2x),
P(4x), and P(6x) is linear ⇒ (24x - 6 is linear)
∵ The form of the linear function is y = ax + b
∴ P(x) = ax + b
Substitute x by 2x
∵ P(2x) = a(2x) + b
∴ P(2x) = 2ax + b
Substitute x by 4x
∵ P(4x) = a(4x) + b
∴ P(4x) = 4ax + b
Substitute x by 6x
∵ P(6x) = a(6x) + b
∴ P(6x) = 6ax + b
Add the three functions
∴ P(2x) + P(4x) + P(6x) = 2ax + b + 4ax + b + 6ax + b
Add like terms
∴ P(2x) + P(4x) + P(6x) = 12ax + 3b ⇒ (1)
∵ P(2x) + P(4x) + P(6x) = 24x - 6 ⇒ (2)
Equate (1) and (2)
∴ 12ax + 3b = 24x - 6
By comparing the two sides
∴ 12a = 24 and 3b = -6
∵ 12a = 24
Divide both sides by 12
∴ a = 2
∵ 3b = -6
Divide both sides by 3
∴ b = -2
Substitute these values in P(x)
∵ P(x) = ax + b
∴ P(x) = 2x + (-2)
∴ P(x) = 2x - 2
Now we can find P(5) - P(3)
∵ P(5) = 2(5) - 2 = 10 - 2 = 8
∵ P(3) = 2(3) - 2 = 6 - 2 = 4
∴ P(5) - P(3) = 8 - 4 = 4
* P(5) - P(3) = 4
D. csc^2 x + sec^2 x = 1
The process for each option is to rewrite the equation, attempting to obtain the identity sin^2 x + cos^2 x = 1. In general convert each function to its equivalent using just sin and cos.
A. cos^2 x csc x - csc x = -sin x
cos^2 x * 1/sin x - 1/sin x = -sin x
(cos^2 x * 1/sin x - 1/sin x) * sin x = -sin x * sin x
cos^2 x * 1 - 1 = -sin^2 x
cos^2 x = -sin^2 x + 1
cos^2 x + sin^2 x = 1
Option A is an identity.
B. sin x(cot x + tan x) = sec x
sin x(cos x/sin x + sin x/cos x) = 1/cos x
cos x + sin^2 x/cos x = 1/cos x
cos^2 x + sin^2 x = 1
Option B is an identity.
C. cos^2 x - sin^2 x = 1- 2sin^2 x
cos^2 x - sin^2 x + 2sin^2 x = 1- 2sin^2 x + 2sin^2 x
cos^2 x + sin^2 x = 1
Option C is an identity.
D. csc^2 x + sec^2 x = 1
1/sin^2 x + 1/cos^2 x = 1
cos^2 x/(cos ^2 x sin^2 x) + sin^2 x/(cos^2 x sin^2 x) = 1
(cos^2 x + sin^2 x)/(cos ^2 x sin^2 x) = 1
1/(cos ^2 x sin^2 x) = 1
1 = cos ^2 x sin^2 x
Option D is NOT an identity.
