Answer:
8² = 4² + 5² - 2(4)(5) cos(P)
which is the third option
Explanation:
The general rule of cosine is:
a² = b² + c² - 2bc*cos(A)
In our triangle:
a is substituted by p = 8 cm
b is substituted by n = 4 cm
c is substituted by m = 5 cm
A is substituted by P which we want to find
Replace the variables in the general equation with the givens as follows:
p² = n² + m² - 2mn*cos(P)
8² = 4² + 5² - 2(4)(5) cos(P)
Hope this helps :)
Let Daniel's age be 'x' years , hence, Lisa's age is (x - 5) years. Let Grandma's age be 'y' = 54 years.
Hence,
x(x - 5) = 2/3 × y
x² - 5x = 2 × 54 years / 3
x² - 5x = 36 years
x² - 5x - 36 = 0
∆ = (-5)² - 4(1)(-36) = 25 + 144 = 169
√∆ = √169 = 13
x1 = (5+13)/2, x2 = (5-13)/2
x1 = 9, x2 = -4
Since, age can't be negative,
Daniel's age = x = 9 years.
The answer is 45.4545454545
I believe the amount of income tax the doctor has to pay is $9,127.5