The answer is b
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hope yhis helps
Answer:
- 8) 4 + 2q²/p² - 4r/p + r²/p²
- 9) (3/4, -9/4)
- 10) (3/8, 41/16)
Step-by-step explanation:
8. ============
Given
- α and β are roots of px² + qx + r = 0
The sum of the roots is α + β = -q/p, the product of then roots αβ = r/p
- (2 + α²)(2 + β²) =
- 4 + 2(α² + β²) + (αβ)² =
- 4 + 2((α + β)² -2αβ) + (αβ)² =
- 4 + 2((-q/p)² - 2r/p) + (r/p)² =
- 4 + 2q²/p² - 4r/p + r²/p²
------------------------------
9. ============
<u>Given function</u>
The minimum point is reached at vertex
<u>The vertex is:</u>
- x = -b/2a
- x = -(-3)/2*2 = 3/4
<u>The corresponding y-coordinate is:</u>
- y = 2(3/4)² - 3(3/4) - 1 = 9/8 - 9/4 - 1 = 1/8(9 - 18 - 9) = - 18/8 = - 9/4
<u>So the point is: </u>
---------------
10. ============
<u>Given function</u>
The maximum is reached at vertex
<u>The vertex is:</u>
- x = -b/2a
- x = -(-3)/2(-4) = -3/8
<u>The corresponding y-coordinate is:</u>
- y = 2 - 3(-3/8) -4(-3/8)² = 2 + 9/8 - 9/16 = 1/16(32 + 18 - 9) = 41/16
<u>So the maximum point is:</u>
6x4 = 24
Therefore, 24 is your answer.
We know that the shortest leg of the largest right triangle (hypotenuse length 16) has a length of the square root of (y^2 + 16) through the pythagoras theorem. We also know that x is equal to the square root of (144 + y^2) as well. Finally, we know that 256 = (y^2 + 16) + (y^2 + 144), since we use the pythagoras theorem one last time and square each of the values we have got for the two legs of the largest right triangle. Therefore, 256 = 2y^2 + 160, 96 = 2y^2, 48 = y^2, y= sqrt48 = 4sqrt3 =
.
Step-by-step explanation:
What is n th term?
The term which comes at the last of number of terms is called the n th Term.
Here, we can see that the last term is 28.
So 28 is the answer.
Hope it helps :)