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>
Answer:
![\large \boxed{\sf \bf \ \ 12 \ \ }](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Csf%20%20%5Cbf%20%5C%20%5C%2012%20%5C%20%5C%20%7D)
Step-by-step explanation:
Hello, we can see that this shape is ...
...at the left, a right triangle of side = 2
area = (2*2)/2 =2
... at the middle, a square of side = 2
area = 2*2 = 4
... at the right, a right triangle of sides 2 and 6
area= (2*6)/2 = 6
So the total is 2 + 4 + 6 = 12
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Rectangle does not have equal sides
Answer:
17
Step-by-step explanation:
because 2×4=8
and 8+9=<u>17</u>