Both 2 and 6 are divisible by 2, so you would divide them by 2 and your fraction would be reduced to 1/3. You would get that answer by simply reducing the fraction.
There are 2 roots for this equation.
The discriminant is given by b²-4ac. This is what goes under the square root in the quadratic formula. Since we will be taking the square root of this, if the discriminant is less than 0, there are no real roots; you cannot have a real square root of a negative number.
If the discriminant is equal to 0, there is 1 real root; the square root of 0 is 0, so the quadratic formula would yield one answer.
If the discriminant is greater than 0, there are 2 real roots. This is because taking the square root of a positive number gives a positive and negative result.
b in our equation is -7, a is 3 and c is 4:
b²-4ac = (-7)²-4(3)(4) = 49 - 48 = 1
There is 1 real root.
Part (i)
I'll use H in place of T to represent the heat of the object. That way there isn't a clash of variables lowercase t vs uppercase T.
The equation we're working with is updated to:
H(t) = 22 + a*2^(bt)
Plugging in t = 0 as the initial time value should lead to the temperature being H = 86 degrees Celsius.
So,
H(t) = 22 + a*2^(bt)
86 = 22 + a*2^(b*0)
86 = 22 + a*2^0
86 = 22 + a*1
86 = 22 + a
a+22 = 86
a = 86-22
a = 64
<h3>Answer: 64</h3>
=====================================================
Part (ii)
We'll use the value of 'a' we found earlier. Plus we'll use the fact that H = 28 when t = 0.5 (since 30 min = 30/60 = 0.5 hr).
H(t) = 22 + a*2^(bt)
28 = 22 + 64*2^(b*0.5)
28-22 = 64*2^(0.5b)
64*2^(0.5b) = 6
2^6*2^(0.5b) = 6
2^(6+0.5b) = 6
log( 2^(6+0.5b) ) = log(6)
(6+0.5b)*log(2) = log(6)
6+0.5b = log(6)/log(2)
6+0.5b = 2.5849625
0.5b = 2.5849625-6
0.5b = -3.4150375
b = -3.4150375/(0.5)
b = -6.830075
<h3>Answer: Approximately -6.830075</h3>
Answer:
see explanation
Step-by-step explanation:
A recursive rule allows us to find the term in a sequence from the previous term.
From the given geometric sequence find r the common ratio
r = 
= 
= - 4
Hence recursive rule is
= - 4
( a₁ = 
)
Each cookie costs 2$.
We can find how much each cookie costs by setting up an equation with x being the amount of cookies, and solve
12x=24 12 cookies equals 24 dollars
x=2 By simplifying and dividing both sides of the equation by 12, we get the variable on its own.
