Please answer this question fast in two minutes
2 answers:
Answer:
S = (3, 5 )
Step-by-step explanation:
Given the endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ (x₁ + x₂ ),
(y₁ + y₂ ) ]
let the coordinates of S be (x, y ), then using the midpoint formula equate the parts to the coordinates of the midpoint M
x = (x + 5) = 4 ( multiply both sides by 2 )
x + 5 = 8 ( subtract 5 from both sides )
x = 3
y = (y + 3) = 4 ( multiply both sides by 2 )
y + 3 = 8 ( subtract 3 from both sides )
y = 5
The coordinates of S = (3, 5 )
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Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
<u />
<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A
Given:
One linear function represented by the table.
Another linear function represented by the graph.
To find:
The greater unit rate and greater y-intercept.
Solution:
Formula for slope (unit rate):
From the given table it is clear that the linear function passes through (0,5) and (5,15). The function intersect the y-axis at (0,15), so the y-intercept is 15.
So, the unit rate of first function is 2.
From the given graph it is clear that the linear function passes through (0,6) and (-4,0). The function intersect the y-axis at (0,6), so the y-intercept is 6.
So, the unit rate of first function is .
Now,
And,
Therefore, the greater unit rate of the two functions is 2. The greater y-intercept of the two functions is 15.