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:
There are 604,800 possible permutations.
Step-by-step explanation:
The order in which the digits are chosen is important, which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
In this question:
7 digits from a set of 10(10 digits to 0-9). So
There are 604,800 possible permutations.
Mary will need 27 yards of fencing to enclose her garden. She has 90 square yards for planting.
We calculate the commission and adding it to the price of the stock to get total cost.
No Price Total Commission Total cost
100 $26.25 0.06 x $2,625 = $157.50 2625 + 157.50 =2782.5
100 $19.32 0.06 x $1,932 = $115.92 1932 + 115.92 =2047.92
40 $9.77 0.06 x $390.80 = $23.45 390.80 + 23.45= 414.25
200 $5.39 0.06 x $1,078 = $64.68 1,078 + 64.68 = 1142.68
100 $33.44 0.06 x $3,344 = $200.64 3,344 + 200.64 = 3544.64
Group A I’m pretty confident with that answer
