Subtracting the weight of the smaller brick from the larger gives us the weight difference:
4 3/8 lb - 2 1/3 lb. The two denominators are 8 and 3 respectively, resulting in an LCD of 24. Thus, our problem becomes:
4 9/24 - 2 8/24, which equals 2 1/24 lb. The weight difference is 2 1/24 lb.
Answer:
60 cm²
Step-by-step explanation:
base = 10
Height = √13² - 5² = √144 = 12
area = 1/2BH = 1/2 * 10 * 12 = 60
Answer:
Verified below
Step-by-step explanation:
We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)
In trigonometric identities;
Cot θ = cos θ/sin θ
Thus;
(cot θ - 1)/(cot θ + 1) gives;
((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)
Simplifying numerator and denominator gives;
((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)
This reduces to;
>> (cos θ - sin θ)/(cos θ + sin θ)
Multiply top and bottom by ((cos θ + sin θ) to get;
>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)
In trigonometric identities, we know that;
cos 2θ = (cos² θ - sin²θ)
cos²θ + sin²θ = 1
sin 2θ = 2sinθcosθ
Thus;
(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:
>> cos 2θ/(1 + sin 2θ)
This is equal to the left hand side.
Thus, it is verified.
Answer:
18 hours
Step-by-step explanation:
n=3; We need a third degree polynomials with the following given zero's: 2 and 5i are zeros; f(-1)=156.
Since these are solutions
x = 2 ; x = 5i. Since imaginaries travel in pairs, the other answer is x= -5i.
We have (x-2)(x-5i)(x+5i) = 0
Now,
f(-1) = (-1-2)(-1-5i)(-1+5i) = 156.
f(-1) = (-3)(26) = -78.
But -78 x -2 = 156, so our polynomial becomes
Y= -2x (<em>x</em> - 2 ) x (<em>x </em>to the power of 2 + 25) = 0
