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Answer:
Please check the explanation.
Step-by-step explanation:
a) How much will you have at the middle of the first year?
Principle P = $300
Annual rate r = 6% = 0.06 per year
Compound n = Semi-Annually = 2
Time (t in years) = 0.5 years
Total amount = A = ?
Using the formula
substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.
Part b) How much at the end of one year?
Principle P = $300
Annual rate r = 6% = 0.06 per year
Compound n = Semi-Annually = 2
Time (t in years) = 1 years
Total amount = A = ?
Using the formula
so substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.
To comlete each square, you just have to take the middle term and divide it by 2, then take its square. Add this to both sides of the equation then simplify. The middle term is the 1st degree x variable.
<span>3. x^2+6x =16
-------------------------
(6/2)^2 = 9
x</span>² + 6x + 9 = 16 + 9
(x + 3)² = 25
<span>4. x^2-10x =11
------------------------
(-10/2)</span>² = 25
x² - 10x + 25 = 11 + 25
(x -5)² = 36
<span>5. x^2-9x =0
--------------
(-9/2)</span>² = 81/4
x² - 9x + 81/4 = 81/4
(x - 9/2)² = 81/4
<span>6. x^2+16x =15
---------------
(16/2)</span>² = 64
x² + 16x +64 = 15 + 64
(x + 8)² = 79
<span>7. 3x^2+18x-81=0
----------------
x</span>² + 6x = 27
(6/2)² = 9
x² + 6x + 9 = 27 + 9
(x + 3)² = 36
A polynomial with a general equation of ax² + bx + c = 0 has a root determined using this formula:
Just substitute the coefficients to the formula to find the roots
8. 1.09, -1.84
9. 3, 1/2
10. No real roots
11. 1.12, -3.12
<span>3. x^2+6x =16
-------------------------
(6/2)^2 = 9
x</span>² + 6x + 9 = 16 + 9
(x + 3)² = 25
<span>4. x^2-10x =11
------------------------
(-10/2)</span>² = 25
x² - 10x + 25 = 11 + 25
(x -5)² = 36
<span>5. x^2-9x =0
--------------
(-9/2)</span>² = 81/4
x² - 9x + 81/4 = 81/4
(x - 9/2)² = 81/4
<span>6. x^2+16x =15
---------------
(16/2)</span>² = 64
x² + 16x +64 = 15 + 64
(x + 8)² = 79
<span>7. 3x^2+18x-81=0
----------------
x</span>² + 6x = 27
(6/2)² = 9
x² + 6x + 9 = 27 + 9
(x + 3)² = 36
A polynomial with a general equation of ax² + bx + c = 0 has a root determined using this formula:
Just substitute the coefficients to the formula to find the roots
8. 1.09, -1.84
9. 3, 1/2
10. No real roots
11. 1.12, -3.12